<blockquote>
  <p>Why would precession affect the motion of the other planets?</p>
</blockquote>

<p>First things first: That's an unreferenced portion of a wikipedia article.</p>

<p><a href="https://i.sstatic.net/pcWZp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/pcWZp.png" alt="Citation needed, xkcd 285."></a></p>

<p><br></p>

<p>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 (<a href="https://space.stackexchange.com/questions/5312/why-would-sun-synchronous-orbits-be-impossible-around-perfectly-spherical-bodies">reference</a>).</p>

<p>The Earth's equatorial bulge adds a quadrupole (inverse quartic, or <span class="math-container">$1/r^4$</span>) 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
<span class="math-container">$$3 J_2 \frac {GM_\oplus a^2}{r^4}\left(\frac 3 2 \cos^2 \lambda - 1\right)$$</span>
where <span class="math-container">$J_2$</span> is the Earth's second dynamic form and <span class="math-container">$\lambda$</span> is the geocentric latitude.</p>

<p>Since this term drops off as <span class="math-container">$1/r^4$</span>, 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 <span class="math-container">$J_2$</span> effect on the other planets.</p>

CC BY-SA 4.0
2018-10-27T05:40:49.427Z
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.
uhoh
CC BY-SA 4.0
2018-10-24T05:50:01.763Z
2018-10-24T05:50:01.763Z
David Hammen
<p>In <a href="https://en.wikipedia.org/wiki/Numerical_model_of_the_Solar_System" rel="nofollow noreferrer">the Wikipedia article on numerical integration of planetary motion</a> it states:</p>

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

<p>Why would precession affect the motion of the other planets?</p>

CC BY-SA 4.0
2018-10-24T03:21:51.510Z
Perhaps gravity? Or are they referring to the movements of the planets in the sky, and not in their actual orbits?
MystaryPi
CC BY-SA 4.0
2018-10-24T04:25:06.953Z
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.
userLTK
CC BY-SA 4.0
2018-10-24T06:27:02.490Z
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."
James K
CC BY-SA 4.0
2018-10-24T14:23:45.673Z
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.
AtmosphericPrisonEscape
CC BY-SA 4.0
2018-10-24T14:26:25.450Z
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.
David Hammen
<celestial-mechanics><precession><modeling>
Why does the precession of the earth affect other planets?
Tyler Durden
# Why does the precession of the earth affect other planets?

(Asked by: username_0 on 2018-10-24)

In [the Wikipedia article on numerical integration of planetary motion](https://en.wikipedia.org/wiki/Numerical_model_of_the_Solar_System) 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?

**Tags:** celestial-mechanics, precession, modeling
> **Comments:**
> **username_1**: Perhaps gravity? Or are they referring to the movements of the planets in the sky, and not in their actual orbits?  
> **username_2**: 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.  
> **username_3**: 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."  
> **username_4**: 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.  
> **username_5**: 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.  

---

## 1 answers

### Answer by username_5 on 2018-10-24. Score: 4

> 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.](https://i.sstatic.net/pcWZp.png)](https://i.sstatic.net/pcWZp.png)

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](https://space.stackexchange.com/questions/5312/why-would-sun-synchronous-orbits-be-impossible-around-perfectly-spherical-bodies)).

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.

> **Comments:**
> **username_6**: 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.  

---

