Methods for visual observation of comets. How to determine the position of stars on the celestial sphere Apparent brightness and color of stars

Celestial navigation for yachtsmen

“There is only one unmistakable way to determine the location and direction of a ship’s path at sea - astronomical, and happy is the one who is familiar with it!” - with these words of Christopher Columbus we open a series of essays - lessons on celestial navigation.

Marine celestial navigation originated in the era of great geographical discoveries, when “iron men sailed on wooden ships”, and over the centuries it has absorbed the experience of many generations of sailors. Over the past decades, it has been enriched with new measuring and computing tools, new methods for solving navigation problems; The recently introduced satellite navigation systems, as they continue to develop, will make all the difficulties of navigation a thing of history. The role of marine celestial navigation (from the Greek aster - star) remains extremely important today. The purpose of our series of essays is to introduce amateur navigators to modern methods of celestial orientation available in yachting conditions, which are most often used on the high seas, but can also be used in cases of coastal navigation when coastal landmarks are not visible or cannot be identified.

Observations of celestial landmarks (stars, Sun, Moon and planets) allow navigators to solve three main problems (Fig. 1):
1) measure time with sufficient accuracy for approximate orientation;

2) determine the direction of movement of the vessel even in the absence of a compass and correct the compass, if available;

3) determine the exact geographical location of the vessel and control the correctness of its route.

The need to solve these three problems on a yacht arises due to inevitable errors in calculating its path according to compass and log readings (or approximately determined speed). Large drift of the yacht, reaching 10-15° in strong winds, but can only be assessed by eye; continuously changing speed; control “by sails” when sailing close-hauled, only with subsequent fixation of compass courses; influence of variable currents; a large number of turns when tacking is not a complete list of reasons that complicate navigation on a yacht! If dead reckoning is not controlled by observations of luminaries, the error in the dead reckoning location, even for experienced yachtsmen, can exceed several tens of miles. It is clear that such a large error threatens the safety of navigation and can lead to large losses of sailing time.

Depending on the nautical instruments, manuals and computing tools used, the accuracy of solving celestial navigation problems will be different. To be able to solve them in full and with accuracy sufficient for navigation on the open sea (location error - no more than 2-3 miles, in compass correction - no more than 1°), you must have:

• a navigation sextant and a good waterproof watch (preferably electronic or quartz);
• a transistor radio receiver for receiving time signals and a microcalculator of the “Electronics” type (this microcalculator must have the input of angles in degrees, provide the calculation of direct and inverse trigonometric functions, and perform all arithmetic operations; the most convenient is the “Electronics” BZ-34); in the absence of a microcalculator, you can use mathematical tables or special tables “Heights and azimuths of luminaries” (“VAS-58”), published by the Main Directorate of Navigation and Oceanography;
• Nautical Astronomical Yearbook (MAE) or other manual for calculating the coordinates of luminaries.

The widespread use of electronic watches, transistor radios and microcalculators has made the use of astronomical navigation methods accessible to the widest range of people without special navigational training. It is no coincidence that there has been a continuous increase in demand for nautical astronomical yearbooks; this serves as the best proof of the popularity of celestial navigation among all categories of navigators and, first of all, among amateur sailors.

In the absence of any of the above celestial navigation means on the ship, the very possibility of celestial navigation orientation is preserved, but its accuracy decreases (while remaining, however, quite satisfactory for many cases of sailing on a yacht). By the way, some tools and computing facilities are so simple that they can be made independently.

Celestial navigation is not only a science, but also an art - the art of observing the stars in sea conditions and accurately performing calculations. Don't let the initial failures disappoint you: with a little patience, the necessary skills will appear, and with them will come high satisfaction in the art of sailing out of sight of the shores.

All the celestial navigation methods that you will master have been tested many times in practice; they have already served sailors well in the most critical situations more than once. Don’t put off mastering them “for later”; master them when preparing for swimming; The success of the campaign is decided on the shore!

Celestial navigation, like all astronomy, is an observational science. Its laws and methods are derived from observations of the visible movement of luminaries, from the relationship between the geographical location of the observer and the apparent directions of the luminaries. Therefore, we will begin the study of celestial navigation with observations of luminaries - we will learn to identify them; Along the way, let’s get acquainted with the principles of spherical astronomy that we need in the future.

Celestial landmarks

1. Navigation stars. At night, with a clear sky, we see thousands of stars, but in principle each of them can be identified based on its location in a group of neighboring stars - its visible place in the constellation, its apparent magnitude (brightness) and color.

For navigation at sea, only the brightest stars are used; they are called navigation stars. The most commonly observed navigation stars are listed in Table. 1; a complete catalog of navigation stars is available in MAE.

The picture of the starry sky is not the same in different geographical areas, in different seasons of the year and at different times of the day.

When starting an independent search for navigation stars in the northern hemisphere of the Earth, use a compass to determine the direction to the North point located on the horizon (indicated by the letter N in Fig. 2). Above this point, at an angular distance equal to the geographic latitude of your place, is the star Polaris - the brightest among the stars of the constellation Ursa Minor, forming the shape of a ladle with a curved handle (Little Dipper). Polar is denoted by the Greek letter "alpha" and is called? Ursa Minor; it has been used by sailors for several centuries as a main navigational landmark. In the absence of a compass, the direction to the north is easily determined as the direction to Polyarnaya.

As a scale for roughly measuring angular distances in the sky, you can use the angle between the directions from your eye to the tips of the thumb and index finger of your outstretched hand (Fig. 2); this is approximately 20°.

The apparent brightness of a star is characterized by a conventional number, which is called magnitude and is designated by the letter m. The magnitude scale looks like this:

Shine m= 0 has the brightest star in the northern sky observed in summer - Vega (? Lyrae). Stars of the first magnitude - with brilliance m= 1 2.5 times fainter in brightness than Vega. Polaris has a magnitude of about m= 2; this means that its brightness is approximately 2.5 times weaker than the brightness of stars of the first magnitude or 2.5 X 2.5 = 6.25 times weaker than the brightness of Vega, etc. Only brighter stars can be observed with the naked eye m < 5.

Stellar magnitudes are indicated in the table. 1; The color of the stars is also indicated there. However, it must be taken into account that color is perceived by people subjectively; in addition, as they approach the horizon, the brightness of stars noticeably weakens, and their color shifts to the red (due to the absorption of light in the earth’s atmosphere). At a height above the horizon of less than 5°, most stars disappear from visibility altogether.

We observe the earth's atmosphere in the form of the firmament (Fig. 3), flattened overhead. In marine conditions at night, the distance to the horizon appears to be approximately twice as great as the distance to the zenith point Z (from the Arabic zamt - top) located overhead. During the day, the visible flatness of the sky can increase one and a half to two times, depending on cloudiness and time of day.

Due to the very large distances to the celestial bodies, they appear to us to be equidistant and located in the sky. For the same reason, the relative position of stars in the sky changes very slowly - our starry sky is not much different from the starry sky of Ancient Greece. Only the celestial bodies closest to us - the Sun, planets, and the Moon - move noticeably in the foyer of constellations - figures formed by groups of mutually stationary stars.

The oblateness of the sky leads to a distortion of the visual estimate of the apparent height of the luminary - the vertical angle h between the direction to the horizon and the direction to the luminary. These distortions are especially large at low altitudes. So, let us note once again: the observed height of the luminary is always greater than its true height.

The direction to the observed star is determined by its true bearing IP - the angle in the horizon plane between the direction to the North and the bearing line of the star OD, which is obtained by the intersection of the vertical plane passing through the star and the horizon plane. The IP of the luminary is measured from the point of North along the arc of the horizon towards the point of East within the range of 0°-360°. The true bearing of Polar is 0° with an error of no more than 2°.

Having identified Polar, find the constellation Ursa Major in the sky (see Fig. 2), which is sometimes called the Big Dipper: it is located at a distance of 30°-40 from Polar, and all the stars of this constellation are navigational. If you have learned to confidently identify Ursa Major, you will be able to find Polaris without the help of a compass - it is located in the direction from the star Merak (see Table 1) to the star Dubhe at a distance equal to 5 distances between these stars. The constellation Cassiopeia with the navigation stars Kaff (?) and Shedar (?) is located symmetrically to Ursa Major (relative to Polaris). In the seas washing the shores of the USSR, all the constellations we mentioned are visible above the horizon at night.

Having found Ursa Major and Cassiopeia, it is not difficult to identify other constellations and navigational stars located near them if you use a star chart (see Fig. 5). It is useful to know that the arc in the sky between the stars Dubhe and Benetnash is approximately 25°, and between the stars? And? Cassiopeia - about 15°; these arcs can also be used as a scale to approximate angular distances in the sky.

As a result of the rotation of the Earth around its axis, we observe a visible rotation of the sky towards the West around the direction to Polar; Every hour the starry sky rotates by 1h = 15°, every minute by 1m = 15", and per day by 24h = 360°.

2. The annual movement of the Sun in the sky and seasonal changes in the appearance of the starry sky. During the year, the Earth makes one full revolution around the Sun in outer space. The direction from the moving Earth to the Sun is constantly changing for this reason; The Sun describes the dotted curve shown on the star chart (see inset), which is called the ecliptic.

The visible place of the Sun makes its own annual movement along the ecliptic in the direction opposite to the apparent daily rotation of the starry sky. The speed of this annual movement is small and equal to 4/day (or 4 m/day). In different months, the Sun passes through different constellations, forming a zodiacal belt (“circle of animals”) in the sky. So, in March, the Sun is observed in the constellation Pisces, and then successively in the constellations Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius.

Constellations located on the same hemisphere with the Sun are illuminated by it and are not visible during the day. At midnight, constellations are visible in the south, distant from the place of the Sun on a given calendar date by 180° = 12 hours.

The combination of the rapid apparent daily movement of stars and the slow annual movement of the Sun leads to the fact that the picture of the starry sky observed today at the moment will be visible tomorrow 4m earlier, in 15 days - 4m earlier.

earlier, in a month - 2 hours earlier, etc.

