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."

 

[pmacias]

I can confirm that determining the orbit of an asteroid from observations is a complex process that requires a combination of mathematics, physics, and observations. The process involves using celestial mechanics principles and methodology to calculate the six orbital elements, which describe the shape, orientation, and position of the asteroid's orbit.

The Keplerian Laws and the geometry of an orbit play a crucial role in this process as they provide the framework for understanding how objects move in space. However, observations are also essential as they provide the data needed to calculate the orbital elements. Without observations, it would be impossible to determine the orbit of an asteroid accurately.

Distances do play a significant role in determining the orbit of an asteroid. While observers may only report time and position (RA, Dec), distances can be calculated using techniques such as parallax or radar ranging. These distances are then used in conjunction with the observations to calculate the orbital elements.

The methodology used to determine an asteroid's orbit takes into account all available data, including observations, celestial mechanics principles, and physics. It is a complex and iterative process that involves continually refining the orbital elements until they accurately match the observed data.

In conclusion, determining the orbit of an asteroid from observations is a multi-faceted process that requires a combination of mathematics, physics, and observations. Each aspect plays a crucial role in producing the final orbit and allowing us to better understand the movements of objects in our solar system.