In the four-observation method of Gauss for orbit determination, the right ascension and declination of an asteroid is observed at specified times, and the heliocentric position of Earth is obtained from tables (or JPL Horizons) for those same times.(adsbygoogle = window.adsbygoogle || []).push({});

I can follow the procedure to the point where the asteroid's heliocentric and geocentric distances converge as the result of successive approximations, leaving me with position vectors for the asteroid in ecliptic coordinates, sun-to-asteroid (x,y,z) and Earth-to-asteroid (X,Y,Z), for time 1 and for time 4.

From there, however, my textbook goes into some weird process for obtaining the state vector that is to be used in finding the elements.

I managed to obtain a state vector by correcting the times of observation for planetary aberration, then using the average position (r₁+r₄)/2 and a numerical derivative for the velocity (r₄−r₁)/(t₄−t₁). That works fairly well, though it seems crude, as if I'm not using all my information to best advantage. I'm thinking that the textbook probably gives a more accurate way of obtaining a state vector for the asteroid. I just don't understand what's going on. Like I said, it looks weird.

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# I How to get state vector in 4-observation method of Gauss

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