3. Geographical and visible location of the star. Star map. Star globe. Our Earth is spherical; Now this is clearly proven by its photographs taken by space stations.

In navigation, it is believed that the Earth has the shape of a regular ball, on the surface of which the yacht’s place is determined by two geographical coordinates:
Geographic latitude? (Fig. 4) - the angle between the plane of the earth’s equator eq and the direction of the plumb line (the direction of gravity) at the observation point O. This angle is measured by the arc of the geographic meridian of the observer’s place (in short, the local meridian) EO from the equatorial plane towards the Earth's pole closest to the observation site within 0°-90°. Latitude can be north (positive) or south (negative). In Fig. 4 the latitude of the place is O? = 43° N. Latitude determines the position of the geographic parallel - a small circle parallel to the equator.

Geographic longitude? - the angle between the planes of the prime geographic meridian (according to international agreement, it passes through the Greenwich Observatory in England - G in Fig. 4) and the plane of the local meridian of the observer. This angle is measured by the arc of the earth's equator towards the East (or West) within the range of 0°-180°. In Fig. 4 the longitude of the place is? = 70° Ost. Longitude determines the position of the local meridian.

The direction of the local meridian at observation point O is determined by the direction of the sun's shadow at noon from a vertically installed pole; at noon this shadow has the shortest length; on a horizontal platform it forms the midday N-S line (see Fig. 3). Any local meridian passes through the geographic poles Pn and Ps, and its plane passes through the Earth’s rotation axis PnPs and the vertical line OZ.

A ray of light from a distant star * comes to the center of the Earth in the direction * C, crossing the earth's surface at some point?. Let's imagine that an auxiliary sphere (celestial sphere) is described from the center of the Earth with an arbitrary radius. Will this same ray intersect the celestial sphere at a point? - visible place of the luminary on the sphere. According to Fig. 4. It is clear that the position of the HMS is determined by geographic sprat?* and geographic longitude?*.

The position of the visible place of the luminary on the celestial sphere is determined similarly:

• arc of the GMS meridian?* is equal to the arc? the celestial meridian passing through the visible place of the luminary; this coordinate on the sphere is called the declination of the luminary, it is measured in the same way as latitude;
• the arc of the earth's equator?* is equal to the arc tgr of the celestial equator; on the sphere this coordinate is called the Greenwich hour angle, it is measured in the same way as longitude, or, in circular calculation - always towards the West, ranging from 0° to 360°.

Coordinates? and tgr are called equatorial; their identity with geographical ones is even more visible if we assume that in Fig. 4, the radius of the celestial sphere will be equal to the radius of the globe.

The position of the meridian of the visible place of the luminary on the celestial sphere can be determined not only relative to the celestial Greenwich meridian. Let us take as the starting point the point of the celestial equator at which the Sun is visible on March 21. On this day, spring begins for the northern hemisphere of the Earth; day is equal to night; the said point is called the Spring point (or Aries point) and is designated by the sign of Aries - ?, as shown in the star chart.

The arc of the equator from the point of Spring to the meridian of the visible place of the luminary, counted in the direction of the apparent daily movement of the luminaries from 0° to 360°, is called the sidereal angle (or sidereal complement) and is designated?*.

The arc of the equator from the point of Spring to the meridian of the visible place of the luminary, counted in the direction of the Sun's own annual movement across the celestial sphere, is called right ascension? (in Fig. 5 it is given in hourly measure, and the sidereal angle is given in degree measure). The coordinates of the navigation stars are shown in Table. 1; it is obvious that, knowing?°, one can always find

and vice versa.

The arc of the celestial equator from the local meridian (its noon part PnZEPs) to the meridian of the luminary is called the local hour angle of the luminaries, denoted t. According to Fig. 4 it is clear that t always differs from tgr in the longitude of the observer’s position:

in this case, the eastern longitude is added, and the western longitude is subtracted if tgr is taken in a circular calculation.

Due to the apparent daily movement of the luminaries, their hour angles are constantly changing. For this reason, the stellar angles do not change, since their origin (the Spring point) rotates along with the sky.

The local hour angle of the Spring point is called sidereal time; it is always measured towards the West from 0° to 360°. It can be determined by eye by the position in the sky of the meridian of the star Kaff (? Cassiopeia) relative to the local celestial meridian. According to Fig. 5 it is clear that it is always

Would you like to practice visually determining equatorial coordinates? and t luminaries you observe in the sky. To do this, use Polyarnaya to determine the position of the North point on the horizon (Fig. 2 and 3), then find the South point. Calculate the complement of latitude of your place? = 90° - ? (for example, in Odessa? = 44°, and in Leningrad? = 30°). The noon point of the equator E is located above the point South at an angular distance equal to?; it is always the origin of the hour angle. The equator in the sky passes through the point East, point E and point West.

It is useful to know that at ?N > 90° - ?N the luminary in the northern hemisphere of the Earth always moves above the horizon, at?< 90° - ? оно восходит и заходит, при?S >90° - ?N it is not observed.
A mechanical model of the celestial sphere, reproducing the appearance of the starry sky and all the coordinates discussed above, is a star globe (Fig. 6). This navigation device is very useful in long voyages: with its help you can solve all problems of celestial navigation (with an angular error of the solution results of no more than 1.5-2° or with a time error of no more than 6-8 minutes. Before work, the globe is set in latitude observation locations (shown in Fig. 6) and local sidereal time t?, the rules for calculating which for the observation period will be explained below.

If desired, a simplified star globe can be made from a school globe by marking the visible places of stars on its surface, guided by Table. I and a star chart. The accuracy of solving problems on such a globe will be somewhat lower, but sufficient for many cases of orientation in the direction of motion of the yacht. Note also that the star map gives a direct image of the constellations (as the observer sees them), and their inverse images are visible on the star globe.

Identification of navigation stars

Of the countless stars, only about 600 are easily visible to the naked eye, shown on the star chart in the Nautical Astronomical Yearbook. This map gives a general picture of what a navigator can generally observe in the dark night sky. To answer the question of where and how to look for certain navigation stars in a certain geographic area, use the seasonal star charts below (Fig. 1-4): they cover the starry sky for all seas of the country and are compiled on the basis of the MAE star map ; they indicate the position and proper names of all 40 navigational stars mentioned in the table in the previous essay.

Each scheme corresponds to evening observations at a certain time of the year: spring (Fig. 1), summer (Fig. 2), autumn (Fig. 3), and winter (Fig. 4) or morning observations in spring (Fig. 2), summer (Fig. 3), autumn (Fig. 4) and winter (Fig. 1). Each seasonal scheme can be used at other times of the year, but at a different time of day.

To select a seasonal scheme suitable for the intended time of observation, use the table. 1. You must enter this table according to the calendar date of observation closest to your planned one and the so-called “meridian” time of day TM.

Meridian time with a permissible error of no more than half an hour can simply be obtained by reducing winter time adopted in the USSR since 1981 by 1 hour, and summer time by 2 hours. The rules for calculating T sea conditions according to the ship's time accepted on board the yacht are explained in the example below. In the bottom two rows of the table, for each seasonal scheme, the corresponding sidereal time tM and the reading of the sidereal angle?K on the scales of the MAE star map are indicated; These values ​​make it possible to determine which of the meridians of the star map at the intended time of observation coincides with the meridian of your geographical location.

When initially mastering the rules for identifying navigation stars, it is necessary to prepare for observations in advance; Both a star chart and a seasonal chart are used. We orient the star map on the ground; from the point of the south on the horizon along the sky towards the north pole of the world, the meridian of the equatorial star chart will be located, which is digitized by the value tM, i.e. for our seasonal schemes - 12H, 18H, 0(24)H and 6H. This meridian is shown as a dotted line on seasonal diagrams. The half-width of each circuit is approximately 90° = 6H; therefore, after a few hours, due to the rotation of the starry sky to the west, the dotted meridian will shift to the left edge of the diagram, and its central constellations - to the right.

The equatorial map covers the starry sky between parallels 60° N and 60° S, but not all stars shown on it will necessarily be visible in your area. Above your head, near the zenith, you can see those constellations whose star declinations are close in magnitude to the latitude of the place (and “of the same name” with it). For example, in latitude? = 60° N at tM = 12H the constellation Ursa Major is located above your head. Further, as already explained in the first essay, it can be argued that when? = 60° N will stars located south of the parallel with declination never be visible? = 30° S, etc.

For an observer in northern latitudes, the equatorial star map shows mainly those constellations that are observed in the southern half of the sky. To determine the visibility of constellations in the northern half of the sky, a north polar map is used, covering an area outlined from the north celestial pole with a radius of 60°. In other words, the north polar map overlaps the equatorial map in a wide zone between the parallels 30° N and 60° N. To orient the polar map on the ground, it is necessary to have its meridian, digitized found from the table. 1st magnitude?, placed above your head so that it coincides with the direction from the zenith to the north pole of the world.

The field of view of the human eye is approximately 120-150°, so if you look at Polaris, then all the constellations of the northern polar map will be in the field of view. Are those northern constellations whose stars have declinations always visible above the horizon? > 90° - ? and “same name” with latitude. For example, at latitude? = 45° N non-setting are stars with declinations greater than? = 45° N, and at latitude? = 60° N - those stars with? > 30° N., etc.

Let us remember that all the stars in the sky have the same size - they are visible as luminous points and differ only in the intensity of their brilliance and color tint. The size of the circles on the star map does not indicate the apparent size of the star in the sky, but the relative strength of its brightness - the magnitude. In addition, the image of the constellation is always somewhat distorted when the surface of the celestial sphere is expanded onto the map plane. For these reasons, the appearance of the constellation in the sky is somewhat different from its appearance on the map, but this does not create significant difficulties in identifying stars.

Learning to identify navigation stars is not difficult. For sailing during your vacation, it is enough to know the location of a dozen constellations and the navigation stars included in them from those listed in the table. 1 of the first essay. Two or three nights of pre-voyage training will give you confidence in navigating by the stars at sea.

