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In this worldbuilding question, the moon is gone:

an extra-solar gas giant passed close by Earth in which the Moon was knocked from orbit to become a planet in an independent orbit, as well as sending Mercury crashing into its parent star.

So by introducing a rogue planetoid, the orbit of both the Moon and Mercury needs to be affected, with at least the former surviving the encounter.

Is this possible? If so, what are the requirements (mass, velocity, proximity)? Would it be possible for it to happen and affect the Earth minimally, so that it remains habital?

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    $\begingroup$ Short answer, no. You'd need something that was planet-sized to move a planet/moon. $\endgroup$ – zephyr Jun 19 '17 at 17:03
  • $\begingroup$ @zephyr that's kinda the point. You would need something that massive, but could it happen without also destroying the Earth's orbit? $\endgroup$ – Baldrickk Jun 20 '17 at 8:05
  • $\begingroup$ @Walter can you flesh that out? that would be a fine answer. $\endgroup$ – Baldrickk Jun 20 '17 at 10:58
  • $\begingroup$ But you asked about asteroids. Asteroids are not planet sized and thus could never move the moon. If they were that large, they wouldn't be asteroids. $\endgroup$ – zephyr Jun 20 '17 at 11:28
  • $\begingroup$ @zephyr that was referencing the most similar question I could find, and pointing out that this scenario is different. The quote references "an extra-solar gas giant". $\endgroup$ – Baldrickk Jun 20 '17 at 12:20
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The Earth and moon orbit around a barycentre that is "about 3/4 the radius of Earth" away from the Earth's centre: https://en.wikipedia.org/wiki/Orbit_of_the_Moon. Removing the moon would almost certainly affect the Earth's orbit around the sun due to the change in the centre of mass, and probably a resultant change in momentum of the Earth system (such as it was). That's without even considering the gravitational tug of the planetoid on the Earth, and that of the moon as it gets snatched away. I would think it spectacularly unlikely for the interaction to leave Earth travelling along the orbit of the centre of mass of the old Earth-moon system. But, I haven't actually modelled it, so I might be wrong there.

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  • $\begingroup$ I don't think that's correct. The binding energy of the Earth-Moon binary is tiny compared to the orbits energy of the Earth orbiting the Sun. $\endgroup$ – Walter Jun 23 '17 at 22:12
  • $\begingroup$ I wasn't saying that removing the moon from the Earth's orbit would dislodge the Earth from its orbit around the sun - only that it would affect Earth's orbit somehow. I did some calculations: at Earth's perihelion, removing the moon (ideal case: it vanishes) would result in Earth's aphelion shifting around +/-250,000km (depending on position of moon in regard to barycenter at that point). Shift in solar energy at aphelion would be several tenths of a percent. Not huge, but it does play into the question of habitability. Obviously not as great an effect as the rogue gas giant's gravitation. $\endgroup$ – hartacus Jun 26 '17 at 4:33
  • $\begingroup$ I didn't imply that you implied it would dislodge Earth form its orbit, but the relative energy change equal the relative change in semi-major axis, i.e. one would expect no significant change to the Earth's orbit, it would certainly stay in the habitable zone. $\endgroup$ – Walter Jun 27 '17 at 22:37
  • $\begingroup$ I guess this plays into the worldbuilding nature of the original hypothetical - remaining within the habitable zone is not necessarily the same as remaining habitable to all the lifeforms existing on a planet. A few tenths of a percent less or more solar radiation at aphelion may, over time, affect the planet's ability to sustain human life it its current modes of habitation. $\endgroup$ – hartacus Jun 29 '17 at 7:03

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