How Do Equatorial and Galactic Coordinates Transform in Astronomy?

[eman2009]

using the astronomical triangle of a source in equatorial and galactic coordinates ,prove that the transformations is true
1) cos b cos(L-33 deg)=cos delta cos(alfa-282.25 deg)

2) sin delta=cos b sin (L-33 deg) sin 62.6 deg +sin b cos 62.6 deg

L,b galactic coordinates
alfa,delta equatorial coordinates .

Homework Equations

L node =123-90=33 deg
alfa node=12 h 49.0m+6h=18h 49.0m=282.25 deg

The Attempt at a Solution

using equatorial equations and cos and sin laws to determine the provment

 

[NateD]

of the above two equations:1)cosbcos(L-33 deg)=cosδcos(α-282.25 deg)= cos b (cosLcos33deg+sinLsin33deg) = cos b (cosLcos33deg+sinLsin33deg) = cos δ (cosαcos282.25deg+sinαsin282.25deg)2) sinδ= cosb sin(L-33 deg)sin62.6deg+sinbcos62.6deg= (cosLsin33deg-sinLcos33deg)sinbcos62.6deg + sinbcos62.6deg= sinb (cosLsin33deg-sinLcos33deg)cos62.6deg + sinbcos62.6deg=sinb (cosLsin33degcos62.6deg-sinLcos33degcos62.6deg + sinbcos62.6deg)=sinb (sin(L-33deg)cos62.6deg + cos(L-33deg)sin62.6deg)=sinb sin(L-33deg+62.6deg) Thus, the transformations given in the question are true.