Computer modeling of motion of planets

1. Aug 17, 2007

eminent_youtom

computer modeling of motion of planets!!!!

hi everybody
what would happen on the position and orbit of the earth and the moon, if the mass of the moon will gradually increase within a day and becomes greater than the mass of the earth. will it brings a big disaster in the earth? will moon escape out of the earth's orbit or earth will start rotating around moon? or moon becomes another planet of the sun?
this change in mass of the moon will effect on the orintation of the other planets in the solar system or not?

Is it possible to do computer modeling of it? what software i have to learn?
thankx you

2. Aug 17, 2007

mgb_phys

The earth and the moon both orbit around their common centre of gravity. Since the earth is much larger this centre of gravity is very close to the centre of the earth. As the mass of the moon increased the centre would move closer to the moon, if they were the same mass it would be half way.
Both objects would continue to go around the sun in the same way,

Such a small change in mass wouldn't have much effect on the rest of the solar system, the only object that has any real effect other than the sun is jupiter - which is quite a bit larger.

You could model the movement in anything you like - but you probably have to understand some simple Newtonian gravity first.

Last edited: Aug 17, 2007
3. Aug 17, 2007

unica

i dont agree that"Both objects would continue to go around the sun in the way". if you know the KAM theory,you will consider it from a new viewpoint.
you can google the relation between the stability of sun system and the KAM theory

4. Aug 17, 2007

pervect

Staff Emeritus
The moon can't spontaneously change it's mass, so its difficult to interpret this question.

I think you may be interested in the general question of the stability of satellites. If you are, there has been theoretical work done and people here have also done simulations. (But I haven't been able to find the thread where people have done simulations, I know the author was tony873004.) But he has a program that is called "gravity simulator" that allows for such simulations, and I believe there may be other freeware programs out there that do similar things. Don't expect astonishingly great accuracy from them, though, the numerical techniques used are not necessarily state of the art.

As far as the theory goes, see for instance the "hill sphere" at
http://apollo.cnuce.cnr.it/~rossi/publications/napoli/node2.html [Broken]

also some some plots at
http://www.geocities.com/syzygy303/

The short (and approximate) answer is this: If the orbit of a satellite (in this case the Earth) around some other massive body, lies within the solar Lagrange points L1 and L2 of said massive body and the sun, the Earth's orbit will be restricted to a finite region, it won't be able to escape.

This happens because the Jacobi integral is a conserved property of motion. (The Jacobi integral is just the Hamiltonian, its existence is guaranteed by the conservation of energy).

See http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html for the Lagrange points, again the Lagrange points of interest are the ones between the sun and the massive body around which the Earth is orbiting.

Because said massive body is heavier than the Earth, these solar lagrange points will be closer to the massive body than the current Earth-Sun Lagrange points, making the maximum stable orbit smaller.

This result is exactly true only if there are no other bodies in the solar system, and the derivations I've seen only cover the case where we can ignore the mass of the Earth relative to the mass of the object it's orbiting around.

Last edited by a moderator: May 3, 2017
5. Aug 17, 2007

AlephZero

As pervect says it's hard to know what you mean by "the moon changing its mass".

If you make a model, the answers will depend strongly on what you do mean by that statement. If you assume the moon magically gets more massive, then it will also magically get more momentum and more energy (M.V and M.V^2/2) at the same time.

On the other hand if you assume it gets more massive by collecting material moving at a different velocity (e.g. it collides with another object) the energy and momentum will be different.

I've never tried this on an astronomical system, but I have done some serious computer simulations on "open" systems that gain and lose mass, and getting the correct momentum and energy changes when material enters and leaves the part of the system that is being simulated is critically important.

6. Aug 17, 2007

eminent_youtom

thankx everybody
oh ya i was just doing thought experiment with my friend, so i consider that the moon magically gain its mass