Equation of an Elliptical Orbit for a Moon around a Planet

[farore]

I am kind of new to astronomy and I have a few questions..

I need to be able to determine an equation expressing the elliptical orbit of Oberon around Uranus. I have four nights of data showing Oberon in different positions relative to Uranus. I am able to calculate the RA and Dec for both Uranus and Oberon from these frames (standard stars are on frame).

I just need to be able to determine the semi-major axis of the orbit so that I can determine the eccentricity. What I am most stuck on is how to apply my RA and Dec coordinates to an equation of an ellipse.

I saw a similar discussion in this thread (astrometry of elliptical orbits) but it was for asteroids and at first glance the analysis involved seemed more complicated than what I was going for.

Thanks for any help.

 

[farore]

Nevermind about the first bit, I figured out that I needed to express the change in RA versus the change in Dec of Oberon with respect to Uranus to get an ellipse.

However, with my data points the eccentricity of the ellipse I fit to the data is on the order of .9 when it should be around .008 or so.

The angular separation between Uranus and its moon goes from about 20 arc seconds to 40 arc seconds, which apparently is significant when determining the eccentricity of the ellipse. Am I missing something? The inclination of Oberon with respect to Uranus' equator is about .012 degrees so I didn't think I would have to rotate it into the plane since that seems like a fairly negligible quantity (and I don't think it would make a .008 eccentricity turn into a .9 eccentricity).

Any help on determining where I went wrong would be much appreciated :).