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JPL Horizons - "highly accurate measurements of planetary positions" - how do they do it?

@PM2Ring's answer does a great job of explaining that folks who do careful numerical integration keep a large number of digits beyond the final accuracy because if they didn't, after tens of thousands ...
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JPL Horizons - "highly accurate measurements of planetary positions" - how do they do it?

The JPL ephemerides are good, but they certainly are not precise to the fraction of a millimetre! From the Horizons docs: Statement of Ephemeris Limitations To produce an ephemeris, observational ...
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What unit of year in JPL Small-Body Database Lookup?

Based on the Astrodynamic Parameters page, It appears to be the astronomical Julian year, defined as exactly 365.25 days of 86400 SI seconds.
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