Two orbiting bodies, one of them stops, what happens next.

[FREEFALL1984]

This is a follow on from another thread, which asked how long it would take to free fall from the moon.

So here's my question. If the moon suddenly completely stopped in its orbit and began to fall towards the earth, what effect would that have on the earths position in relation to is. I can visualize what would happen, both bodies would spiral together (assuming both bodies where just single points for the sake of the maths) Is there an equation which can back this up and include for the movement of both bodies relative to each other instead of just the movement of the moon?

[ZetaX]

Kepler's/Newton's laws hold for two bodies as well, with the center being the barycenter. In other words, they will orbit in ellipses around it and follow the "usual" rules in regard to that, with the central mass being the sum of both. See http://en.wikipedia.org/wiki/Gravitational_two-body_problem for more details.

Especially, they can't spiral because that would violate conservation of energy.

[FREEFALL1984]

I've searched high and low and cannot find anything which tells me what happens if the one of the orbiting bodies simply stops.

Edited April 16, 2014 by FREEFALL1984

[Nibb31]

It falls towards the parent body and crashes into it unless you do something to slow it down.

That's how spacecraft come back from orbit.

[shynung]

They will both fly towards the barycenter of their system, and smack themselves into one another. What happens then depends on the type of the body involved in the impact (e.g. rocky planet? Gas giant? Comet? Star?).

[FREEFALL1984]

So because the barycentre is always a fixed point in relation to both bodies (but not fixed in relation to any single body) the earth would be pulled a considerable distance towards the moon (although obviously the moon would be pulled a much greater distance)

[Nibb31]

Yes, but the barycenter of the Earth-Moon system is inside the Earth, so it won't move much.

[FREEFALL1984]

So the final resting place of the moon and the earth is always directly on the barycentre, and because the barycentre is based on the proportion of mass each body has compared to the other, the moon will cover the same distance from its current location to the barycentre in the same amount of time the earth moves from current location to barycentre. meaning that according to your sketch the earth will only move a total of 3000miles towards the moon in the event that the moon should stop moving?

[Nibb31]

I guess so.

[R0cketC0der]

The gravitational force of the moon can be ignored if you don't want to be super accurate about this, because the moon weighs less than two percent of earths mass.

[ZetaX]

As explained in the other thread: stoping (note: you will need to stop both in this case) one is the same as making its orbit an ellipse of very very high excentrity. This is thus just a special case of orbital dynamics and can easily be calculated with Kepler's laws.

Edited April 16, 2014 by ZetaX

[Doozler]

I replied on the other thread, but was too slow!

If you are talking about the moon stopping all motion relative to the earth (or both bodies stopping) then you can just consider this as a weird narrow "orbit" with a zero semi-minor axis, and an Apoapsis equal to the original height of the moon.

So really your standard orbital equations should all still be valid.

Edit: Ninja'd

[FREEFALL1984]

Thanks for the replies guys, but I really wanted to know how much the falling moon would effect the earth. I kinda imagined it would be pulled towards the moon with a more significant force (at least enough to pull it more than its own diameter)

[Brotoro]

Thanks for the replies guys, but I really wanted to know how much the falling moon would effect the earth. I kinda imagined it would be pulled towards the moon with a more significant force (at least enough to pull it more than its own diameter)

Nibb31's diagram and answer was correct. If you stop the motions of both the Moon and Earth, they will fall together and merge at the barycenter. The Earth DOES get pulled toward the Moon (with exactly the same force as the Moon is pulled toward the Earth), but because of the Moon's much lower mass, it moves a long way in response to this force, which the much more massive Earth will move less than one Earth-radius.

[KerbMav]

In another thread someone said it would take four days for Moon to hit Earth. As they are both still orbiting the sun and depending on the position of the moon on its former orbit around Earth ... would these facts change anything?

(Unless you are saying the moon stops ALL its movement - relative to the universe? - than everything in the galasy would zip away from it. )

[ZetaX]

It changes "anything", but the changes are rather minor (assuming you stop them either in regard to their barycenter or in regard to the sun).

And there is nothing like "relative to the universe".

[KASASpace]

I'm quite sure they would just orbit each other still, and then the Moon would go towards Earth, and then they would fall towards their common barycenter, and then they would end up just colliding.

Either that or, due to the movement of the barycenter, the moon just falls right back into orbit, albeit a slightly smaller one.

Two-body physics is used for this kind of thing, and patched conics simplifies N-body physics to multiple two-body physics problems.

[MrZayas1]

If the moon actually stopped spinning, and was freefalling to earth, I could imaine that the moon would drag earth closer to it before it collides. Because orbital force, that could be represented by centrifugal force, keeps the earth pretty much stable, even though the moon tugs it around a little bit. So as the moon moves towards earth, it continually pulls earth towards it just a bit, and as it gets closer, it's gravity is more intense. So I guess that would happen.

From my original assumption, if binary stars orbiting eachother, one stopped dead in one second the other would probably fling off into space because of it's momentum with it's partner. Maybe that's how it is, I'm not an orbital scientist but that seems to make sense!