# Kepler Orbital Elements to Cartesian (xyz)

I'm not really sure if this is the place to ask this, but anyway here is my question:

Let's say I have the Kepler orbital elements of the ISS, for example, (NASA stuff). Now I want to compute the coordinates relative to the earth at a specific time so that it can be displayed, like in a sky map (I am actually experimenting with Google Sky Map).

I found many websites discussing Kepler orbital elements, but I have only found 2 pdf's that talk about this conversion:

http://www.phas.ubc.ca/~newhouse/p210/orbits/cometreport.pdf and I can't post a 3rd link yet.

I do not fully understand which values I need to calculate, and which are given by NASA.

I am also assuming that the data given by NASA is valid for the vector time provided, meaning that time obviously has to come into the calculations somewhere.

Thanks, I would appreciate some clarification.

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The reference you link to is for objects orbiting Sun (i.e. comets or asteroids). If you're wanting to deal with satellites in low Earth orbit, you'll need a good book on orbital dynamics or astrodynamics. Objects in solar orbit are typically dealt with in celestial mechanics. In both cases, the physics is the same (two body gravitational interaction) but the terminology is different. For satellites, one doesn't speak of "perihelion" or "aphelion" but rather "perigee" and "apogee." Some of the orbital parameters have slightly different names too.

For satellites, orbital elements are disseminated in a highly standardized form called TLE, which stands for Two Line Element. There are also highly standardized algorithms for taking elements in TLE form and turning them into topocentric RA and DEC values as a function of time. Your best bet, aside from an appropriate textbook on orbital dynamics, is to look at the source code for the algorithms themselves. The free satellite program PREDICT

http://www.qsl.net/kd2bd/predict.html

stands out as being reliable and well documented. Of course, the source code is included in the download. If you Google around you may even find the NASA papers that document the SGP4/SDP4 algorithms.

Here are some C++ and C# implementations of the NORAD SGP4/SDP4 algorithms (I've not tested or otherwise evaluated them).

http://www.zeptomoby.com/satellites/

Here's another site I just found via Google that looks potentially useful.

http://satelliteorbitdetermination.com

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Hi thanks for the quick reply. I did assume that the physics would be the same, and I realized a lot of the terminology is different. I had been trying to parse the TLEs from NASA (reading them in to the program is easy) but from there I have absolutely no idea what to do. I will look through the source code you linked to. Also, I did find the NORAD documentation for SGP4, but it refers to even more parameters that I don't understand. – geniass Oct 22 '12 at 8:15
@geniass Here's a quick reference on the TLE format: celestrak.com/NORAD/documentation/tle-fmt.asp – user11266 Oct 22 '12 at 11:42