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Question:
How would you calculate the age of the universe scientifically in regards to the rotation of the moon on its axis, and the distance from the moon to the earth?



Replies:
I do not think you can get a meaningful answer from the data provided here.

Jasjeet


Assuming the earth is younger than the universe, figuring out something about how long the earth and moon have been together tells you the universe must be at least that old. I believe that the earth-moon system is more complicated than it looks because of the earth's rotation, combined with the moon's orbit about the earth. The axis of the earth's rotation and the moon's orbit are different, and the gravitational forces between them cause a gradual change in both. There is some evidence that the earth spun faster on its axis a billion years ago or so (perhaps every 22 hours instead of 24?) and the moon was closer in then. Newton's equations for the earth-moon system can then confirm that this kind of trading of angular momentum has actually taken place. This kind of problem with rotating interacting bodies may be treatable using the Lagrange method - look in an advanced mechanics book (Goldstein perhaps) for a discussion of these approaches. However, the problem may be more complicated than I think (involving energy dissipation through the tides for example) but I do not know a good reference on the subject.

Arthur Smith



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