Recently I had to implement Laplace method and apply it to 3 observations of Mars (10 days in between two observations). The results were pretty good, with discrepancies with real data well below 5% in most of the orbital elements.

I supposed that Laplace method was very accurate, so I tried to apply it to an asteroid (CASLEO, 5387). The 3 observations were also 10-days spaced but now the results widely diverge from the real orbital elements.

I expected it to be less accurate than in the Mars case since the observations covered less fraction of the orbit, but some of the elements were quite far from expected.

So my question is: What is the accuracy of the Laplace Method? Is it really that sensitive to the distance?


In principal, Laplace's method (and Gauss's method) should be very accurate for determining orbits.

Of course "garbage in garbage out" applies, and if the observations were inaccurate the results may also be inaccurate. However, you should not get great discrepancies. I would consider careful checking of your calculation, and perhaps comparing your results with those of an independent orbital determiner, to check for a mistake in the maths.


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