Calculating the distance between stars

[KennyR]

That's what I wanna do. I know a star's location in the sky by its altitude and azimuth at any point in time, and I can look up the distance from our Sun to them in the same way.

But what I want to do is compare two stars and calculate the distance between them, non-relative to Earth. I've tried using everything I know about maths, which is a lot, but apparently not enough. Google isn't helping either; the internet has a few formulae, but the only ones I could find measure the distance in radians of arc, which are only useful relative to Earth. I want the distance in parsecs or light years. If I could convert radians of arc to light years I'd be happy, but I can't.

Sperical trigonometry isn't one of the things I had to learn as a chemist (phew), so has any mathematician or astronomer or astrophysisist out there got an easy formula or method?

[KennyR]

Thanks for your replies. It seems to me that working out the cartesian coords first and then doing pythagoras on them, like Cymric said, would be the best way to do it. At least, it would be the most accurate way. I'm not convinced that 2D math is any good on a sphere.

But...! Why don't we all test our theories? Blobrana gave us two stars, with coordinates:

Betelgeuse RA: 5h55m00.00s DE:+07°00'00.0"

RIGEL RA: 5h10m00.00s DE:-08°00'00.0"

Betelgeuse is 650 ly from Earth, Rigel is 1400 ly. Now, what is the distance between them?

[KennyR]

Blob, the answer to that equation you printed is:

1180723.5909957732

Thats way, way off what I got. :-o

[KennyR]

I did it with cartesians, and I got:

798.949 light years.

[KennyR]

@Karlos

I just put it in c:ev as-is (replacing ² for ^2 of course). It's usually good at precedences. Not this time though.

Ok, so Blobrana was very close with the 2D trick. Seems her maths works too.

[KennyR]

Blobrana wrote:
Where on earth did you get those figures?

An advanced scientific method. First I put the text "betelguese distance" into google and took the first distance that appeared. In this case it was

Betelguese > Earth
Betelgeuse is ~1400 light years from Earth, Betelgeuse. BV Color. Common Names.
Constellation. Coordinates. Distance from Earth. Harvard Revised Number. ...

And for Rigel, more of the same.

Try it yourself. =)