# SOHO-3165

Today saw my first success of establishing an orbital linkage for a SOHO comet, SOHO-3165 , with observations from three consecutive apparitions. I have never done this work on my own — all the previous similar works I’ve done were either verifying Rainer’s solutions, or simply lucky because of lacking influential nongravs. SOHO-3165 doesn’t seem to be an easy one, as neither Bill nor Karl managed to get a solution. Bill managed to get a linkage with the first two apparitions, and third one was left unsuccessful with huge residuals. Therefore I was curious if I could solve this problem.

I haven’t done this job for long, perhaps over three years. As a result it took me a while before I could get onto the right track. A few tweaks of starting conditions enabled Aldo’s Exorb to get a decent orbit for the first apparition. In this step, a parabolic orbit had to be assumed. I then forced the program to solve an orbit for semimajor axis $a = 3.05~\mathrm{AU}$. With observations from the second apparitions the orbital solution was quickly refined. The trick was to fit for the first observation from the second apparition initially. Once the RMS decreased, more subsequent data could be fed in.

If there were no nongravs, the third apparition could be linked without much difficulty. However, this is not the case this time, which exactly complicated the computation work. In fact there is a huge offset in positions in the first observation of the third apparition (which was the only observation from the third apparition at this step). So there must be a nonzero transverse nongrav parameter. I tried $A_2 = 10^{-8} \mathrm{AU ~ day}^{-2}$, no success, and even worsened the solution to the previous two apparitions. Yet the program turned the optimised $A_2$ into a negative number, from which I immediately realised that the third apparition was postponed. Then $-10^{-10}~ \mathrm{AU~day}^{-2}$. Success! The program quickly shrunk the RMS of the fit. My last step was adding all the remaining observations and let the program find the best-fit solution.

Yet seems like there is something wrong with the code about completing iterations. The code somehow continuously looked for but never succeeds in yielding a final convergence. I therefore manually paused the program. Luckily because the code was generally looping around small RMS. Although the above solution may well not have the smallest RMS, it has one close to already.

The motivation of this writing is simply to provide me as a reminder in the future about how I can obtain an orbital linkage when nonzero nongravs are presented.