Asteroid orbit determination from observations

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Discussion Overview

The discussion revolves around the determination of asteroid orbits from observational data, focusing on the necessary observations, the role of celestial mechanics, and the relationship between measurements and orbital elements. It touches on theoretical aspects as well as practical implications of the methodology used in orbit calculation.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that several nights of observations are required to calculate an asteroid's orbit and questions how time and position measurements (RA, Dec) relate to determining distances and the resulting orbital elements.
  • Another participant argues that without gravity, measuring all six degrees of freedom would be impossible, as one could only determine five parameters due to the scaling of distance and velocity. They suggest that the distance to the sun affects the asteroid's path and that time-separated measurements allow for the determination of all six degrees of freedom, although they express uncertainty about the existence of simple formulas for this process.
  • A link to a document is provided by a participant, presumably containing relevant information on the topic.
  • A subsequent post indicates that the previous participant missed part of their point and provides a link they believe is more pertinent.

Areas of Agreement / Disagreement

Participants express differing views on the methodology for determining orbital elements from observations, with some uncertainty regarding the role of gravity and the specifics of the calculations involved. No consensus is reached on the best approach or the existence of straightforward formulas.

Contextual Notes

The discussion does not resolve the complexities involved in the relationship between observational data and orbital calculations, nor does it clarify the assumptions regarding the influence of gravity on the measurements.

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

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