# Equatian of the Ecliptic

BlogAdvanced AstrologyMathematics of the Celestial SphereSpherical Geometry

March 15, 2023, 1:29 p.m. Mark Rusborn 1 min. to read

In the previous article about ecliptic-equator coordinate conversion, we derived the equation for converting ecliptical coordinates to equatorial ones.

Any elliptical point, by definition, has celestial latitude $\delta$ equals zero. It means from (1) that

$$\begin{cases} \tan RA = \cos\epsilon\tan\lambda \\ \sin D = \sin\epsilon\sin\lambda\tag{1} \end{cases}$$

Here

We can rewrite (1) to rid off from $\lambda$ and express $RA$ as a function of $D$ for any elliptic point:

$$\sin RA = \frac{\tan D}{\tan\epsilon}\tag{2}$$

P.S. We can get the same equation (2) by observing a right spherical triangle with sides $RA$, $D$, and angle $\epsilon$ between the ecliptic and the equatorial plane and applying eq (3)

Mark Rusborn

I am a former Soviet physicist, now a professional astrologer. I have been lucky to get familiar with eminent scientists, including the Nobel laureate in physics. It helped me a lot in the proper structuring of thinking.