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
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.
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
Are you aware of the experimental fact that the moon is getting farther from the earth, rather than closer?
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.
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.
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.
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.
You appear to be having trouble with the concepts. Any reasonably accurate simulation of the Earth-Moon system will end up with the Moon receding rather than decaying. That seems to be central to your question - maybe you want to rephrase it? Do you intend that there should be some additional mechanism to retard the Lunar orbit in your simulation? Start here: http://home.comcast.net/~szemengtan/ ... you want: Classical Mechanics L1 Motion of a single particle 1.7 Central force problem. Recommend "mathematical modelling" same page. You will still want to know about tidal drag and conservation of angular momentum if you are going to model the Earth and Moon as large bodies. As pumila says, you also want a mechanism for the decay. But the references I gave you should fill you in on the mathematical framework.
Perhaps you could consider a planet / moon combination where the rotation rates and orbital rates for both bodies are locked. But would that be of any 'local' interest? The major factors in our own system have been identified and it's tidal effects that count.
this is quite an old thread. also, the op'er was thinking (in principle) what are some possible ways we could use to make the moon crash into the earth (in a fairly fast timeframe, I'm guessing). For example, if we could send up big rockets, attach them to the moon to try to get earth and moon to collide. I think any tidal effects are not important to what the op'er was asking.