Do not try to identify constellations by looking for figures of mythical heroes or animals on yourself that correspond to their tempting-sounding names. One can, of course, guess that the constellations of the northern animals - Ursa Major and Ursa Minor - should most often be looked for in the direction to the north, and the constellation of the southerner Scorpio - in the southern half of the sky. However, the actually observed appearance of the same northern “ursa” constellations is better conveyed by well-known verses:

Two bears laugh:
- Did these stars deceive you?
They are called by our name,
And they look like saucepans.

When identifying stars, it is more convenient to call the Big Dipper the Big Dipper, which is what we will do. Those wishing to know details about the constellations and their names are referred to the excellent “star primer” by G. Ray and the interesting book by Yu. A. Karpenko.

For a navigator, a practical guide to the starry sky can be diagrams - indicators of navigation stars (Fig. 1-4), showing the location of these stars relative to several reference constellations that are easily identified from star charts.

The main supporting constellation is Ursa Major, the bucket of which in our seas is always visible above the horizon (at a latitude of more than 40° N) and is easily identified even without a map. Let us remember the proper names of the stars of the Big Dipper (Fig. 1): ? - Dubhe, ? - Merak, ? - Fekda, ? - Megrets, ? - Aliot, ? - Mizar, ? - Benetnash. You already know the seven navigation stars!

In the direction of the line Merak - Dubhe and at a distance of about 30° is located, as we already know, Polar - the end of the handle of the Ursa Minor bucket, in the bottom of which Kokhab is visible.

On the line Megrets - Polar and at the same distance from Polar, the “maiden breast” of Cassiopeia and her stars Kaff and Shedar are visible.

In the direction Fekda - Megrets and at a distance of about 30° we will find the star Deneb, located in the tail of the constellation Cygnus - one of the few that at least to some extent corresponds in configuration to its name.

In the direction Fekda - Alioth, in an area approximately 60° away, the brightest northern star is visible - the blue beauty Vega (a Lyrae).

In the direction Mizar - Polar and at a distance of about 50°-60° from the pole is the constellation Andromeda - a chain of three stars: Alferraz, Mirakh, Alamak of equal brightness.

In the direction Mirakh - Alamak, Mirfak (? Perseus) is visible at the same distance.

In the direction Megrets - Dubhe, at a distance of about 50°, the pentagonal bowl of Auriga and one of the brightest stars, Capella, are visible.

In this way we found almost all the navigation stars visible in the northern half of our sky. Using Fig. 1, it is worth practicing searching for navigation stars on star charts first. When training “on the ground”, keep the rice. 1 “upside down”, pointing with the * icon to point N.

Let's move on to considering the navigation stars in the southern half of the spring sky in the same fig. 1.

Perpendicular to the bottom of the Big Dipper at a distance of about 50° is the constellation Leo, in the front paw of which there is Regulus, and at the tip of the tail - Denebola. To some observers, this constellation does not resemble a lion, but an iron with a bent handle. In the direction of Leo's tail are the constellation Virgo and the star Spica. To the south of the constellation Leo, in a star-poor region near the equator, dim Alphard (and Hydra) will be visible.

On the line Megrets - Merak at a distance of about 50° you can see the constellation Gemini - two bright stars Castor and Pollux. On the same meridian with them and closer to the equator, bright Procyon (? Canis Minor) is visible.

Moving your gaze along the curve of the handle of the Big Dipper, at a distance of about 30° you will see the bright orange Arcturus (? Boötes - a constellation resembling a parachute above Arcturus). Next to this parachute, a small and dim bowl of the Northern Crown is visible, in which Alfacca stands out,

Continuing in the direction of the same bend of the handle of the Big Dipper, not far from the horizon we will find Antares - the bright reddish eye of the constellation Scorpio.

On a summer evening (Fig. 2), the “summer triangle” formed by the bright stars Vega, Deneb and Altair (? Orla) is clearly visible on the eastern side of the sky. The constellation Eagle in the form of a diamond is easily found in the direction of flight of Cygnus. Between Eagle and Bootes there is a dim star Ras-Alhage from the constellation Ophiuchus.

On autumn evenings in the south, the “Pegasus Square” is observed, formed by the star Alferraz, which we have already considered, and three stars from the constellation Pegasus: Markab, Sheat, Algenib. The Pegasus square (Fig. 3) is easily found on the Polar - Kaff line at a distance of about 50° from Cassiopeia. Regarding the Pegasus Square, it is easy to find the constellations Andromeda, Perseus and Auriga to the east, and the constellations of the “summer triangle” to the west.

To the south of Pegasus Square, near the horizon, Difda (? Whale) and Fomalhaut are visible - “the mouth of the Southern Fish”, which Whale intends to swallow.

On the Markab - Algeinb line, at a distance of about 60°, bright Aldebaran (? Tauri) is visible in the characteristic “splashes” of small stars. Hamal (? Aries) is located between the constellations Pegasus and Taurus.

In the southern half of the winter sky, rich in bright stars (Fig. 4), it is easy to navigate relative to the most beautiful constellation Orion, which can be recognized without a map. The constellation Auriga is located midway between Orion and Polaris. The constellation Taurus is located on the continuation of the arc of Orion's belt (formed by the “three sisters” stars ?, ?, ? of Orion) at a distance of about 20°. On the southern continuation of the same arc, at a distance of about 15°, the brightest star sparkles - Sirius (? Canis Major). Towards? - ? Porcyon is observed at a distance of 20° of Orion.

In the constellation Orion, the navigation stars are Betelgeuse and Rigel.

It should be borne in mind that the appearance of constellations can be distorted by planets appearing in them - “wandering stars”. The position of the planets in the starry sky in 1982 is indicated in the table below. 2 So, having studied this table, we will establish that, for example, in May Venus will not be visible in the evening, Mars and Saturn will distort the view of the constellation Virgo, and not far from them in the constellation Libra a very bright Jupiter will be visible (a rarely observed “parade of planets” ). Information about the visible places of the planets is given for each year in the MAE and the Astronomical Calendar of the Nauka publishing house. They must be plotted on a star map in preparation for the trip, using the right ascensions and declinations of the planets indicated in these manuals for the date of observation.

The provided seasonal diagrams - indicators of navigation stars (Fig. 1-4) are most convenient for working at twilight, when the horizon and only the brightest stars are clearly visible. Constellation configurations depicted on star charts can only be detected after complete darkness.

The search for navigation stars must be meaningful; one must learn to perceive the appearance of the constellation as a whole - as an image, a picture. A person quickly and easily recognizes what he expects to see. That is why, when preparing for a voyage, it is necessary to study a star map in the same way as a tourist studies a route for a walk through an unfamiliar city using a map.

When going out to observe, take with you a star chart and an indicator of navigation stars, as well as a flashlight (it is better to cover its glass with red nail polish). A compass will be useful, but you can do without it by determining the direction to the North along the Polyarnaya. Think of something that will serve as a “scale bar” for estimating angular distances in the sky. The angle at which an object held in an outstretched hand and perpendicular to it is visible contains as many degrees as the number of centimeters in height of this object. In the sky, the distance between the stars Dubhe and Megrets is 10°, between the stars Dubhe and Benetnash - 25°, between the outermost stars Cassiopeia - 15°, the eastern side of Pegasus Square - 15°, between Rigel and Betelgeuse - about 20°.

Having reached the area at the appointed time, orient yourself in the directions of North, East, South and West. Find and identify the constellation passing above your head - through the zenith or near it. Make a reference to the area of ​​the seasonal scheme and the equatorial map - at point S and the direction of the local celestial meridian perpendicular to the horizon line at point S; tie the north polar map to the area - along the ZP line. Find a reference constellation - Ursa Major (Pegasus Square or Orion) and practice identifying navigation stars. In this case, one must remember about distortions in the visually observed heights of luminaries due to the oblateness of the sky, about distortions in the color of stars at low altitudes, about the apparent increase in the size of constellations near the horizon and decrease as they approach the zenith, about changes in the position of constellation figures during the night relative to the visible horizon from -for the rotation of the sky.

B. An example of calculating meridian time and choosing a seasonal star chart

On May 8, 1982, in the Baltic Sea (latitude? = 59.5° N; longitude? = 24.8° Ost, observations of the starry sky are planned at the moment TC = 00:30M standard (Moscow summer) time. Select and orient the star map and index navigation stars.

On the shore, we can approximately take TM equal to summer, reduced by 2 hours. In our example:

In all cases, when the standard observation time of the TC is less than NС, before performing the subtraction it is necessary to increase the TC by 24 hours; in this case, the world date will be less than the local date by one. If it turns out that after performing the addition, Tgr turned out to be more than 24H, you need to discard 24H and increase the date of the result by one. The same rule applies when calculating TM from Ggr and?.

Selection of seasonal scheme and its orientation

Local date May 7 and moment TM = 22H09M according to table. 1 most closely corresponds to the seasonal scheme in Fig. 1. But this scheme was built for TM = 21H on May 7, and we will conduct observations 1H09M later (in degree measure 69M: 4M = 17°). Therefore, the local meridian (line S - PN) will be located to the left of the central meridian of the diagram by 17° (if we had observed earlier, not later, the local meridian would have shifted to the right).

In our example, the constellation Virgo will pass through the local meridian above the point of the South and the constellation Ursa Major near the zenith, and Cassiopeia will be located at the point of the North (see star map for t? = 13H09M and? K = 163°).

To identify navigation stars, orientation relative to the Big Dipper will be used (Fig. 1).

- small bodies of the Solar System (along with meteoroid bodies), moving in highly elongated orbits and dramatically changing their appearance as they approach the Sun. K., being far from the Sun, look like foggy, faintly luminous objects (blurry disks with a condensation in the center). As the sky approaches the Sun, it forms a “tail” directed in the direction opposite to the Sun.

Bright K. can have several. tails of different lengths and colors, parallel stripes may be observed in the tail, and concentric stripes around the “head” of K. rings-galos.

