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In the Wikipedia article on numerical integration of planetary motion it states:

...the flattening of the Earth causes precession, which causes the axial tilt to change, which affects the long-term movements of all planets.

Why would precession affect the motion of the other planets?

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    $\begingroup$ Perhaps gravity? Or are they referring to the movements of the planets in the sky, and not in their actual orbits? $\endgroup$ – MystaryPi Oct 24 '18 at 3:21
  • $\begingroup$ I don't believe it does, not significantly. The paragraph is addressing small changes that are very difficult to predict over timescales of tens of millions of years, however, so I'm not 100% certain. $\endgroup$ – userLTK Oct 24 '18 at 4:25
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    $\begingroup$ my reading would be "the Flattening of the Earth causes precession, which affects its orbit; other planets are similarly flattened, so precession affects the long term movement of all planets." $\endgroup$ – James K Oct 24 '18 at 6:27
  • $\begingroup$ I would read this as "Thus, each planet's motion individually is affected in long-term by its own flattening." But that phrase is not very clear on its own meaning. $\endgroup$ – AtmosphericPrisonEscape Oct 24 '18 at 14:23
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    $\begingroup$ The flattening alone doesn't cause precession. A somewhat flexible (i.e., lossy) oblate spheroid in empty space will eventually rotate about the axis of symmetry, no precession at all. What the flattening does is give the Moon, the Sun, and the planets other than the Earth a handle by which those objects can exert a gravitational torque on the Earth. $\endgroup$ – David Hammen Oct 24 '18 at 14:26
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Why would precession affect the motion of the other planets?

First things first: That's an unreferenced portion of a wikipedia article.

Citation needed, xkcd 285.


That said, a perfectly spherical body acts exactly like a point mass in Newtonian mechanics. A non-spherical body does not. The Earth's equatorial bulge has a significant effect on satellites in low Earth orbit. Sun synchronous orbits would be impossible without that bulge. For example, a sun synchronous orbit about Venus with its very slow rotation rate and hence very small equatorial bulge is not possible (reference).

The Earth's equatorial bulge adds a quadrupole (inverse quartic, or $1/r^4$) term to the inverse square law relation for point masses, and this inverse quartic term depends not only on distance but also on latitude. The added term is $$3 J_2 \frac {GM_\oplus a^2}{r^4}\left(\frac 3 2 \cos^2 \lambda - 1\right)$$ where $J_2$ is the Earth's second dynamic form and $\lambda$ is the geocentric latitude.

Since this term drops off as $1/r^4$, it becomes very small beyond the Moon's orbit. But it still exists beyond the Moon's orbit. However, I've yet to see a paper that does account for (or says we need to account for) Earth's $J_2$ effect on the other planets.

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  • $\begingroup$ An unlikely hypothesis for the origin of the quote might be that it started out somewhere else as being a reference to the Sun's $J_2$ affecting all of the planets. $\endgroup$ – uhoh Oct 27 '18 at 5:40

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