The spherical triangle formed by arcs of observer's meridian, vertical circle as well as hour circle through the same celestial body is known as an astronomical triangle. The vertices of an astronomical triangle are Zenith point (Z), celestial pole (P) and the celestial body (S) and thus termed as ZPS triangle (Figure 25.4a). In each astronomical triangle, there are six important elements. Three of them are the three sides and other three are the three angles of the triangle. It is important to know these elements as some of these will be required to be observed in the field and others are to be computed to find the position / direction of celestial body.
Polar distance (PS or p): The angular distance from the celestial pole (P) to the celestial body (S) along the hour circle is known as polar distance. It is also known as co-declination and is designated by p (= 90°- d), where d is the declination of the celestial body, S.
Zenith distance (ZS or z) : The angular distance from observer's zenith (Z) to the celestial body (S) along the vertical circle is known as zenith distance. It is also known as co-altitude and is designated by z (= 90°- h), where h is the altitude of the celestial body, S.
Co-latitude, ZP : The angular distance from observer's zenith (Z) to the celestial pole (P) along the observer's meridian is known as co-latitude and is given by (90°- f), where f is the latitude of the observer.
Angle Z : The angle at the zenith (A) is measured from the observer's meridian to the vertical circle passing through the celestial body in a plane parallel to the observer's horizon. It is nothing but the azimuth of the celestial body (Figure 25.2). It is measured clockwise from the observer's meridian and its value ranges from zero to 360°.
Angle P : The angle at the pole (P) is measured from the observer's meridian to the hour circle passing through the celestial body in a plane parallel to the equatorial plane. It is nothing but (360°– H, hour angle of the celestial body) (Figure 25.4b). Hour angle is measured clockwise from the upper branch of the observer's meridian.
Angle S : angle at a celestial body between the hour circle and the vertical circle passing through the celestial body. It is known as the parallactic angle.
If any of the three elements are known, the remaining three can be computed from formulae of spherical trigonometry (Appendix- 25A).