Title "K." comes from the Greek. the words kometes, literally - long-haired (bright K. look like a head with flowing hair, Fig. 1). 5-10 K are opened annually. Each of them is assigned a preliminary designation, including the name of the K. who discovered it, the year of discovery and a letter of the Latin alphabet in the order of discovery. Then he will be replaced and finished. a designation including the year of passage through perihelion and a Roman numeral in order of the dates of passage through perihelion.

K. are observed when a small body - the K.'s core, resembling a lump of snow, contaminated with fine dust and larger solid particles, approaches the Sun closer than 4-6 AU. e., is heated by its rays and begins to release gases and dust particles. Gases and dust create a foggy shell around the core (C.'s atmosphere), called a coma, the brightness of the swarm quickly decreases towards the periphery. The atmosphere of the planet continuously dissipates into space and exists only when gases and dust are released from the core. In many comas, a star-shaped core is visible in the center of the coma, which is a dense part of the atmosphere that hides the true (solid) core, which is practically inaccessible to observation. The visible nucleus, together with the coma, makes up K.'s head (Fig. 2). From the side of the Sun, the K.'s head has the shape of a parabola or a chain line, which is explained by the constant action of light pressure and solar wind on the K.'s atmosphere. The K.'s tails consist of ionized gases and dust carried away in the direction from the Sun (dust is mainly under the influence of light pressure , and ionized gases - as a result of interaction with ). Large solid particles, under the influence of light pressure, acquire small accelerations and, having low velocities relative to the nucleus (due to their weak entrainment by gases), gradually spread along the orbit of the meteor, forming a meteor swarm. Neutral atoms and molecules experience only a small amount. light pressure and therefore scatter almost evenly in all directions from the K nucleus.

As the moon approaches the Sun and the heating of the core increases, the intensity of the release of gases and dust sharply increases, which is manifested in a rapid increase in the brightness of the moon and an increase in the brightness of the tails. As stars move away from the Sun, their brightness quickly decreases. If we approximate the change in the brightness of K.’s head by the law 1/ rn, r- distance from the Sun), then on average 4 (individual K. have significant deviations from this law). On the smooth change in the shine of K.’s head associated with changes r, superimposed are fluctuations in brightness and bright flares caused by the “explosive” ejection of matter from cometary nuclei with a sharp increase in the flux of particles of solar origin.

The diameters of K.'s nuclei are presumably 0.5-20 km, and, therefore, with a density of ~ 1 g/cm 3, their masses are within the range of 10 14 -10 19 g.

However, cells with significantly larger nuclei occasionally appear. Numerous nuclei smaller than 0.5 km generate weak nuclei that are practically inaccessible to observation. The visible diameters of the stars' heads are 10 4 -10 6 km, varying with distance from the Sun. Some K. have max. the size of the head exceeded the size of the Sun. Shells of atomic hydrogen around the head have even larger sizes (over 10 7 km), the existence of which was established by observations in the spectrum, lines during extra-atmospheric studies of K. As a rule, the tails are less bright than the head, and therefore they can be observed not all K. The length of their visible part is 10 6 -10 7 km, i.e. They are usually immersed in a hydrogen shell (Fig. 2). In some K., the tail could be traced to distances of more than 10 8 km from the nucleus. In the heads and tails of K. the substance is extremely rarefied; Despite the gigantic volume of these formations, almost the entire mass of the crystal is concentrated in its solid core.

Kernels consist mainly of water ice (snow) and ice (snow) of CO or CO 2 with an admixture of ice and other gases, which also means. amounts of non-volatile (stony) substances. Apparently, an important component of the nuclei of the phenomenon. clathrates, i.e. ices, crystalline the lattice of which includes atoms and molecules of other substances. Judging by the abundance of chemicals. elements in the substance of K., the nucleus of K. should consist (by mass) of approx. of 2/3 ice and 1/3 rocky substances. The presence of a certain amount of radioactive elements in the rocky component of K.'s nuclei should have led, in the distant past, to the heating of their interior by several degrees. dec. Kelvin. At the same time, the presence of highly volatile ice in K.'s cores shows that their internal. the temperature never exceeded ~ 100 K. Thus, the nuclei of the solar system are, apparently, the least altered samples of the primary matter of the Solar system. In this regard, projects for direct research of the substance and structure of carbon using an automatic spacecraft are being discussed and prepared.

Activity of K nuclei at distances less than 2-2.5 a. e. from the Sun, is associated with the sublimation of water ice, and at large distances - with the sublimation of ice from CO 2 and other more volatile ices. At a distance of 1 a. i.e. from the Sun, the rate of sublimation of the water component is ~ 10 18 molecules/(cm 2 s). In a planet with perihelia near the Earth's orbit, during one approach to the Sun, the outer layer of the core is lost several times thick. m (K., flying through the solar corona, can lose a layer of hundreds of m).

The long existence of a series of periodic K., which repeatedly flew near the Sun, is apparently explained insignificantly. loss of substance during each flight (due to the formation of a porous heat-insulating layer on the surface of the cores or the presence of refractory substances in the cores).

It is assumed that K.'s cores include blocks of different composition (macro-breccia structure) with different volatility, which can lead, in particular, to the appearance of jet outflows noticed near certain cores.

During the sublimation of ice, not only rocky particles are separated from the surface of the ice core, but also ice particles, which then evaporate into the interior. parts of the head. Non-volatile dust grains are apparently also formed in the immediate vicinity of the nucleus as a result of the condensation of atoms and molecules of non-volatile substances. Dust particles simply reflect and scatter sunlight, which gives a continuous component of the spectra of the K. With a small emission of dust, a continuous spectrum is observed only in the central part of the head of the K., and with its abundant release - in almost the entire head and in the tails of certain types (see . below).

Atoms and molecules located in the heads and gas tails of celestial molecules absorb quanta of sunlight and then re-emit them (resonant fluorescence). Neutral (apparently complex) molecules sublimating from the nucleus do not reveal themselves in the optical. spectrum areas. When they disintegrate under the influence of sunlight (photodissociation), then the radiation of some of their fragments is due to optical radiation. part of the spectrum. Study of optical K.'s spectra showed that the heads contain the following neutral atoms and molecules (more precisely, chemically unstable radicals): C, C 2, C 3, CH, CN, CO, CS, HCN, CH 3 CN; H, 0, OH, HN, H 2 O, NH 2; ions C0 +, CH +, CN +, OH +, CO, H 2 O +, etc. are also present. The nature of the spectrum of radiation changes as they approach the Sun. In K. located at a distance from the Sun r> 3-4 a. That is, the spectrum is continuous (solar radiation at such distances cannot excite a significant number of molecules). When K. crosses the asteroid belt (3 AU), the emission band of the CN molecule appears in its spectrum. At 2 a. e. molecules C 3 and NH 2 are excited and begin to emit at 1.8 a. That is, carbon bands appear in the spectrum. At the distance of the orbits of Mars (1.5 AU), lines of OH, NH, CH, etc. are observed in the spectrum of the heads of the planet, and lines of CO +, CO, CH +, OH +, H 2 O + ions are observed in the tails. etc. When crossing the orbit of Venus (at distances of the Earth from the Sun less than 0.7 AU), Na lines appear, from which an independent tail is sometimes formed. In rare K. that flew extremely close to the Sun (for example, K. 1882 II and 1965 VIII), sublimation of rocky dust particles occurred and a spectrum was observed. lines of metals Fe, Ni, Cu, Co, Cr, Mn, V. During observations of comet Kohoutek 1973 XII and comet Bradfield 1974 III, it was possible to detect radio emission lines of acetylnitrile (CH 3 CN, = 2.7 mm), hydrocyanic acid (HCN, = 3.4 mm) and water (H 2 O, = 13.5 mm) - molecules that are directly released from the nucleus and represent some of the parent molecules (with respect to atoms and radicals observed in the optical region of the spectrum). Radio lines of CH (= 9 cm) and OH (= 18 cm) radicals were observed in the centimeter range.

The radio emission of some of these molecules is due to their thermal excitation (collisions of molecules in the perinuclear region), while for others (for example, hydroxyl OH) it apparently has a maser nature (see). In the tails of the sun, directed almost directly from the Sun, ionized molecules CO +, CH +, C0, OH + are observed, i.e., these tails are phenomena. plasma. When observing the spectrum of the tail of comet Kohoutek 1973 XII, it was possible to identify the H 2 O + lines. Emission from ionized molecules occurs at a distance of ~ 10 3 km from the nucleus.

According to the classification of K. tails, proposed in the 2nd half of the 19th century. F. Bredikhin, they are divided into three types: type I tails are directed almost directly from the Sun; Type II tails are curved and deviate from the extended radius vector backwards with respect to the orbital motion of the star; Type III tails are short, almost straight, and from the very beginning, deflected in the direction opposite to the orbital motion. At certain mutual positions of the Earth, Earth, and the Sun, tails of types II and III can be projected onto the sky in the direction of the Sun, forming a tail called anomalous. If, in addition, the Earth is near the plane of the comet's orbit at this time, then a layer of large particles leaving the core with low relative velocities and therefore propagating near the plane of the orbit K is visible in the form of a thin peak. Explanation of physics. The reasons leading to the appearance of tails of different types have changed significantly since the time of Bredikhin. According to modern According to data, type I tails are plasma: they are formed by ionized atoms and molecules, which are carried away from the nucleus at speeds of tens and hundreds of km/s under the influence of the solar wind. Due to the non-isotropic release of plasma from the perinuclear region of the solar system, as well as due to plasma instabilities and inhomogeneities of the solar wind, type I tails have a stream structure. They are almost cylindrical. shape [diameter km] with an ion concentration of ~ 10 8 cm -3. The angle at which the type I tail deviates from the Sun-K line depends on the speed v sv of the solar wind and on the speed of orbital motion K. Observations of type I cometary tails made it possible to determine the speed of the solar wind up to distances of several. A. e. and far from the ecliptic plane. Theoretical An examination of the solar wind flow around the celestial body allowed us to conclude that in the celestial head, on the side facing the Sun, at a distance of ~ 10 5 km from the core, there should be a transition layer separating the solar wind plasma from the plasma of the solar wind, and at a distance of ~ 10 6 km - a shock wave separating the region of supersonic solar wind flow from the region of subsonic turbulent flow adjacent to the head of the solar wind.

