Exercise:
Show that, for any object on
the ecliptic,
tan(δ) = sin(α)
tan(ε),
where (α, δ)
are the object's Right Ascension and declination,
and ε
is the obliquity of the ecliptic.
Use the cosine rule again:
cos
KX = cos PX cos KP + sin PX sin KP cos P
On the ecliptic, latitude β
= 0
So we have
cos 90° = cos(90°-δ) cos(ε)
+ sin(90°-δ) sin(ε) cos(90°+α)
i.e. 0 = sin(δ) cos(ε) - cos(δ) sin(ε)
sin(α)
Divide throughout by cos(δ) cos(ε) to get
tan(δ) = tan(ε) sin(α)
Back to "ecliptic coordinates".