Would a destroyed orbital body's orbit decay?

Question

I recently finished reading the novel "Seveneves" by Neil Stevenson. The central premises of the novel is that an unknown object has caused the moon to break into several large pieces, with an immeasurable amount of smaller ones floating around. In the novel, the quantity of objects is sufficient to cause a Kessler Syndrome type 'white sky' event, which then somehow jumps to a bombardment of the Earth with many of the smaller pieces. Overall, my question is

A) Would breaking the moon into pieces cause a white-sky event, even in lunar orbit?

B) Would the pieces' orbits decay?

Answer 1

Some would. Basically the most likely event that would cause the moon to break up is a collision with another object. That collision would impart kinetic energy to the various pieces of the moon in different amounts and along different force vectors, which would cause the pieces to drift away from the moon's former location in various directions.

They wouldn't "suddenly" deorbit, but the force imparted by the collision to the pieces would be like a Saturn IVb rocket in orbit around Earth firing its engine to break LEO and head out to the moon; or, conversely, the CSM firing its engine to deorbit the moon and head back to Earth. The only difference is that the rocket engine imparts force gradually over time (a long "impulse") while a collision imports force in a fraction of a second (a short impulse). Well, there's another difference, and that's that the imparting of force to each piece of the former moon is much less precise, so predicting where the various pieces will all go, and thus whether and when they'll deorbit and where they'll impact, is impossible to calculate prior to the impact and very difficult for hours thereafter, by which time the smallest, fastest chunks will probably be causing a meteor shower for Earth observers.

Answer 2

If the Moon disintegrated as in Seveneves, certainly not all of its mass would end up hitting the Earth, but some of it would, and it'd only take a small fraction to produce catastrophic results.

In general, if something in orbit breaks into pieces moving away from each other, then by definition neither piece is still in the original orbit, because (due to conservation of momentum) neither piece has the original combination of velocity and altitude. One piece will be spiralling toward Earth, the other away from it, at a rate determined by how hard the object broke apart. As the fragments of the Moon collide and break each other into smaller and smaller bits, they will spread into a wider and wider distribution of orbits, some of which will eventually pass within the Earth's atmosphere, while others escape into deep space.

To put it another way, the Moon disintegrates, and becomes an expanding debris cloud like the Death Star exploding. That debris cloud is a disc centered on where the Moon's center of mass used to be (more or less). Sooner or later, the disc will expand to touch the Earth's atmosphere, and at that point the dust / rocks / huge boulders that make up the cloud will start falling out of the sky. Even if most of it burns up, this could easily heat up the atmosphere by tens or hundreds of degrees (which is what Stephenson calls the "white sky").

Answer 3

Decay in the classic sense the way a satellite in the upper fringes of the atmosphere decays? No. It's complicated.

When two objects interact gravitationally energy is conserved. In center of mass coordinates each leaves (assuming they miss) with the same speed they came in on. In the reference system of a large group of such interactions, the small bodies pick up speed at the expense of the large ones. This is the principle of the sling shot effect used by NASA. E.g. routing a probe by Venus to give it enough energy to get to Saturn.

In effect the cloud of mutually orbiting rocks 'boils' off the smaller rocks. SevenEves doesn't make clear how fast this can happen.

Rock has essentially no structural strength compared to it's mass when in large chunks. This is why planets are round. Even Ceres, the largest asteroid is essentially a large lumpy ball. Doesn't take much of a hit to make a big fragment into a large bunch of smaller fragments.

This is important: The rate that rocks are expelled from the cloud depends on:

• How often interactions happen.
• The difference in velocity between each rock and the center of mass of the cluster.
• The ratio of the mass of the large rock to the small rock

Complication: The moon is outside the earth's Hill Sphere. The sun is a stronger force than the earth is.

A rock that comes off the cloud toward the earth has basically one chance to hit the earth before being slung off into deep space.

If all moon were converted to gravel, and spread evenly in all directions, then a "White Sky" would certainly be the outcome. Figure out what fraction of the sphere the earth intercepts, and how long the gravel takes to arrive. All of it arrives at essential earth escape velocity.

(it's more complicated. You have to figure out the effective cross section for the earth because the gravitation will bend paths toward it.)