Types II and III tailings are dusty; Dust grains continuously released from the nucleus form type II tails; type III tails appear in cases where a whole cloud of dust particles is simultaneously released from the nucleus. Dust grains of different sizes receive different acceleration under the influence of light pressure, and therefore such a cloud is stretched into a strip - the tail of the spectrum. Di- and triatomic radicals observed in the head of the spectrum and responsible for resonance bands in the visible region of the spectrum of the spectrum (in the region of maximum solar radiation ), under the influence of light pressure they obtain an acceleration close to the acceleration of small dust particles. Therefore, these radicals begin to move in the direction of the type II tail, but do not have time to move far along it due to the fact that their lifetime (before photodissociation or photoionization) is ~ 10 6 s.

K. yavl. members of the Solar System and, as a rule, move around the Sun in elongated ellipticals. orbits of various sizes, arbitrarily oriented in space. The dimensions of the orbits of most planets are thousands of times larger than the diameter of the planetary system. The stars are located near the aphelion of their orbits most of the time, so that on the distant outskirts of the solar system there is a cloud of stars - the so-called. Oort cloud. Its origin is apparently connected with gravity. the ejection of icy bodies from the zone of the giant planets during their formation (see). The Oort cloud contains ~10 11 cometary nuclei. In K., moving away to the peripheral. parts of the Oort cloud (their distances from the Sun can reach 10 5 AU, and the periods of revolution around the Sun - 10 6 -10 7 years), orbits change under the influence of the attraction of nearby stars. At the same time, some K. become parabolic. speed relative to the Sun (for such distant distances ~ 0.1 km/s) and forever lose contact with the Solar System. Others (very few) acquire speeds of ~ 1 m/s, which leads to their movement in an orbit with perihelion near the Sun, and then they become available for observation. For all planets, as they move in the region occupied by planets, their orbits change under the influence of the planets' attraction. Moreover, among the K. who came from the periphery of the Oort cloud, i.e. moving along quasi-parabolic lines. orbits, about half becomes hyperbolic. orbit and is lost in interstellar space. For others, on the contrary, the size of their orbits decreases, and they begin to return to the Sun more often. Changes in orbits are especially great during close encounters with giant planets. ~100 short-periods are known. K., which approach the Sun after several. years or tens of years and therefore relatively quickly waste the substance of their core. Most of these K. belong to the Jupiter family, i.e. they acquired their modern small orbits as a result of approaching it.

The orbits of spacecraft intersect with the orbits of the planets, so collisions of spacecraft with planets should occasionally occur. Some of the craters on the Moon, Mercury, Mars and other bodies were formed as a result of impacts from K nuclei. The Tunguska phenomenon (the explosion of a body flying into the atmosphere from space on Podkamennaya Tunguska in 1908) may also have been caused by a collision of the Earth with a small comet core.

Lit.:
Orlov S.V., On the nature of comets, M., 1960; Dobrovolsky O.V. Comets, meteors and zodiacal light, in the book. Course of astrophysics and stellar astronomy vol. 3, M., 1964; him. Comets, M., 1966; Whipple F.L., Comets, in the book: Cosmochemistry of the Moon and Planets, M., 1975; Churyumov K.I., Comets and their observation, M., 1980; Tomita Koichiro, Discourses on Comets, trans. from Japanese, M., 1982.

(B.Yu. Levin)

1. What cosmic bodies, visible to the naked eye in the starry sky of the Earth, can change the direction of their movement (against the background of stars) by more than ? Why is this happening?

Solution: As is known, all the planets of the Solar system perform both direct and retrograde movements. This loop-like motion of the planets is a consequence of the addition of the movements of the Earth and the planets in their orbit around the Sun. Reasoning similarly, we can conclude that any other bodies revolving around the Sun should move in the same way against the background of stars. Of these, five planets are visible to the naked eye (Mercury, Venus, Mars, Jupiter, Saturn), as well as bright comets.

2. What celestial bodies have tails? How many of them can there be, what do they consist of?
Solution: Gas and gas-dust tails directed away from the Sun appear in comets as they approach the Sun. A comet may also have a dust tail directed along the comet's orbit. In addition, comets have small anomalous tails directed towards the Sun (consisting of massive coma dust particles). As a result, a comet can have up to four tails. A gas tail has also been discovered near the Earth, directed away from the Sun. According to calculations, it extends over a distance of about 650 thousand km. It is likely that other planets with atmospheres also have gas tails. In addition, structures, which are often called “tails,” are found in interacting galaxies (as a rule, one galaxy has only one such structure). They consist of stars and interstellar gas.

3. Two stars in the sky are located so that one of the stars is visible at the zenith when observed from the north geographic pole, and the second passes through the zenith every day when observed from the earth's equator. It is known that light travels from Earth to the first star in just over 430 years. Light travels from the second star to Earth for almost 16 years. How long does it take for light to travel from the first star to the second?

Solution: Since the first star is visible at the zenith at the pole, it is located at the north pole of the World. The second star is located on the celestial equator. Therefore, the angular distance between the stars is , and the time it takes light to travel from one to the other can be calculated using the Pythagorean theorem. However, by comparing the distances to the stars in light years, one can understand that the time it takes light to travel from the first star to the second practically coincides with the time it takes light to travel from the first star to the Earth, i.e. the answer to the problem is 430 years.

4. On what single planet can both a total and an annular eclipse of the Sun be observed by the same satellite?

Solution: As is known, both total and annular eclipses of the Sun occur on Earth, so it is this only planet. Due to the ellipticity of the orbits of the Earth around the Sun and the Moon around the Earth, the angular diameter of the Sun varies from to , and the diameter of the Moon from to . If the angular diameter of the Moon is greater than the angular diameter of the Sun, then a total solar eclipse can occur; if, on the contrary, the angular diameter of the Sun exceeds the diameter of the Moon, then an annular eclipse can occur. All other planets in the Solar System do not have satellites whose angular dimensions, when observed from the planet, would be close to the angular dimensions of the Sun.

5. What is the maximum number of months in a year such that the same phase of the Moon is repeated twice during each of these months? The repetition period of the Moon's phases (the so-called "synodic month") varies from day to day (due to the ellipticity of the lunar orbit).

Solution: Obviously, the phases of the Moon cannot repeat in February - its duration, even in leap years, is less than the smallest possible value of the synodic month. All other months in the calendar, on the contrary, are always longer than the synodic month, so in each of these months there can be phases of the Moon that repeat twice. Let's consider an unrealistic "limiting" case - let all calendar months contain 31 days, and the synodic month always turns out to be exactly 29 days. Then suppose that in a certain month (let's call it "month No. 1") some phase of the Moon was just after midnight on the 1st. The second time the same phase will repeat on the 30th of the same month. The next time it will occur is on the 28th of the next month (“month No. 2”), then on the 26th of “month No. 3” and so on - in all calendar months up to “month No. 12” this phase will occur only once times (in “month No. 12” it will fall on the 8th day). Those. in such a situation, during the year we will find only one month we need (the first). Obviously, due to the longer duration of the synodic month and the shorter duration of some calendar months (if they are longer than the synodic month), the situation will not change. However, having a short February on the calendar allows you to find a better solution. If a certain phase of the Moon occurred at the end of the day on January 31, then it occurred again in January - on the 2nd. The same phase will be absent in February, the next time after January 31 it will repeat on March 1st or 2nd (depending on whether it is a leap year or not). Its next repetition will occur approximately on March 30-31, i.e. the same phase will be repeated twice in two calendar months. There will be no other such months in the year - the “limiting” case discussed above excludes their presence. From here we get the answer: there are two such months (January and March), and this maximum is realized in any year (but, of course, for different phases of the Moon).

I will again use the brochure “Didactic Material on Astronomy” written by G.I. Malakhova and E.K. Strout and published by the Prosveshcheniye publishing house in 1984. This time the first tasks of the final test on page 75 are being distributed.

To visualize formulas, I will use the LaTeX2gif service, since the jsMath library is not able to render formulas in RSS.

Task 1 (Option 1)

Condition: The planetary nebula in the constellation Lyra has an angular diameter of 83″ and is located at a distance of 660 pc. What are the linear dimensions of the nebula in astronomical units?

Solution: The parameters specified in the condition are related to each other by a simple relationship:

1 pc = 206265 AU, respectively:

Task 2 (Option 2)

Condition: The parallax of the star Procyon is 0.28″. The distance to the star Betelgeuse is 652 light years. of the year. Which of these stars and how many times is farther from us?

Solution: Parallax and distance are related by a simple relationship:

Next, we find the ratio of D 2 to D 1 and find that Betelgeuse is approximately 56 times further than Procyon.

Task 3 (Option 3)

Condition: How many times did the angular diameter of Venus, as seen from Earth, change as a result of the planet moving from its minimum distance to its maximum? The orbit of Venus is considered to be a circle with a radius of 0.7 AU.

Solution: We find the angular diameter of Venus for the minimum and maximum distances in astronomical units and then their simple ratio:

We get the answer: it decreased by 5.6 times.

Task 4 (Option 4)

Condition: What angular size will our Galaxy (whose diameter is 3 × 10 4 pc) be seen by an observer located in the M 31 galaxy (Andromeda nebula) at a distance of 6 × 10 5 pc?

Solution: An expression connecting the linear dimensions of an object, its parallax and angular dimensions is already in the solution to the first problem. Let’s use it and, slightly modifying it, substitute the required values ​​from the condition:

Problem 5 (Option 5)

Condition: Resolution of the naked eye is 2′. What size objects can an astronaut discern on the surface of the Moon when flying above it at an altitude of 75 km?

Solution: The problem is solved similarly to the first and fourth:

Accordingly, the astronaut will be able to distinguish surface details measuring 45 meters.

Problem 6 (Option 6)

Condition: How many times is the Sun larger than the Moon if their angular diameters are the same and their horizontal parallaxes are respectively 8.8″ and 57′?

