RoboSapien said:
I am sorry . All of U have failed to tell me why is moon gaining height in orbit. Something as heavy as moon to do that would require fantastic amount of energy. Where is the energy comming form ?
By the way if Earth is slows down by moon then moon too should get slowed down.
Thanks for posting the this :
There's been a few wrong answers, but a lot of correct answers too, which have answered your question.
To provide yet another recap:
As various other people have said, the Earth is losing kinetic energy as its rotation speeds down. It's also losing angular momentum.
The moon is gaining some of the energy the kinetic energy the Earth loses, and all of the angular momentum the Earth loses.
Thus the spin angular momentum of the Earth is being changed into orbital angular momentum of the moon. This prcoess is sometimes known as spin-orbit coupling.
The total angular momentum of the Earth-moon system remains constant. I was going to give some formulas, but they got too messy and long. If you want to calculate the total angular momentum of the Earth-moon system you have to add together the
spin angular momentum of the earth
orbital angular momentum of the Earth around the earth-moon center of mass
spin angular momentum of the moon
orbital angular momentum of the moon around the earth-moon center of mass
The energy formulas are also somewhat long. ONe specific formula that might be of interest is that the energy of a rotating body is .5*I*w^2, where I is the moment of inertia of the body around it's spin axis, and w is the angular frequency at which the body rotates.
For the Earth-moon system, the total energy iof the system s the sum of the following:
the spin energy of the Earth
the spin energy of the Moon
the kinetic energy of the Earth due to it's orbital velocity around the COM
the kinetic energy of the Moon due to it's orbital velocity around the COM
the gravitational potential energy between the Earth and moon.
Angular momentum must stay constant - but energy can be dissipated in the form of heat, so it is allowed to decrease.