I have a project in which a Monte-Carlo method is used to find the optimal parameters for some model that is fit to a data set. I want to fit a model for the orbit of Mercury using this methods, but I can't find any data to fit it to. I have found a lot of papers on the orbit of Mercury that mention observational data, but no actual observational data. Where could I find data indicating the position of Mercury around the sun over a time period, or even a relatively accurate mathematical model from which I can generate my own data by defining it as a function that is stepped through some time interval?
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$\begingroup$ This is a great question! There is already a similar question with a great answer and I think you question will be closed as duplicate to it. Don't worry, that happens to all of us, it's just Stack Exchange's way of directing future readers who land on a a question to be directed towards high value answers. $\endgroup$– uhohMar 16, 2019 at 0:17
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$\begingroup$ I would personally recommend either the gold standard of JPL's spice package, or JPL's Horizons web interface (here's a how-to) to it (like I used in this answer including several perturbations important for Mercury) or the most convenient solution; the Python package Skyfield. $\endgroup$– uhohMar 16, 2019 at 0:21
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$\begingroup$ by the way this question could probably be answered using a Monte-Carlo orbit solution as well; seems like it would be fun! $\endgroup$– uhohMar 16, 2019 at 1:12
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The available astrometric data for Mercury come from meridian transit timings (right ascension and declination) and radar or spacecraft ranging (distance). NASA JPL has some here, and the French IMCCE has some here. To use those, you'll have to work out some geometry including the position of Earth in its own orbit.
For your purpose it may be easier to use numerical ephemerides via JPL HORIZONS or SPICE, or IMCCE Miriade or Multisat, which can output Cartesian coordinates if requested. Of course these are fit to observational data themselves. The underlying data files (e.g. DE430, INPOP17a) come with papers detailing sources, methods, uncertainties, etc.
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2$\begingroup$ The construction of the DE430 ephemeris and its data sources are described in this JPL "memo" in Table 1. Mercury data is roughly 50/50 ranges to Messenger and radar ranges $\endgroup$ Mar 16, 2019 at 3:59