Astrometry and Elliptical orbits

[Mu naught]

You can measure the distance to an object orbiting the sun using parallax, and you can determine its angular velocity by measuring its change in position over several hours or days.

From this you can calculate its orbit... if it were circular. However, comets and asteroids follow elliptical orbits, not circular ones. How do you determine the true orbit of an object and its eccentricity?

 

[Ich]

http://www.schillerinstitute.org/fid_97-01/982_Gauss_Ceres.html

EDIT:
Just read a bit into the paper. Sorry, seems to be crap written by a philosopher. It's 85 pages, though, so maybe there's something worth reading in the rest of the paper.
However, what I wanted to say: You determine orbits not on the assumption of circles, but of conic sections. That covers everything.

 

[Mu naught]

http://www.schillerinstitute.org/fid_97-01/982_Gauss_Ceres.html

EDIT:
Just read a bit into the paper. Sorry, seems to be crap written by a philosopher. It's 85 pages, though, so maybe there's something worth reading in the rest of the paper.
However, what I wanted to say: You determine orbits not on the assumption of circles, but of conic sections. That covers everything.

thanks i don't have time to look at it now but i will tomorrow. I understand that an ellipse is a conic section, but what I don't really understand is how to apply the measurements you can make - distance and average angular velocity over some interval of time - to the equation for an ellipse.

I should mention the reason I ask is because I'm taking a course in observation astronomy and I'd like to calculate the orbit of comet Hartley for my research project.

 

[Ich]

Actually, what you measure is angular position at different times, and nothing else. I hereby frankly admit that I don't know how to calculate orbits from these measurements, but CFG seems to have devised a valid method 200 years ago. Try to find it.

 

[Filip Larsen]

For a fairly extensive description of the process I can recommend [1]. For an introduction I would recommend that you find an astronomy textbook suitable for your level that also describes orbital determination (like Gauss method). There is a fairly big difference between just knowing what practical observations to make in order to determine orbits, and then to derive the theory and computer code needed to make the actual calculations.

[1] Statistical Orbit Determination, Byron D. Tapley, Bob E. Schutz, George Henry Born. Elsevier Academic Press, 2004. (http://books.google.com/books?id=qePVQF9v15kC)