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What are the highest accuracy (and hence precision) orbital periods of Jupiter, Saturn and earth in units of days. Note have Allen’s Astronomical Quant(Cox1991)/ Wolfram-α / Wikipedia / 3ea. don’t agree.

Joe Horwath
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    Hi. It would be helpful to have links to all the references so that all the readers do not need to try to find them. Plus, there are different definitions of "orbital period", so that might be some of the discrepancies. If you can clarify which period you want, that would be helpful. – JohnHoltz Oct 03 '23 at 00:34
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    To be very precise, a planet’s orbital period is never the same from one orbit to the next, mostly because of gravitational interactions. I find Wikipedia and Wolfram Alpha to give the same values (though rounded for Wα), while Astrophysical Quantities (I have the 2002 edition) does give slightly different results; NASA’s Solar System Fact Sheet also differs slightly. The epoch of measurement would be important to know, as it can have an influence. – Pierre Paquette Oct 03 '23 at 01:16
  • FWIW, the JPL Horizons Body Data pages give Earth = 365.25636, Jupiter = 4332.589, Saturn = 10755.698 for the sidereal periods (in days of 86400 SI seconds). See https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=399 for the Earth page. OTOH, those pages are just for general info, & not intended for orbit calculations. – PM 2Ring Oct 03 '23 at 05:17
  • https://astronomy.stackexchange.com/q/40919/16685 has some good info about real orbits vs ideal Kepler orbits. – PM 2Ring Oct 03 '23 at 05:36
  • It also might be helpful to know why you want this information. For instance, if it's to compute relative positions at some tim 7m the past or future software or websites could be recommended, for more accurate results than hand calculations. – notovny Oct 03 '23 at 11:41
  • Thank you responders for your comments, all helpful espcl. PM 2Ring re: NASA: Horizons am comparing results from several sources. – Joe Horwath Oct 05 '23 at 01:54
  • As John said, you need to tell us exactly which definition of orbital period you want. Options include the anomalistic period (the period between successive perihelion passages), and the sidereal period (the period relative to a frame defined by the stars, eg the ICRF). Horizons (& other ephemeris software) can be used to calculate these periods. Its data spans from 9999 BC to 9999 AD. The data for the planets themselves covers a smaller time span, but we can use planet system barycentres outside those intervals. – PM 2Ring Oct 05 '23 at 17:56
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    @JoeHorwath I see things differently. With n-body problems like solar systems there's really no such thing as actual, purely periodic motion. All these definitions of "period" are artificially constructed, but none of these are going to really be periodic. If one were to measure each of them for a million hears, "period" after "period", and plot them, they'd all have scatter from one "period" to the next. I think a good follow up question would be "Why is 'period' such a complicated thing to define for solar system objects, and why are there so many different definitions for period?" – uhoh Oct 05 '23 at 23:45
  • @JoeHorwath the reason we have numerically computed ephemerides (like the ones that Horizons and Skyfield provides access to) is because periodic models are not accurate because for gravity, everything pulls on everything. All we have is F=ma, or more accurately dp/dt = (ΣF)/m where ΣF is the sum of all forces on mass m. We have to integrate that equation for all bodies simultaneously to really know how they're going to move. – uhoh Oct 05 '23 at 23:52
  • for more on using dp/dt = F/m instead of a = F/m see 1, 2 – uhoh Oct 05 '23 at 23:59
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    @uhoh Sure, the period is variable on any n-body system for n>2, but Pierre already mention that. A mean period can still be useful, though. – PM 2Ring Oct 06 '23 at 01:10
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    @PM2Ring yep for sure etc. I'm just replying to the OP's comments here. – uhoh Oct 06 '23 at 02:12

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