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Where is the Solar system's barycenter located? The solar system as a whole, Where is the center of the mass for the combined mass of the Sun, inner planets, and gas giants, is it inside the Sun? Is there an AU measured distance of it?

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The solar system barycenter (SSB) is sometimes inside the Sun and sometimes outside. As an observer outside the solar system could detect with Doppler spectroscopy, the Sun is what's wobbling around.

The Sun's offset from the SSB is a vector sum of roughly:

  • 0.00496 au ±5% away from Jupiter
  • 0.00272 au ±6% away from Saturn
  • 0.00083 au ±5% away from Uranus
  • 0.00155 au ±1% away from Neptune

The other planets contribute much smaller amounts to the total. Each planet's contribution is proportional to the product of its mass and its orbital distance.

When these components add constructively as in 2020-2023, the center of the Sun can be as far as 2 R away from the SSB. When they cancel as in 2029-2030, the center of the Sun is within 0.5 R of the SSB. The solar radius R is 0.00465 au, shown here with a dashed line.

Plot of Sun-SSB distance vs. time

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  • $\begingroup$ Nice graph! Did you create it using JPL Horizons data? You can clearly see the ~20 year period of the Jupiter-Saturn conjunction cycle. It'd also be interesting to see the corresponding graph of the SSB's (heliocentric) ecliptic latitude. Of course, the 20 year period would be less obvious in the direction graph, but I assume there'd be a ~60 year period (60 ~= 5 Jupiter periods ~= 2 Saturn periods). $\endgroup$
    – PM 2Ring
    Commented Jan 18, 2021 at 19:17
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    $\begingroup$ @PM2Ring Almost: I used Skyfield to read JPL DE430. $\endgroup$
    – Mike G
    Commented Jan 18, 2021 at 19:22
  • $\begingroup$ @PM2Ring: What there is is rather a 179-year period, which I believe is due to what is called the great inequality of Jupiter and Saturn (which Laplace originally calculated to ~877 years, then to ~924 years, but now would be estimated to around ~895 years if I'm not mistaken (someone correct me if I'm wrong). Here I've used a JPL ephemeris to plot out the Sol-SSB distance in terms of Solar radii from year -2999 to 3000, demonstrating the cyclical nature of it: i.postimg.cc/k7sN5n4Z/Figure-1.png $\endgroup$
    – Outis Nemo
    Commented Jul 5, 2023 at 9:56
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    $\begingroup$ @Outis The ~179 year period relates to the synodic periods of (Saturn, Uranus, Neptune), relative to Jupiter, which are (19.863261, 13.812176, 12.782075) Julian years, respectively. Multiply those periods by (9, 13, 14) & we get (178.769349, 179.558288, 178.949050). We can find longer period solutions using the LLL algorithm. Here's a demo in Sage. Try larger numbers for the scale. You can put numeric expressions in the data list, and comment out data lines with leading #. $\endgroup$
    – PM 2Ring
    Commented Jul 5, 2023 at 19:15
  • $\begingroup$ sagecell.sagemath.org/… $\endgroup$
    – PM 2Ring
    Commented Jul 5, 2023 at 19:16
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The fact is, Sun can't exert any moment about the barycenter unless Sun and its planets may be resting on some solid object which may be physically resting on some fulcrum type of thing. Of course Sun wobbles about SSB but not due to balancing of moments. It wobbles due to a different reason. It occupies a place where the gravitational forces exerted by it on all planets get balanced which gives us an impression that it is revolving about SSB.

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