Moon Gravity Vs Earth Gravity Pull

Question

Suppose, sometime in the future I develop an experimental superweapon capable of blowing up the entire Moon. If I used it to break the Moon into multiple pieces of varying sizes, we would then have giant chunks of Moon rocks floating around.

We all know the Moon is drifting away from us at a constant rate. But now, rather than there being a single concentrated mass we have multiple masses.

If I understand Newtonian Gravitation correctly, the bigger the object the more gravitational pull it has. For example, if I landed on Phobos (if that is possible) and jumped, it would take a longer time for me to fall down than it would, say if I jumped while on Earth's Moon.

After being broken up into smaller pieces, which of the following would happen to the Earth's Moon?

A) The Moon remnants keep drifting away from us, regardless of the fact that the pieces are now smaller.

B) The Moon now does not have the "power" to counter Earth's gravity due to not being the massive object it used to be, so the pieces all fall to the Earth and that ends everything.

C) The Moon gets close to Earth but does not fall down on the surface. The pieces form an asteroid belt made of lunar remains much like the Jovian planets, which will never get away or closer to us and remain in a relatively perfect ellipse?

Answer 1

While the Moon is a concentrated rock, it exerts a tidal force on the Earth; this results in a transfer of angular momentum, and it is the cause of the Moon slowly drifting away.

If your debris magically dispersed into a rotating shell at the same distance as the current Moon orbit, but with a little bit of mass everywhere (like Saturn's rings), then I believe the tidal force component would disappear and there would be no transfer of angular momentum from the Earth to the moon (dust). However, the particles would exert a force on each other, which would over time result in a "Earth ring" (just like Saturn).

That sounds a lot like your answer C, but without the "get close to Earth" bit.

Answer 2

The moon's distance is increasing because of the tidal bulge that it causes on the earth. This bulge causes the moon and the earth to pull on each other in a way that slows the earth's rotation and increases the distance to the moon. The more spread out the moon's mass is, the less of a bulge it can induce. So in the short term, if all the chunks spread out almost evenly, then there's no bulge and (to a first order) no exchange of angular momentum. The average distance would not increase via this mechanism.

Instead, (greatly depending on how the initial breakup distributed the remains) the pieces would start hitting each other. This process removes kinetic energy (by turning it into heat) and lowers the average orbit over time.

Over long periods, the pieces would tend to coalesce back into a smaller number of objects. If a large moon reforms, then it could begin to induce a tidal bulge on the earth again that would drive altitude changes in the orbit.