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If the Moon became suddenly gained 20% of its mass, would it come crashing down to the Earth, or would it just stabilize at a lower orbit? Similarly, if it suddenly lost 20% of its mass, would it fly off into space, or just stabilize at a higher orbit?

Assume that the mass just spontaneously appears/disappears without giving any extraneous momentum or destroying space-time or any other crazy effect that might happen for this fake scenario >.<. And you can ignore extreme changes in mass (since, obviously, if the moon became as massive as a black hole, it would crash into the Earth and much worse).

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To first order, it would be unaffected. The orbit of a satellite such as the moon around a central body is not affected by the mass of the satellite. The forces on the satellite will increase by 20%, but the 20% increase in inertia will compensate.

At a higher order, you would see some change in the orbit of the Earth around the moon. The orbit would become slightly more elliptical. The idea of "stabilize at a higher orbit" is a bit of a misnomer. It would stabilize, but instantaneously. Orbits are always stabilized at all times and, unless the system has enough energy to eject one of the bodies, it will always be roughly an ellipse.

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As long as the energy and orbital angular momentum also grows with mass, linearly. If any one of them is out of step with the others, there would be serious consequences. You can look up the Kepler orbit on Wikipedia, along with the orbital eccentricity. Once these things are in lockstep with the others, then there would be a large parameter range where you can alter the mass a lot and still get the same physical result.

That is, the answer to your problem actually does not depend so much upon the mass, but rather whether you changed the relevant parameters in the same way or not.

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  • $\begingroup$ What happens if it grows.. say exponentially? $\endgroup$
    – Savitr̥
    Commented Apr 27, 2023 at 7:11
  • $\begingroup$ If all three grows at the same time, in linear lockstep, then even exponential growth is acceptable. $\endgroup$ Commented Apr 27, 2023 at 8:54

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