The horizontal coordinate system [1] , or the horizontal coordinate system [2] is a celestial coordinate system in which the main plane is the plane of the mathematical horizon , and the poles are the zenith and nadir . It is used when observing the stars and the movement of the celestial bodies of the solar system on the ground with the naked eye, through binoculars or a telescope with an azimuthal setup [1] . The horizontal coordinates of not only the planets and the Sun, but also of the stars are continuously changing during the day due to the daily rotation of the celestial sphere .
Content
Description
Lines and planes
The horizontal coordinate system is always topocentric. The observer is always at a fixed point on the surface of the earth (marked with the letter O in the figure). We will assume that the observer is in the Northern hemisphere of the Earth at latitude φ. Using a plumb line , the direction to the zenith (Z) is determined as the upper point to which the plumb line is directed, and the nadir (Z ') - as the lower point (underground) [1] . Therefore, the line (ZZ ') connecting the zenith and nadir is called a sheer line [3] .
The plane perpendicular to the plumb line at point O is called the plane of the mathematical horizon . On this plane, the direction to the south (geographical, not magnetic!) And north is determined, for example, in the direction of the shortest shadow from the gnomon in a day. It will be the shortest at true noon , and the line (NS) connecting the south with the north is called the midday line [1] . The points of east (E) and west (W) are taken 90 degrees apart from the south point, respectively, counterclockwise and clockwise, as viewed from the zenith. Thus, NESW is the plane of the mathematical horizon.
The plane passing through the midday and plumb lines (ZNZ'S) is called the plane of the celestial meridian , and the plane passing through the celestial body is called the vertical plane of the given celestial body. The large circle along which it crosses the celestial sphere is called the vertical of the celestial body [1] .
Coordinates
In the horizontal coordinate system, one coordinate is either the height of the star h or its zenith distance z . The other coordinate is the azimuth of A.
The height h of the star is called the arc of the vertical of the star from the plane of the mathematical horizon to the direction to the star. Heights are counted in the range from 0 ° to + 90 ° to the zenith and from 0 ° to −90 ° to the nadir [1] .
The zenith distance z of the star is called the arc of the vertical of the star from the zenith to the star. Anti-aircraft distances are measured from 0 ° to 180 ° from zenith to nadir.
The azimuth of the star is called the arc of the mathematical horizon from the point of the south to the vertical of the body. Azimuths are measured in the direction of the daily rotation of the celestial sphere, that is, to the west of the south, in the range from 0 ° to 360 ° [1] . Sometimes azimuths are measured from 0 ° to + 180 ° to the west and from 0 ° to −180 ° to the east. (In geodesy, azimuths are measured from the north point [4] .)
Features of changing the coordinates of celestial bodies
For a day, a star (and also, to a first approximation, the body of the solar system) describes a circle perpendicular to the axis of the world (PP '), which at a latitude φ is inclined to the mathematical horizon by an angle φ. Therefore, it will move parallel to the mathematical horizon only at φ equal to 90 degrees, that is, at the North Pole . Therefore, all the stars visible there will be non-descending (including the Sun for six months, see longitude of the day ) and their height h will be constant. At other latitudes, stars available for observation at a given time of the year are divided into
- entering and ascending [3] (h during the day passes through 0)
- non-stopping [3] (h is always greater than 0)
- non-ascending [3] (h is always less than 0)
The maximum height h of the star will be observed once a day at one of its two passage through the celestial meridian - the upper climax, and the minimum - at the second of them - the lower climax. From the lower to the upper culmination, the height h of the star increases, from the upper to the lower it decreases.
Transition to the first equatorial
In addition to the NESW horizon plane, the plumb line ZZ 'and the world axis PP', we draw a celestial equator perpendicular to PP 'at point O. Denote the t-hour angle of the star, δ - its declination, R - the star itself, z - its zenith distance . Then the spherical triangle PZR, called the first astronomical triangle [1] , or the parallactic triangle [2] will connect the horizontal and first equatorial coordinates. The transition formulas from the horizontal coordinate system to the first equatorial coordinate system are as follows [5] :
The sequence of applying the formulas of spherical trigonometry to the spherical triangle PZR is the same as when deriving similar formulas for the ecliptic coordinate system : the cosine theorem, the sine theorem and the five-element formula [2] . By the cosine theorem, we have:
The first formula is obtained. Now we apply the sine theorem to the same spherical triangle:
The second formula is obtained. Now apply the formula of five elements to our spherical triangle:
The third formula is obtained. So, all three formulas are obtained from the consideration of one spherical triangle.
Transition from the first equatorial
The transition formulas from the first equatorial coordinate system to the horizontal coordinate system are derived when considering the same spherical triangle, applying the same spherical trigonometry formulas to it as in the reverse transition [2] . They have the following form [5] :
Notes
- ↑ 1 2 3 4 5 6 7 8 Tsesevich V.P. What and how to observe in the sky. - 6th ed. - M .: Nauka , 1984. - 304 p.
- ↑ 1 2 3 4 Belova N.A. The course of spherical astronomy. - M .: Nedra , 1971. - 183 p.
- ↑ 1 2 3 4 Vorontsov-Velyaminov B.A. Astronomy: Textbook. for 10 cl. wednesday school - 17th ed. - M .: Education , 1987 .-- 159 p.
- ↑ N. Aleksandrovich “Horizontal coordinate system” Archived copy of March 20, 2012 on Wayback Machine
- ↑ 1 2 Balk M. B., Demin V. G., Kunitsyn A. L. A collection of problems in celestial mechanics and cosodynamics. - M .: Nauka , 1972.- 336 p.
See also
- Sky coordinate system
- Spherical coordinate system