Solution: This is a classic problem of determining the size of luminaries by their parallax. The formula for the connection between the parallax of a luminary and its linear and angular dimensions has been repeatedly found above. As a result of reducing the repeating part, we get:

The answer is that the Sun is almost 400 times larger than the Moon.

“There is only one unmistakable way to determine the location and direction of a ship’s path at sea - astronomical, and happy is the one who is familiar with it!” - with these words of Christopher Columbus we open a series of essays - lessons on celestial navigation.

Marine celestial navigation originated in the era of great geographical discoveries, when “iron men sailed on wooden ships”, and over the centuries it has absorbed the experience of many generations of sailors. Over the past decades, it has been enriched with new measuring and computing tools, new methods for solving navigation problems; The recently introduced satellite navigation systems, as they continue to develop, will make all the difficulties of navigation a thing of history. The role of marine celestial navigation (from the Greek aster - star) remains extremely important today. The purpose of our series of essays is to introduce amateur navigators to modern methods of celestial orientation available in yachting conditions, which are most often used on the high seas, but can also be used in cases of coastal navigation when coastal landmarks are not visible or cannot be identified.

Observations of celestial landmarks (stars, Sun, Moon and planets) allow navigators to solve three main problems (Fig. 1):

• 1) measure time with sufficient accuracy for approximate orientation;
• 2) determine the direction of movement of the vessel even in the absence of a compass and correct the compass, if available;
• 3) determine the exact geographical location of the vessel and control the correctness of its route.

The need to solve these three problems on a yacht arises due to inevitable errors in calculating its path according to compass and log readings (or approximately determined speed). Large drift of the yacht, reaching 10-15° in strong winds, but can only be assessed by eye; continuously changing speed; “by sail” control when sailing close-hauled, only with subsequent fixation of compass courses; influence of variable currents; a large number of turns when tacking is not a complete list of reasons that complicate navigation on a yacht! If dead reckoning is not controlled by observations of luminaries, the error in the dead reckoning location, even for experienced yachtsmen, can exceed several tens of miles. It is clear that such a large error threatens the safety of navigation and can lead to large losses of sailing time.

Depending on the nautical instruments, manuals and computing tools used, the accuracy of solving celestial navigation problems will be different. To be able to solve them in full and with accuracy sufficient for navigation on the open sea (location error - no more than 2-3 miles, in compass correction - no more than 1°), you must have:

• a navigation sextant and a good waterproof watch (preferably electronic or quartz);
• a transistor radio receiver for receiving time signals and a microcalculator of the “Electronics” type (this microcalculator must have the input of angles in degrees, provide the calculation of direct and inverse trigonometric functions, and perform all arithmetic operations; the most convenient is the “Electronics” BZ-34); in the absence of a microcalculator, you can use mathematical tables or special tables “Heights and azimuths of luminaries” (“VAS-58”), published by the Main Directorate of Navigation and Oceanography;
• Nautical Astronomical Yearbook (MAE) or other manual for calculating the coordinates of luminaries.

The widespread use of electronic watches, transistor radios and microcalculators has made the use of astronomical navigation methods accessible to the widest range of people without special navigational training. It is no coincidence that there has been a continuous increase in demand for nautical astronomical yearbooks; this serves as the best proof of the popularity of celestial navigation among all categories of navigators and, first of all, among amateur sailors.

In the absence of any of the above celestial navigation means on the ship, the very possibility of celestial navigation orientation is preserved, but its accuracy decreases (while remaining, however, quite satisfactory for many cases of sailing on a yacht). By the way, some tools and computing facilities are so simple that they can be made independently.

Celestial navigation is not only a science, but also an art - the art of observing the stars in sea conditions and accurately performing calculations. Don't let the initial failures disappoint you: with a little patience, the necessary skills will appear, and with them will come high satisfaction in the art of sailing out of sight of the shores.

All the celestial navigation methods that you will master have been tested many times in practice; they have already served sailors well in the most critical situations more than once. Don’t put off mastering them “for later”; master them when preparing for swimming; The success of the campaign is decided on the shore!

Celestial navigation, like all astronomy, is an observational science. Its laws and methods are derived from observations of the visible movement of luminaries, from the relationship between the geographical location of the observer and the apparent directions of the luminaries. Therefore, we will begin the study of celestial navigation with observations of luminaries - we will learn to identify them; Along the way, let’s get acquainted with the principles of spherical astronomy that we need in the future.

Celestial landmarks

1. Navigation stars. At night, with a clear sky, we see thousands of stars, but in principle each of them can be identified based on its location in a group of neighboring stars - its visible place in the constellation, its apparent magnitude (brightness) and color.

For navigation at sea, only the brightest stars are used; they are called navigation stars. The most commonly observed navigation stars are listed in Table. 1; a complete catalog of navigation stars is available in MAE.

The picture of the starry sky is not the same in different geographical areas, in different seasons of the year and at different times of the day.

When starting an independent search for navigation stars in the northern hemisphere of the Earth, use a compass to determine the direction to the North point located on the horizon (indicated by the letter N in Fig. 2). Above this point, at an angular distance equal to the geographic latitude of your place φ, is the star Polaris - the brightest among the stars of the constellation Ursa Minor, forming the shape of a ladle with a curved handle (Little Dipper). The polar one is denoted by the Greek letter “alpha” and is called α Ursa Minor; it has been used by sailors for several centuries as a main navigational landmark. In the absence of a compass, the direction to the north is easily determined as the direction to Polyarnaya.

As a scale for roughly measuring angular distances in the sky, you can use the angle between the directions from your eye to the tips of the thumb and index finger of your outstretched hand (Fig. 2); this is approximately 20°.

The apparent brightness of a star is characterized by a conventional number, which is called magnitude and is designated by the letter m. The magnitude scale looks like this:

Shine m= 0 has the brightest star in the northern sky observed in summer - Vega (α Lyrae). Stars of the first magnitude - with brilliance m= 1 2.5 times fainter in brightness than Vega. Polaris has a magnitude of about m= 2; this means that its brightness is approximately 2.5 times weaker than the brightness of stars of the first magnitude or 2.5 X 2.5 = 6.25 times weaker than the brightness of Vega, etc. Only brighter stars can be observed with the naked eye m
Stellar magnitudes are indicated in the table. 1; The color of the stars is also indicated there. However, it must be taken into account that color is perceived by people subjectively; in addition, as they approach the horizon, the brightness of stars noticeably weakens, and their color shifts to the red (due to the absorption of light in the earth’s atmosphere). At a height above the horizon of less than 5°, most stars disappear from visibility altogether.

We observe the earth's atmosphere in the form of the firmament (Fig. 3), flattened overhead. In marine conditions at night, the distance to the horizon appears to be approximately twice as great as the distance to the zenith point Z (from the Arabic zamt - top) located overhead. During the day, the visible flatness of the sky can increase one and a half to two times, depending on cloudiness and time of day.

Due to the very large distances to the celestial bodies, they appear to us to be equidistant and located in the sky. For the same reason, the relative position of stars in the sky changes very slowly - our starry sky is not much different from the starry sky of Ancient Greece. Only the celestial bodies closest to us - the Sun, planets, and the Moon - move noticeably in the foyer of constellations - figures formed by groups of mutually stationary stars.

The oblateness of the sky leads to a distortion of the visual estimate of the apparent height of the luminary - the vertical angle h between the direction to the horizon and the direction to the luminary. These distortions are especially large at low altitudes. So, let us note once again: the observed height of the luminary is always greater than its true height.

The direction to the observed star is determined by its true bearing IP - the angle in the horizon plane between the direction to the North and the bearing line of the star OD, which is obtained by the intersection of the vertical plane passing through the star and the horizon plane. The IP of the luminary is measured from the point of North along the arc of the horizon towards the point of East within the range of 0°-360°. The true bearing of Polar is 0° with an error of no more than 2°.

Having identified Polar, find the constellation Ursa Major in the sky (see Fig. 2), which is sometimes called the Big Dipper: it is located at a distance of 30°-40 from Polar, and all the stars of this constellation are navigational. If you have learned to confidently identify Ursa Major, you will be able to find Polaris without the help of a compass - it is located in the direction from the star Merak (see Table 1) to the star Dubge at a distance equal to 5 distances between these stars. The constellation Cassiopeia with the navigation stars Kaff (β) and Shedar (α) is located symmetrically to Ursa Major (relative to Polaris). In the seas washing the shores of the USSR, all the constellations we mentioned are visible above the horizon at night.

Having found Ursa Major and Cassiopeia, it is not difficult to identify other constellations and navigational stars located near them if you use a star chart (see Fig. 5). It is useful to know that the arc in the sky between the stars Dubge and Bevetnash is approximately 25°, and between the stars β and ε Cassiopeia - about 15°; these arcs can also be used as a scale to approximate angular distances in the sky.

As a result of the rotation of the Earth around its axis, we observe a visible rotation of the sky towards the West around the direction to Polar; Every hour the starry sky rotates by 1 hour = 15°, every minute by 1 m = 15", and per day by 24 hours = 360°.

2. The annual movement of the Sun in the sky and seasonal changes in the appearance of the starry sky. During the year, the Earth makes one full revolution around the Sun in outer space. The direction from the moving Earth to the Sun is constantly changing for this reason; The Sun describes the dotted curve shown on the star chart (see inset), which is called the ecliptic.

The visible place of the Sun makes its own annual movement along the ecliptic in the direction opposite to the apparent daily rotation of the starry sky. The speed of this annual movement is small and equal to I/day (or 4 m/day). In different months, the Sun passes through different constellations, forming a zodiacal belt (“circle of animals”) in the sky. So, in March, the Sun is observed in the constellation Pisces, and then successively in the constellations Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius.

Constellations located on the same hemisphere with the Sun are illuminated by it and are not visible during the day. At midnight, constellations are visible in the south, distant from the place of the Sun on a given calendar date by 180° = 12 hours.

The combination of the rapid apparent daily movement of stars and the slow annual movement of the Sun leads to the fact that the picture of the starry sky observed today at the moment will be visible tomorrow 4 m earlier, in 15 days - 4 m earlier.

earlier, in a month - 2 hours earlier, etc.

