Formula

[Demonperformer]

Hope this is the right bit of the forum ...

Can anyone tell me, or point me in the right direction of, the formula to calculate the angular distance between two points expressed in RA & Dec (as per astronomical objects). I know CdC will do the calc if it is between two positions containing current objects, but I can't find a way of finding it for two 'random' points (eg distance travelled by a solar system object between two dates).

Thanks

[George Jones]

I'll have a go at it. I did something similar here,

Coverting decimal degrees to statute miles - sci.physics | Google Groups.

I'll try and rework it for the celestial sphere.

[George Jones]

Try the formula below. It seems to work for the pointer stars in the Big Dipper, but I have not checked it for any other cases, so there could be problems in some octants (or other problems).

Here d = declination, R = right ascension, and A and B are the two locations. d and R need to be converted to decimal angular form, and some calculation methods might require degrees , while others might use radians.

If you have questions, just fire away.

[Demonperformer]

George

Many many thanks, and ... gulp ... I am going to have to work through that equation very carefully.

[George Jones]

I've somewhat lost my drive right now, but maybe tomorrow or the weekend, I'll post the example of the pointer stars, working through all the details.

[George Jones]

Pointer Stars Example

Position A:

d_A = declination = 56 degrees 22m 57s = 56 + 22/60 + 57/3600 = 56.38 degrees

R_A = right ascension = 11h 1m 50s = (11 + 1/60 + 50/3600)*360/24 = 165.46 degrees

Position B:

d_B = declination = 61 degrees 45m 3s = 56 + 45/60 + 3/3600 = 61.75 degrees

R_B = right ascension = 11h 3m 44s = (11 + 3/60 + 44/3600)*360/24 = 165.93 degrees

Then,

cos(56.38)*cos(165.46)*cos(61.75)*cos(165.93) + cos(56.38)*sin(165.46)*cos(61.75)*sin(165.93) + sin(56.38)*sin(61.75) = 0.99560

and

cos^-1(0.99560) = 5.38 degrees.

Again, there could be lots of mistakes, so this formula should be checked using other known separations.

[George Jones]

Demonperformer, do you use/have access to Excel spreadsheet software? I have attached a file that calculates the angle between any two locations on the celestial sphere. When declination and right ascension (in standard format) are entered, the angle, in degrees, between the locations is calculated. The locations pre-entered in the file are for Regulus and Denebola (a test).

Do not enter anything for angle, as this would wipe out the formula used.

Unfortunately, Excel files cannot be attached to posts, so I had to attach a zipped folder from which the file has to be extracted.

Celestial Angle.zip

[TheThing]

George, would it be impolite to ask what you do for a living? You're formula seems exquisite! I like to think I'm lukewarm on maths, but this has left me standing!

[George Jones]

I'm a theoretical physicist who teaches physics (for at least and probably only one more year) to engineering students.

[Demonperformer]

George, you are an absolute *** STAR ***

An excel spreadsheet was where I was heading and you have prepared one for me.

Thank you so much