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
- $RA, D$ are the right ascension and declination of the ecliptic point with celestial latitude $\lambda$,
- $\epsilon$ is the inclination of the ecliptic.
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)
