Given two celestial coordinates....?

Question

Given two celestial coordinates....?

Answer 1

There is a missing word in your question... "in the sky" might be what you mean. A given azimuth coordinate leaves you with a line from directly overhead to a point on the horizon at that azimuth angle from north (northeast would be azimuth 45 degrees, east would be 90 degrees, etc.), but you have a wide range of altitudes (or elevation angles) along that line. So... you need two coordinates. Altitude or elevation angle alone gives you a circle all the way around you just like the horizon, only higher in the sky. Then you need azimuth to know which direction to look at that altitude. Think that you need latitude and longitude, range and azimuth, "X" and "Y" coordinates....

Answer 2

Use trigonometry to find how far apart they. That means understanding what sines and cosines are and how to use them.

Answer 3

Lookup "Spherical Trigonometry".

Answer 4

Let

α = right ascension

δ = declination



Suppose one object is at coordinates (α1,δ1) and the other is at (α2,δ2). The angle D between the two is given by



cos D = sin δ1 sin δ2 + cos δ1 cos δ2 cos (α1 - α2)



You find D by taking the arc-cosine of the right side, and D will be between 0 and 180 degrees. (Of course, if D=10 degrees, another solution is D=350 degrees. These are the short and long paths along the great circle that passes through the two points.)



This formula can be derived easily by forming a triangle consisting of the two objects and the north celestial pole, and applying the rules of spherical trigonometry (specifically, the law of cosines for three sides and an angle).

http://en.wikipedia.org/wiki/Spherical_law_of_cosines



Instead of using the above formula, you might use this online calculator:

http://celestialwonders.com/tools/starAngleCalc.html