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(this question could also fit in Astronomy or Physics)

Jupiter, with it's huge mass, is the obvious culprit for messing with Earth's orbit (and possibly climate). Although Jupiter is extremely massive, Venus is much closer.

Peak delta-a

Lets start with a Fermi estimation.

In order to change Earth's orbit it is necessary to accelerate the Earth and the Sun by different amounts. The Sun's gravity on the Moon is about twice Earth's, but because the sun pulls on both it does not yank the moon out of orbit.

Using this factsheet we can compute the maximum Earth-Sun difference in acceleration induced by the other planets. This is a tidal force of sorts.

Jupiter: Delta-a is maximized when Earth is aligned with Jupiter. In such a situation Jupiter pulls on Earth more strongly than the sun. We can squeeze out slightly more by having Earth at aphelion and Jupiter at perihelion. The Sun-Earth difference is 0.135 microns/s^2.

Venus: Put Venus between Earth and the sun, Venus in aphelion and Earth in perihelion. The Sun and Earth accelerations act in opposite directions and so we add these terms. This gives us 0.250 microns/second^2. About twice Jupiter.

Mercury: The planet is so close to the Sun that Earth would "care more" about the combined mercury-sun barycenter than the Sun itself. Our Fermi estimation would thus be an over-estimate.

Other gas giants: They are both less massive and further than Jupiter and so would be much less important.

Jupiter is 389 Venus masses, but Venus gets 15 times closer to Earth and distance is much more important than mass.

And many more factors

Inclination, eccentricity, Orbital resonance, and more all play a role and it is seems that both Venus and Jupiter together would dominate Earth's changing orbit, while the other planets are less relevant. Is this the case?

Edit: I am considering how eccentricity, semi major axis, and inclination vary on Milankovitch time scales, about 10^5 years. How would it be different with Venus alone vs Jupiter alone vs all planets except those two?

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  • $\begingroup$ astronomy.stackexchange.com/questions/35026/… $\endgroup$ Oct 5, 2023 at 0:54
  • $\begingroup$ This is an excellent question and can be a great Stack Exchange question. But wow do you mean on short timescales, or for solar system evolution over a billion years? What does "affect more" mean for you? $\endgroup$
    – uhoh
    Oct 6, 2023 at 0:42
  • $\begingroup$ @uhoh: I was thinking on Milankovitch time scales, about 10^5 yr. How much and how quickly would eccentricity, inclination, and semi-major axis vary if we only had Venus, or only Jupiter, or all planets except those two? $\endgroup$ Oct 6, 2023 at 1:43
  • $\begingroup$ @KevinKostlan great! You might consider adding that information to your question post (click edit) Usually we don't modify questions too much after answers start to be posted, but the current answer doesn't get into timescales at all so in this case that would be fine. Thanks! $\endgroup$
    – uhoh
    Oct 6, 2023 at 2:10

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Let's calculate this.

F=(GMm)/r^2

Jupiter: M=1.8E27kg, r is 800 Gm from the Sun, minus 150 Gm for Earth's distance to the sun is 650 Gm.

Venus: M=4.8E24kg, r is 107 Gm, distance to Earth is 50 Gm.

Mearth is 6E24 kg

G is 6.674E-11

Fjupiter = 1E18 N

Fvenus = 8E17 N

That's pretty close. So the changes in distance due to their orbits has an influence. Jupiter's distance from Earth varies between 590 and 966 Gm, and Venus' distance varies between 50 and 257 Gm.

Then the length of their orbits plays a role. Jupiter exerts a higher maximum force, but Venus is closer more often. I don't know how to take this into account.

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    $\begingroup$ Jupiter will tend to pull on the Sun and Earth a similar amount, since it's much further away. I think it's the difference that matters, since that will affect Earth's velocity with respect to the sun. $\endgroup$ Oct 6, 2023 at 1:46

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