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How would the Earth be affected if the Moon was destroyed as far as our orbit around the Sun? What if Mars or Jupiter was destroyed?

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The orbital speed of the Moon around the Earth is 1022 m/s. The Earth is 81 times more massive, than the Moon. Thus, a sudden disappearance of the Moon would cause an $\frac{1022}{81}=12 \frac{m}{s}$ change of the Earth's orbit, which would be negligible.

The disappearance of the Mars or Jupiter would have yet lesser effect.

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    $\begingroup$ How do you justify that claim - in particular since the moon's orbital momentum does not directly affect the Earth's orbit (it does affect wobble and rotation) $\endgroup$ Oct 3 '18 at 16:05
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    $\begingroup$ The Earth and Moon both rotate about their common barycentre. The Earth at roughly 12.5 m/s the Moon at about 1 km/s. The barycentre is in orbit around the Sun. So if the Moon vanished the Earth would be moving at 12.5 m/s relative to the orbit of the former barycentre, and would settle into a slightly different orbit as a result. $\endgroup$ Oct 3 '18 at 21:30

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