Answer to Question #201541 in Astronomy | Astrophysics for VYAS

Question

Problem A.1: Equatorial Coordinate System (4 Points) Astronomers need to identify the position of objects in the sky with very high precision. For that, it is essential to have coordinate systems that specify the position of an object at a given time. One of them is the equatorial coordinate system that is widely used in astronomy. (a) Explain how the equatorial coordinate system works. (b) What is the meaning of J2000 that oen occurs together with equatorial coordinates? The object NGC 4440 is a galaxy located in the Virgo Cluster at the following equatorial coordinates (J2000): 12h 27m 53.6s (right ascension), 12◦ 170 3600 (declination). The Calar Alto Observatory is located in Spain at the geographical coordinates 37.23◦N and 2.55◦W. (c) Is the NGC 4440 galaxy observable from the Calar Alto Observatory?

Answer 1

(a) the equatorial coordinates consist of right ascension $\alpha$ and declination $\delta$ . The declination is the angular distance of an object perpendicular to the celestial equator, right ascension is the angular distance of an object eastward along the celestial equator from the vernal equinox to the hour circle passing through the object. For the small time intervals such as a day we may say these coordinates are constant for the particular star (or for another sufficiently distant object).

(b) J2000 means the epoch for which the coordinates are written. J2000 epoch corresponds to January 1.5, 2000 of terrestrial time. Due to the proper motions and the precession the coordinates of objects are slightly changing over time, so if we want to use coordinates of J2000, we should calculate the bias of the system to date.

(c) Let us determine the maximum height of the NGC 4440 when being observed from the Calar Alto Observatory. The maximum height is

$h = 90^\circ - \varphi + \delta = 90^\circ - 37.32^\circ + 12^\circ17'36'' = 64.76^\circ >0,$ therefore the galaxy may be observed on a sufficiently large height.