Converting from cartesian to RA/Dec

[george7378]

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!

[Demonperformer]

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

[JamesF]

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

[Astrobits]

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

[George Jones]

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.