Jump to content

sgl_imaging_challenge_banner_31.thumb.jpg.b7a41d6a0fa4e315f57ea3e240acf140.jpg

Converting from cartesian to RA/Dec


Recommended Posts

Hi everyone,

I have the position of a satellite in topocentric cartesian coordinates (i.e. the position of the satellite is given in [x,y,z] coordinates with the Earth-bound observer at the origin) and I want to convert this to and RA and Dec position as seen by the observer. I have seen formulae on this site:

http://www.castor2.ca/04_Propagation...uat/index.html

...and the one for declination works fine, but the RA formula sometimes gives me a number larger than 360 (I'm working in degrees rather than hours) and even when I subtract 360 it isn't correct. This seems to happen about half the time, and I can't find any alternative formulae! Can anyone help?

Thanks!

Link to post
Share on other sites

http://www.stargazing.net/kepler/rectang.html has some (what appear to be) simple formulae. They are written the other way round, but presumably you can find dec from the angle whose sin is Z, and then plug that angle into one (or both) of the X/Y equations to find the sin or cos of RA and from that the actual RA angle.

My math is not great, I may be being too simplistic, but it seems logical to me.

HTH

Link to post
Share on other sites

Can you give an example of a set of co-ordinates that don't give you the right answer? (And your working might be helpful, too.)

James

Link to post
Share on other sites

Stellarium shows a number of satellites, does this not have the one you are interested in? You can download an update for Stellarium satellites or you could put the TLE for the satellite into the Stellarium library and then it would show it as seen from your position.

Nigel

Link to post
Share on other sites

Hi everyone,

I have the position of a satellite in topocentric cartesian coordinates (i.e. the position of the satellite is given in [x,y,z] coordinates with the Earth-bound observer at the origin) and I want to convert this to and RA and Dec position as seen by the observer. I have seen formulae on this site:

http://www.castor2.c....uat/index.html

...and the one for declination works fine, but the RA formula sometimes gives me a number larger than 360 (I'm working in degrees rather than hours) and even when I subtract 360 it isn't correct. This seems to happen about half the time, and I can't find any alternative formulae! Can anyone help?

Thanks!

I have never looked at the conversion from topocentric cartesian coordinates to RA and declination, but, based on

1) the assumption that the coordinate transformation in question is a standard cartesian to polar angle transformation

2) the properties of the inverse tangent function,

I think that there is mistake in the third case (i.e., when y_s < 0 and x_s >0). I think that

a = 360 - arctan( y_s / x_s )

should be

a = 360 + arctan( y_s / x_s ).

Let's try the test case y_s = -1 and x_s = 1. Then,

arctan( y_s / x_s ) = arctan( -1 / 1 ) = -45.

The website's expression then gives

a = 360 -(-45) = 360 + 45 = 405,

which is greater than 360. My expression gives

a = 360 + (-45) = 315.

This seems to work. As can be seen by plotting, in standard polar coodinates, the point (x_s , y_s) = (-1 , 1) (in the fourth quadrant) has angle 315 = 90 + 90 + 90 +45 when measured counter-clockwise from the positive x -axis.

Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue. By using this site, you agree to our Terms of Use.