3. Geographical and visible location of the star. Star map. Star globe. Our Earth is spherical; Now this is clearly proven by its photographs taken by space stations.

In navigation, it is believed that the Earth has the shape of a regular ball, on the surface of which the yacht’s place is determined by two geographical coordinates:

Geographic latitude φ (Fig. 4) - the angle between the plane of the earth’s equator eq and the direction of the plumb line (the direction of gravity) at the observation point O. This angle is measured by the arc of the geographic meridian of the observer’s place (in short, the local meridian) EO from the equatorial plane towards the Earth's pole closest to the observation site within 0°-90°. Latitude can be north (positive) or south (negative). In Fig. 4, the latitude of place O is equal to φ = 43° N. Latitude determines the position of the geographic parallel - a small circle parallel to the equator.

Geographic longitude λ is the angle between the planes of the prime geographic meridian (according to international agreement, it passes through the Greenwich Observatory in England - G in Fig. 4) and the plane of the observer’s local meridian. This angle is measured by the arc of the earth's equator towards the East (or West) within the range of 0°-180°. In Fig. 4 the longitude of the place is λ = 70° O st . Longitude determines the position of the local meridian.

The direction of the local meridian at observation point O is determined by the direction of the sun's shadow at noon from a vertically installed pole; at noon this shadow has the shortest length; on a horizontal platform it forms the midday N-S line (see Fig. 3). Any local meridian passes through the geographic poles P n and P s, and its plane passes through the Earth’s rotation axis P n P s and the plumb line OZ.

A ray of light from a distant body * comes to the center of the Earth in the direction *C, crossing the earth's surface at some point σ. Let's imagine that an auxiliary sphere (celestial sphere) is described from the center of the Earth with an arbitrary radius. The same ray will intersect the celestial sphere at point σ". Point σ is called the geographic location of the luminary (GLM), and point σ" is the visible location of the luminary on the sphere. According to Fig. 4. It can be seen that the position of the HMS is determined by the geographic sprat φ* and geographic longitude λ*.

The position of the visible place of the luminary on the celestial sphere is determined similarly:

• the arc of the GMS meridian φ* is equal to the arc δ of the celestial meridian passing through the visible place of the luminary; this coordinate on the sphere is called the declination of the luminary, it is measured in the same way as latitude;
• the arc of the earth's equator λ* is equal to the arc t gr of the celestial equator; on the sphere this coordinate is called the Greenwich hour angle, it is measured in the same way as longitude, or, in circular calculation - always towards the West, ranging from 0° to 360°.

The coordinates δ and t gr are called equatorial; their identity with geographical ones is even more visible if we assume that in Fig. 4, the radius of the celestial sphere will be equal to the radius of the globe.

The position of the meridian of the visible place of the luminary on the celestial sphere can be determined not only relative to the celestial Greenwich meridian. Let us take as the starting point the point of the celestial equator at which the Sun is visible on March 21. On this day, spring begins for the northern hemisphere of the Earth; day is equal to night; the said point is called the Spring point (or Aries point) and is designated by the sign of Aries - ♈, as shown in the star chart.

The arc of the equator from the point of Spring to the meridian of the visible place of the luminary, counted in the direction of the apparent daily movement of the luminaries from 0° to 360°, is called the sidereal angle (or sidereal complement) and is denoted τ*.

The arc of the equator from the point of Spring to the meridian of the visible place of the luminary, counted in the direction of the Sun's own annual movement across the celestial sphere, is called right ascension α (in Fig. 5 it is given in hourly measure, and the sidereal angle - in degree measure). The coordinates of the navigation stars are shown in Table. 1; it is obvious that, knowing τ°, one can always find

and vice versa.

The arc of the celestial equator from the local meridian (its noon part P n ZEP s) to the meridian of the luminary is called the local hour angle; the luminaries are designated t. According to Fig. 4 it is clear that t always differs from t gr by the value of the longitude of the observer’s position:

in this case, the eastern longitude is added, and the western longitude is subtracted if t gr is taken in a circular calculation.

Due to the apparent daily movement of the luminaries, their hour angles are constantly changing. For this reason, the stellar angles do not change, since their origin (the Spring point) rotates along with the sky.

The local hour angle of the Spring point is called sidereal time; it is always measured towards the West from 0° to 360°. It can be determined by eye by the position in the sky of the meridian of the star Kaff (β Cassiopeia) relative to the local celestial meridian. According to Fig. 5 it is clear that it is always

Practice using your eye to determine the equatorial coordinates δ and t of the luminaries you observe in the sky. To do this, use Polyarnaya to determine the position of the North point on the horizon (Fig. 2 and 3), then find the South point. Calculate the complement of the latitude of your place Θ = 90° - φ (for example, in Odessa Θ = 44°, and in Leningrad Θ = 30°). The noon point of the equator E is located above the point South at an angular distance equal to Θ; it is always the origin of the hour angle. The equator in the sky passes through the point East, point E and point West.

It is useful to know that at δ N > 90° - φ N the luminary in the northern hemisphere of the Earth always moves above the horizon; at δ 90° - φ N it is not observed.

A mechanical model of the celestial sphere, reproducing the appearance of the starry sky and all the coordinates discussed above, is a star globe (Fig. 6). This navigation device is very useful in long voyages: with its help you can solve all problems of celestial navigation (with an angular error of the solution results of no more than 1.5-2° or with a time error of no more than 6-8 minutes. Before work, the globe is set in latitude observation locations (shown in Fig. 6) and according to local sidereal time t γ , the rules for calculating which for the observation period will be explained below.

If desired, a simplified star globe can be made from a school globe by marking the visible places of stars on its surface, guided by Table. I and a star chart. The accuracy of solving problems on such a globe will be somewhat lower, but sufficient for many cases of orientation in the direction of motion of the yacht. Note also that the star map gives a direct image of the constellations (as the observer sees them), and their inverse images are visible on the star globe.

Identification of navigation stars

Of the countless stars, only about 600 are easily visible to the naked eye, shown on the star chart in the Nautical Astronomical Yearbook. This map gives a general picture of what a navigator can generally observe in the dark night sky. To answer the question of where and how to look for certain navigation stars in a certain geographic area, use the seasonal star charts below (Fig. 1-4): they cover the starry sky for all seas of the country and are compiled on the basis of the MAE star map ; they indicate the position and proper names of all 40 navigational stars mentioned in the table in the previous essay.

Each scheme corresponds to evening observations at a certain time of the year: spring (Fig. 1), summer (Fig. 2), autumn (Fig. 3), and winter (Fig. 4) or morning observations in spring (Fig. 2), summer (Fig. 3), autumn (Fig. 4) and winter (Fig. 1). Each seasonal scheme can be used at other times of the year, but at a different time of day.

To select a seasonal scheme suitable for the intended time of observation, use the table. 1. You must enter this table according to the calendar date of observation closest to your intended one and the so-called “meridian” time of day T M.

Meridian time with a permissible error of no more than half an hour can simply be obtained by reducing winter time adopted in the USSR since 1981 by 1 hour, and summer time by 2 hours. The rules for calculating T sea conditions according to the ship's time accepted on board the yacht are explained in the example below. The two bottom rows of the table for each seasonal scheme indicate the corresponding sidereal time t M and the reading of the sidereal angle τ K on the scales of the MAE star map; These values ​​make it possible to determine which of the meridians of the star map at the intended time of observation coincides with the meridian of your geographical location.

When initially mastering the rules for identifying navigation stars, it is necessary to prepare for observations in advance; Both a star chart and a seasonal chart are used. We orient the star map on the ground; from the point of the south on the horizon along the sky towards the north pole of the world, the meridian of the equatorial star map will be located, which is digitized by the value t M, i.e. for our seasonal schemes - 12 H, 18 H, 0(24) H and 6 H. meridian and is shown as a dotted line on seasonal diagrams. The half-width of each circuit is approximately 90° = 6 H; therefore, after a few hours, due to the rotation of the starry sky to the west, the dotted meridian will shift to the left edge of the diagram, and its central constellations - to the right.

The equatorial map covers the starry sky between parallels 60° N and 60° S, but not all stars shown on it will necessarily be visible in your area. Above your head, near the zenith, you can see those constellations whose star declinations are close in magnitude to the latitude of the place (and “of the same name” with it). For example, at latitude φ = 60° N at t M = 12 H, the constellation Ursa Major is located above your head. Further, as already explained in the first essay, it can be argued that at φ = 60° N, stars located south of the parallel with declination δ = 30° S, etc. will never be visible.

For an observer in northern latitudes, the equatorial star map shows mainly those constellations that are observed in the southern half of the sky. To determine the visibility of constellations in the northern half of the sky, a north polar map is used, covering an area outlined from the north celestial pole with a radius of 60°. In other words, the north polar map overlaps the equatorial map in a wide zone between the parallels 30° N and 60° N. To orient the polar map on the ground, it is necessary to have its meridian, digitized found from the table. 1 of magnitude τ, place it above your head so that it coincides with the direction from the zenith to the north pole of the world.

The field of view of the human eye is approximately 120-150°, so if you look at Polaris, then all the constellations of the northern polar map will be in the field of view. Those northern constellations are always visible above the horizon, the stars of which have declinations δ > 90° - φ and " are of the same name" with latitude. For example, at a latitude φ = 45° N, non-setting are the stars with declinations greater than δ = 45° N, and at a latitude φ = 60° N - those stars with δ > 30° N., etc.

Let us remember that all the stars in the sky have the same size - they are visible as luminous points and differ only in the intensity of their brilliance and color tint. The size of the circles on the star map does not indicate the apparent size of the star in the sky, but the relative strength of its brightness - the magnitude. In addition, the image of the constellation is always somewhat distorted when the surface of the celestial sphere is expanded onto the map plane. For these reasons, the appearance of the constellation in the sky is somewhat different from its appearance on the map, but this does not create significant difficulties in identifying stars.

