Decaying moon's orbit

moon42

Hello,

Here's my challenge: I want a physics model for how one would go about in order to decay the moon's orbit. I'm assuming it would involve using the velocity vector of the moon whereby Earth would be a reference system, coupled with the mass, and devise a theoretical way of degenerating the relational movement so that it crashes into our planet. I'm pretty much a rookie when it comes to classical mechanics, so I do not know how to model this. How complex would this sort of modelling be? Could it be done on a forum such as this?

Thanks,
moon42

jedishrfu

Welcome to PF.

Is this a homewok assignment or school project?

We would like to help you but you need to show us some work before we do.

Its not hard to do if you're taking HS physics and have studied Newton's law of gravitation.

moon42

Neither! It's just something I would like to be able to understand and solve... I do not have a starting point for it though, so if you could give me some direction, that would be appreciated. Also, once you come up with a force F to do the job, what would be the ideal method to translate that force to the moon? I'm assuming you would just fit a massive set of propulsion devices on one side of it. What type of devices would be most efficient? What if you want to have it decay instantly instead of progressively? How long would it take for a planetary collision to occur, given you would apply a force F, for a period of T, in a given direction?

Best regards,
moon42

Chestermiller

Are you aware of the experimental fact that the moon is getting farther from the earth, rather than closer?

moon42

Yes I am, but what does this have to do with my theoretical problem? It would of course be taken into consideration when trying to decay the orbit, but it doesn't change much.

jedishrfu

I thought I just gave you some direction: Newton's Law of Gravity

and here's a link to some info on it:

http://en.wikipedia.org/wiki/Law_of_gravitation

The forces needed to stop the moon would be fairly obvious: rocket motors or nuclear explosions on one side to slow it down.

Asteroid delflection is similar. The newest idea there was painting the asteroid with some sort of reflective paint and effectively using sun light to deflect it from its course. You could do that with the moon though.

BruceW

interesting question. The two-body problem is really weird, because all initial conditions with eccentricity less than 1 will produce periodic motion. In other words, if you perturb the moon slightly, then you will simply shift it into a slightly different orbit. There is no 'critical force' which will cause the moon to change behaviour and suddenly fall into the earth. In other words, the orbit is neither stable nor unstable. (In the sense of stability of the Poincare map).

So to get the moon to crash into the earth, you would have to keep pushing it until the moon's orbit changed enough that the moon and earth would happen to 'overlap' in the course of the moon's orbit.

pumila

The decay mechanism must be formulated to start. At present the earth's rotation drags the moon via the mechanisation of the tides, to speed up the moon's orbital speed, because the moon's orbital period at 28 days is longer than the earth's rotation period of one day. If the angular speed of the earth was slower than the angular speed of the moon's orbit then the situation would be reversed and the moon would be slowing down. The sum of the angular momentum of the earth's rotation and of the moon's orbit is a constant. As the moon speeds up the earth's rotation slows, and vice-versa.