Moon's future rotation

1. Mar 7, 2008

oswaler

[SOLVED] Moon's future rotation

1. The problem statement, all variables and given/known data

COnsider the earth and moon as if they formed an isolated system. The length of the day increases every year, a feature attributed to tidal effects. At some distant time in the future the earth moon system will be orbiting such that the same face of the earth will be pointed at the same face of the moon and the distance between the earth and moon will reach a final value. Assuming that the earth and moon can be treated as uniformly dense spheres and that the masses will be what they are at present, what will be the final distance between the earth and moon?

2. Relevant equations

3. The attempt at a solution

According to conservation laws, energy and angular momentum should be conserved since according to the problem there is no external force to provide a torque. From the question, at the final distance, the orbital period of the earth will = the orbital period of the moon. I'm not quite sure where to go from there though. A push in the right direction would be appreciated.

Last edited: Mar 7, 2008
2. Mar 7, 2008

Dick

If you assume both kinetic plus rotational kinetic energy and angular momentum are conserved, then you have two equations in three unknowns, the unknowns being the rotation rates of the earth and moon and the radius of the earth/moon orbit. If you introduce the constraint that they are tidally locked - this means that the rotation rate of the earth is the same as the orbital period of the moon AND the rotation period of the moon is the same, then you have introduced too many constraints. You won't be able to solve the equations. You need to relax the conservation of kinetic energy. Tidal effects produce heating. You can't assume kinetic energy is conserved.

3. Mar 8, 2008

oswaler

Thank you, that makes sense. I think at this point I'm mainly having trouble getting started with the equations.

4. Mar 8, 2008

Dick

Write down an equation for the combined angular momentum of the earth moon system first. Include both rotational parts and orbital parts. Put the numbers in and get the total. That's where to start.