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Recently I had to implement the 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 thought the Laplace method was very accurate, so I tried to apply it to an asteroid (CASLEO, 5387). The 3 observations were also taken at intervals of 10-days, 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 a smaller proportion 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?

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  • $\begingroup$ Is the date of the “control” orbital elements the same as the date you made your measurements? Minor planet orbits change enough in comparatively “short” periods—at least compared to major planets. Maybe that’s part of the answer. $\endgroup$ Jan 10, 2022 at 4:13
  • $\begingroup$ It'd be better to post some concrete examples, "less accurate", "smaller portion", "very accurate" are pretty abstract terms. Can you post the actual data? $\endgroup$ Jan 10, 2022 at 15:05

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In principle, 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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Interesting project! Perhaps first determine convergence criteria for alternative methods being considered and if possible acquire more widely distributed observations of target's position. Then to the extent appropriate to examine how least squares estimates for various parameters of the selected method correlate (or not) with results obtained by applying that method to available observations of the orbiting object under study, one may decide to use consequent approximations of orbital elements as basis for examining differences in sensitivity to distance for combinations of feasible methods, observations, and elements. This is a suggestion, not a validated process.

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