How can I calculate the degrees between the Moon and Sun with these values?

Question

I need to calculate the degrees on the celestial sphere between the Moon and the Sun, but all I have are these values:

Moon:
RA/DE 14h16m / -19*19'
Az/Alt +243*25' / +0*57'

Sun:
RA/DE 13h11m / -7*32'
Az/Alt +262*43' / -3*4'

I know this is probably a bizarre question. I know you can estimate the degrees in the sky using a "finger and fist" method, but the trick is I'm trying to calculate it for a date in the past. I'm not sure if all of these values are relevant, it is just what I have. Is there any way to do it?

Answer 1

Hi. I would use the az/alt values since they are already in degrees. If you want great accuracy I think you need to use spherical trig (not my favorite subject!). For an approximate answer subtract the Sun's az coordinates from the Moon's. Do the same with the alt. fudge them together. Remember that each body is about 30 or so minutes of arc in diameter. (The limbs will be closer by a degree then the centers.)