Position Of Sun on Celestial Sphere at Input Universal Time

July 11, 2015

by R C Chakraborty, July 11, 2015, Pages 57 – 67.

(This is Sec. 3, pp 57 – 67, of Orbital Mechanics – Model & Simulation Software (OM-MSS), Sec 1 to 10, pp 1 – 402.)

Sun is a star at the center of our Solar System. Although stars are fixed relative to each other, but Sun moves relative to stars.

Sun follows a circular path on the celestial sphere, once a year. This path is known as the ‘Ecliptic’, representing the plane of the Earth’s orbit.

The Inclination of the Earth’s equator to the Ecliptic (or earth’s rotation axis to a perpendicular on ecliptic) is called Obliquity of the ecliptic.

The Obliquity of the ecliptic is currently 23.4392794383 deg with respect to the celestial equator, at standard epoch J2000 .

The position of any point on the Celestial Sphere is given with reference to the equator or the ecliptic.

The Earth moves in an elliptical orbit around the Sun. Therefore the distance from Earth to Sun is not same at all points on the orbit.

(a) Find Julian day of interest corresponding to the input Universal Time;

(b) Find Corresponding Ecliptic coordinates : Mean anomaly of the Sun, Mean longitude of the Sun, Ecliptic longitude of the Sun,

Ecliptic latitude of the Sun is always nearly zero, Distance of the Sun from the Earth in astronomical units, Obliquity of the ecliptic

In addition to these Ecliptic and Equatorial coordinates, computed many other parameters related to Sun’s Position on Celestial Sphere.

The Position of Sun on Celestial Sphere is represented by computing following parameters :

1. Semi-major axis (SMA), 2. Mean movement per day (n sun), 3. Mean distance (As),

4. Mean anomaly (m sun), 5. True anomaly (T sun), 6. Eccentric anomaly (E sun),

7. Right ascension (Alpha), 8. Declination (Delta), 9. Mean longitude (Lmean),

10. Ecliptic longitude (Lsun), 11. Nodal elongation (U sun), 12. Argument of perigee (W sun),

14. Obliquity of ecliptic (Epcylone), 14. Mean dist (d_sun), 15. Radial distance (Rs).