Asteroid orbit determination from observations

[solarblast]

It is said in the literature, I believe, one needs several nights of observations to calculate an orbit for, say,an asteroid. Using celestial mechanics mathematics and methodology, one produces the six orbital elements. It seems to me that most introductory texts on the subject, talk about Keplerian Laws, and the geometry of an orbit. Physics too, but how do observations fit into all this to finally produce the "orbit".

An observer is only reporting time and position (RA, Dec), so how do distances figure into this? An observer cannot provide them. Do they fall out of the methodology I refer to above?

 

[mfb]

Without gravity, it would be impossible to measure all 6 degrees of freedom - you could always scale distance and velocity by arbitrary factors, and determine just 5 parameters. However, the distance to the sun influences the bending of the asteroid path. Therefore, if the measurements have some time in between, you can determine all 6 degrees of freedom. I don't think there are simple formulas for that (maybe there are), and the best way is probably a numerical evaluation.

 

[solarblast]

http://copernico.dm.unipi.it/~gronchi/PDF/gronchi_discuss.pdf

 

[solarblast]

Missed part of the above. "This link is more to the point."