The equatorial cooedinates of a star are ( α , δ) = (171° 23' ,79°46'). ta ke the obliquity of the ecli

Question

The equatorial coordinates of a star are ( α , δ) = (171° 23' ,79°46'). Take the obliquity of the ecliptic ε = 23° 27' and calculate the ecliptic coordinates ( λ , β) of the star.

Answer 1

We'll take the first point of areas (spring equinox) that is reference for equatorial system as the reference for ecliptic system too.

My favourite equation is

tan δ = tan (theta)  sin α

where (theta) = angle to star from equator (ref.)  

= 23° 27' (=ε) + eta

where (eta) = angle (as above), but with Ecliptic as reference.

(eta) = 88° 27' 2.43"- 23° 27' =65° 0' 2.43"

If

(gama) = Arc distance to the star from spring equinox,

sin (gama) = sinδ / sin (theta) = sin β / sin (eta)

(gama) =79° 53' 0.22"

β = 63° 9' 13.56"

since (like the first equation above),

tan β = tan(eta) sin λ

λ = 112° 53' 22.6"