Parallactic triangle (navigation triangle, PZX-triangle) - in astronavigation, a spherical triangle on the celestial sphere whose vertices are the pole (P), zenith (Z), and any selected star (X). In other words, the parallactic triangle is formed by the mutual intersection of the celestial meridian , the circle of height and the circle of declination .
The sides of the triangle are arcs PZ = 90 Β° - Ο, ZR = z and PR = 90 Β° - Ξ΄, where Ο is the latitude of the observer, z is the zenith distance of the star, and Ξ΄ is its declination .
The angles of the triangle are in turn: at the apex Z = 180 Β° - A, where A is the azimuth , at the apex P = t, that is, the hour angle is equal and the third angle, with the star R, is denoted q and is called the parallactic angle [1] .
The configuration of the parallactic triangle depends on the latitude at which the observer is located, and on time.
Content
Application
The solution of the parallactic triangle makes it possible to determine the coordinates of the place of observation, as well as to calculate the moments of time of sunrise and sunset of the stars in relation to the place of observation, the azimuths of the stars at sunrise and sunset, to determine the local stellar time.
Astronomical Triangles
Particular cases of parallactic triangles are astronomical triangles, used to transition between different spherical coordinate systems used in astronomy using the formulas of spherical trigonometry.
The first astronomical triangle is used to translate coordinates from the first equatorial system to horizontal and vice versa.
The second astronomical triangle is used to translate coordinates from the second equatorial system to the ecliptic and vice versa.
The third astronomical triangle is used to translate coordinates from the second equatorial system to the galactic and vice versa.
|
Notes
- β Popov P.I., Baev K.L., Vorontsov-Veliaminov B.A., Kunitsky R.V. Β§19 Parallactic triangle. Transformation of coordinates. // Astronomy. - the fourth. - M: Uchpedgiz, 1958. - S. 57 - 60. - 462 p.
Links
- V.E. Zharov. 3.5. Transformation of coordinates from one system to another // Spherical astronomy .
- dic.academic.ru // TSB: Parallactic Triangle
- Parallactic Triangle - article from the Great Soviet Encyclopedia .
- www.bibliotekar.ru // Parallactic triangle and coordinate transformation.