The mobile celestial map (MCM) is used to determine the pattern of the star sky in any day and at any time relative the given observation place. MCM consists of two parts: actually a celestial map and a movable circle on it. The map is the projection of the celestial sphere on the plane. On the map the characteristic figures of bright constellations, their borders and a grid of celestial equatorial coordinates are drawn. At the map center where the projections of celestial meridians drawn in the form of radial lines intersect there is the celestial North Pole. The magnitudes of a right ascension in hours are put down along the internal circle of the map in clockwise direction with one hour interval. Concentric circles represent celestial parallels. The degrees on these parallels are their declinations put down with 30 ° interval along the celestial meridian passing through vernal and autumnal equinoxes (a straight line 0 -12h on the map). These quantities help to determine approximately the equatorial coordinates of celestial bodies. Inside of the celestial equator (declination is 0°) there is the northern celestial hemisphere. Outside of it there is a part of the southern celestial hemisphere with declination up to -45°.
Ecliptic is an eccentric oval. The points of intersection of the ecliptic and the celestial equator have the following coordinates: d = 0o, a = 0h – the vernal equinox and d = 0o, a = 12h – the autumnal equinox. The summer solstice occurs in the Northern hemisphere of the sky at the point of intersection of the ecliptic and the celestial meridian of 6h and the winter solstice occurs in the Southern hemisphere of the sky at the point of intersection of the ecliptic and the celestial meridian of 18h.
On the very brink of the celestial map there is a limb of date with the names of months of year and their calendar days. These dates specify the position of the Sun on an ecliptic.
On a movable circle there are several ovals with degrees corresponding to geographic latitude of observer location. If to cut out an opening along the oval corresponding to geographic latitude of observer location then the border of an oval will represent the celestial horizon of the place where the observation is made. On the horizon line four points of the celestial horizon are noted. If to connect the North and the South by a thread then it will show the celestial meridian. The middle of this thread determines approximately zenith. Its exact position corresponds to the point of intersection of the thread and the celestial parallel with declination equal to geographic latitude of observer location. For example, for Almaty j = 43.25 ° then the position of the observer zenith corresponds to the intersection of the thread and the circle with declination d = 43.25°.
On the brink of the celestial map circle there are 24 divisions each corresponding to one hour, each hour is divided into 6 intervals with 10 minutes for each interval. This is a local average solar time (the local time is given in § 43).
The MCM helps to solve various astronomical problems, such as the determination of the time and dates of rise and set; the upper and lower culminations (i.e. the highest or the lowest position above the horizon) of stars in different days of year at a certain observation place.
For example, to determine what constellations are visible in the sky at a certain time of a definite date, it is necessary to place the required time on the hour limb of the movable circle against the date on the celestial map. Then in the opening of the movable circle there will be stars which can be seen in the sky at the appointed time. The stars that are located on a thread are at their culmination: between the celestial North Pole and the South of the horizon are at their upper culmination and between the celestial North Pole and the North of the horizon are at their lower culmination. The rising stars are on the east side of the horizon and the setting stars are on the west side of the horizon.
Example. In the Kazakh national astronomy there are «Star rules» in which regularities or peculiarities of rising and setting of some stars and constellations are formulated. Here one of them: «The Pleiades, the Belt of Orion and the Sirius ascend within three months and descend during one month».
Let us verify this rule using the MCM and find out when the rise and set of stars occur. This rule regulates the last evening set and the first morning rise of these stars called heliacal. The set and rise of stars also depend on the latitude of the region where the observations are made. Let's say that we are at the latitude of 45°, and respectively the oval opening on the circle is cut out along the line with this number.
We put the movable circle on the celestial map and rotate it until the above mentioned stars appear at the western horizon, i.e. at the brink of the oval opening of the movable circle.
The readings on the hour circle and on the limb of dates show that evening set of the three above mentioned stars occurs approximately on May 5-15 at 20 o’clock of the local time in the following order: the Pleiades, the Belt of Orion and the Sirius.
Rotating the movable circle in the clockwise direction, we determine that the Pleiades is first constellation that rises. It occurs approximately on June 23 at 2 o’clock of the local time. In the same way we find that the Belt of Orion rises approximately on July 27 at 3 h 25 min., Sirius rises approximately on August 20 at 3 h 54 min.
1. Where is on the map the Polaris (North Pole) located?
2. What system of celestial coordinates is used on the map?
3. What are the equatorial coordinates of the points of intersection of the celestial equator and the ecliptic?
4. Why the Earth, the Sun, the Moon and other planets are not noted on the celestial map?
5. How to find the location of the celestial meridian on the celestial map?
6. How to determine the position of a zenith for a given region on the map?
1. Find on the celestial map the stars by their coordinates given in tab. 9.
2. Using the celestial map determine the equatorial coordinates of the following stars: a) a Orion; b) a Lira. Compare the received results with the coordinates of these stars given in tab. 9.
3. Using the MCM determine which of following constellations are circumpolar in your location : a) Great Bear; b) Lira; c) Cephei; d) Aquila (Eagle); e) Cygnus (Swan); e) Cassiopeia; g) Auriga (Charioteer).
4. Check the above-mentioned star rule for latitude j = 55°. Compare the results with those received for latitude j = 45°.
5. Using the MCM determine the equatorial coordinates of the Sun on days of equinoxes and a solstices, sunrise and sunset times on these days.