Learning to identify navigation stars is not difficult. For sailing during your vacation, it is enough to know the location of a dozen constellations and the navigation stars included in them from those listed in the table. 1 of the first essay. Two or three nights of pre-voyage training will give you confidence in navigating by the stars at sea.

Do not try to identify constellations by looking for figures of mythical heroes or animals on yourself that correspond to their tempting-sounding names. One can, of course, guess that the constellations of the northern animals - Ursa Major and Ursa Minor - should most often be looked for in the direction to the north, and the constellation of the southerner Scorpio - in the southern half of the sky. However, the actually observed appearance of the same northern “ursa” constellations is better conveyed by well-known verses:

Two bears laugh:
- Did these stars deceive you?
They are called by our name,
And they look like saucepans.

When identifying stars, it is more convenient to call the Big Dipper the Big Dipper, which is what we will do. Those wishing to know details about the constellations and their names are referred to the excellent “star primer” by G. Ray and the interesting book by Yu. A. Karpenko.

For a navigator, a practical guide to the starry sky can be diagrams - indicators of navigation stars (Fig. 1-4), showing the location of these stars relative to several reference constellations that are easily identified from star charts.

The main supporting constellation is Ursa Major, the bucket of which in our seas is always visible above the horizon (at a latitude of more than 40° N) and is easily identified even without a map. Let us remember the proper names of the stars of the Big Dipper (Fig. 1): α - Dubge, β - Merak, γ - Fekda, δ - Megrets, ε - Aliot, ζ - Mizar, η - Benetnash. You already know the seven navigation stars!

In the direction of the line Merak - Dubge and at a distance of about 30° is located, as we already know, Polar - the end of the handle of the Ursa Minor bucket, in the bottom of which Kokhab is visible.

On the line Megrets - Polar and at the same distance from Polar, the “maiden breast” of Cassiopeia and her stars Kaff and Shedar are visible.

In the direction Fekda - Megrets and at a distance of about 30° we will find the star Deneb, located in the tail of the constellation Cygnus - one of the few that at least to some extent corresponds in configuration to its name.

In the direction Fekda - Alioth, in an area approximately 60° away, the brightest northern star is visible - the blue beauty Vega (a Lyrae).

In the direction Mizar - Polar and at a distance of about 50°-60° from the pole is the constellation Andromeda - a chain of three stars: Alferraz, Mirakh, Alamak of equal brightness.

In the direction Mirakh - Alamak, Mirfak (α Perseus) is visible at the same distance.

In the direction Megrets - Dubge, at a distance of about 50°, the pentagonal bowl of Auriga and one of the brightest stars, Capella, are visible.

In this way we found almost all the navigation stars visible in the northern half of our sky. Using Fig. 1, it is worth practicing searching for navigation stars on star charts first. When training “on the ground”, keep the rice. 1 “upside down”, pointing with the * icon to point N.

Let's move on to considering the navigation stars in the southern half of the spring sky in the same fig. 1.

Perpendicular to the bottom of the Big Dipper at a distance of about 50° is the constellation Leo, in the front paw of which there is Regulus, and at the tip of the tail - Denebola. To some observers, this constellation does not resemble a lion, but an iron with a bent handle. In the direction of Leo's tail are the constellation Virgo and the star Spica. To the south of the constellation Leo, in a star-poor region near the equator, dim Alphard (and Hydra) will be visible.

On the line Megrets - Merak at a distance of about 50° you can see the constellation Gemini - two bright stars Castor and Pollux. On the same meridian with them and closer to the equator, bright Procyon (α Canis Minor) is visible.

Moving your gaze along the curve of the handle of the Big Dipper, at a distance of about 30° we will see the bright orange Arcturus (α Bootes - a constellation resembling a parachute above Arcturus). Next to this parachute, a small and dim bowl of the Northern Crown is visible, in which Alfacca stands out,

Continuing in the direction of the same bend of the handle of the Big Dipper, not far from the horizon we will find Antares - the bright reddish eye of the constellation Scorpio.

On a summer evening (Fig. 2), the “summer triangle” formed by the bright stars Vega, Deneb and Altair (α Orla) is clearly visible on the eastern side of the sky. The constellation Eagle in the form of a diamond is easily found in the direction of flight of Cygnus. Between Eagle and Bootes there is a dim star Ras-Alhage from the constellation Ophiuchus.

On autumn evenings in the south, the “Pegasus Square” is observed, formed by the star Alferraz, which we have already considered, and three stars from the constellation Pegasus: Markab, Sheat, Algenib. The Pegasus square (Fig. 3) is easily found on the Polar - Kaff line at a distance of about 50° from Cassiopeia. Regarding the Pegasus Square, it is easy to find the constellations Andromeda, Perseus and Auriga to the east, and the constellations of the “summer triangle” to the west.

To the south of the Pegasus Square, near the horizon, Difda (β Cetus) and Fomalhaut are visible - the “mouth of the Southern Fish”, which the Whale intends to swallow.

On the Markab - Algeinb line, at a distance of about 60°, bright Aldebaran (α Tauri) is visible in the characteristic “splashes” of small stars. Hamal (α Aries) is located between the constellations Pegasus and Taurus.

In the southern half of the winter sky, rich in bright stars (Fig. 4), it is easy to navigate relative to the most beautiful constellation Orion, which can be recognized without a map. The constellation Auriga is located midway between Orion and Polaris. The constellation Taurus is located on the continuation of the arc of Orion's belt (formed by the “three sisters” stars ζ, ε, δ Orion) at a distance of about 20°. On the southern continuation of the same arc, at a distance of about 15°, the brightest star, Sirius (α Canis Majoris), sparkles. In the γ - α direction of Orion, Portion is observed at a distance of 20°.

In the constellation Orion, the navigation stars are Betelgeuse and Rigel.

It should be borne in mind that the appearance of constellations can be distorted by planets appearing in them - “wandering stars”. The position of the planets in the starry sky in 1982 is indicated in the table below. 2 So, having studied this table, we will establish that, for example, in May Venus will not be visible in the evening, Mars and Saturn will distort the view of the constellation Virgo, and not far from them in the constellation Libra a very bright Jupiter will be visible (a rarely observed “parade of planets” ). Information about the visible places of the planets is given for each year in the MAE and the Astronomical Calendar of the Nauka publishing house. They must be plotted on a star map in preparation for the trip, using the right ascensions and declinations of the planets indicated in these manuals for the date of observation.

The provided seasonal diagrams - indicators of navigation stars (Fig. 1-4) are most convenient for working at twilight, when the horizon and only the brightest stars are clearly visible. Constellation configurations depicted on star charts can only be detected after complete darkness.

The search for navigation stars must be meaningful; one must learn to perceive the appearance of the constellation as a whole - as an image, a picture. A person quickly and easily recognizes what he expects to see. That is why, when preparing for a voyage, it is necessary to study a star map in the same way as a tourist studies a route for a walk through an unfamiliar city using a map.

When going out to observe, take with you a star chart and an indicator of navigation stars, as well as a flashlight (it is better to cover its glass with red nail polish). A compass will be useful, but you can do without it by determining the direction to the North along the Polyarnaya. Think of something that will serve as a “scale bar” for estimating angular distances in the sky. The angle at which an object held in an outstretched hand and perpendicular to it is visible contains as many degrees as the number of centimeters in height of this object. In the sky, the distance between the stars Dubge and Megrets is 10°, between the stars Dubge and Benetnash - 25°, between the outermost stars Cassiopeia - 15°, the eastern side of Pegasus Square - 15°, between Rigel and Betelgeuse - about 20°.

Having reached the area at the appointed time, orient yourself in the directions of North, East, South and West. Find and identify the constellation passing above your head - through the zenith or near it. Make a reference to the area of ​​the seasonal scheme and the equatorial map - at point S and the direction of the local celestial meridian perpendicular to the horizon line at point S; tie the north polar map to the area - along the ZP line. Find a reference constellation - Ursa Major (Pegasus Square or Orion) and practice identifying navigation stars. In this case, one must remember about distortions in the visually observed heights of luminaries due to the oblateness of the sky, about distortions in the color of stars at low altitudes, about the apparent increase in the size of constellations near the horizon and decrease as they approach the zenith, about changes in the position of constellation figures during the night relative to the visible horizon from -for the rotation of the sky.

A. Calculation of meridian time

B. An example of calculating meridian time and choosing a seasonal star chart

On May 8, 1982, in the Baltic Sea (latitude φ = 59.5° N; longitude λ = 24.8° O st, observations of the starry sky were planned at the moment T S = 00 H 30 M standard (Moscow summer) time. Select and orientate the star chart and navigation star index.

On the shore, one can approximately take T M equal to summer, reduced by 2 hours. In our example:

In all cases when the standard observation time T C is less than No. C, before performing the subtraction, T C must be increased by 24 hours; in this case, the world date will be less than the local date by one. If it turns out that after performing the addition, T gr turns out to be more than 24 hours, you need to discard the 24 hours and increase the date of the result by one. The same rule applies when calculating T M from G gr and λ.

Selection of seasonal scheme and its orientation

Local date May 7 and moment T M = 22 H 09 M according to table. 1 most closely corresponds to the seasonal scheme in Fig. 1. But this scheme was built for T M = 21 H on May 7, and we will conduct observations 1 H 09 M later (in degree measure 69 M: 4 M = 17°). Therefore, the local meridian (line S - P N) will be located to the left of the central meridian of the diagram by 17° (if we had observed earlier, not later, the local meridian would have shifted to the right).

In our example, the constellation Virgo will pass through the local meridian above the point of the South and the constellation Ursa Major near the zenith, and Cassiopeia will be located above the point of North (see star chart for tγ = 13 H 09 M and τ K = 163°).

To identify navigation stars, orientation relative to the Big Dipper will be used (Fig. 1).

Notes

1. The weak constellations Pisces and Cancer are not shown on the map.

2. The titles of these books. G. Ray. Stars. M., “Mir”, 1969. (168 pp.); Yu. A, Karpenko, Names of the starry sky, M., “Science”, 1981 (183 pp.).