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Q & A: lunar history

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Most recent answer: 10/22/2007
Q:
Lunar tides churn earth’s oceans and soils. The resulting fricitional heat energy accumulates in earth or radiates to the space. Conversely, earth’s tidal force on the moon accumulates heat energy in moon. These energies come from, and diminish, the kinetic energy of moon’s revolution around the earth. The diminished kinetic energy of moon results in the reduction of the radial distance of moon’s orbit around the earth. As this process has been going on for billions of years, from the time of moon’s formation until now, the orbital distance of moon must have significantly reduced. 1) What is the name of this phenomenon? 2) What is the percentage reduction of the average distance of moon-to-earth (say) per million years? 3) When will moon fall on earth due to this phenomenon? Thank you.
- Mehran (age 54)
Miami
A:
Mehran- You've left out one other energy source for the problem, the Earth's rotational energy. The astronomers say that actually the Moon has been getting FARTHER from the Earth, so the net kinetic plus gravitational potential of that part of the system is going UP, even as tides heat the Earth. The source of that energy is the earth's rotation, which is slowing down. When you think of it, the almost-twice-daily changes in the tides must be more driven by the Earth's daily spin than by the Moon's monthly rotation, so it's not surprising that it's the Earth's spin that's losing energy. Then if you remember that angular momentum must be conserved, you see that the lost spin angular momentum has to go somewhere- and that's to the Moon orbit. The direction of the orbit is such that its absolute angular momentum increases, so that the orbit size increases.

As for how quickly all this is happening, a quick Google search turned up a reference
(http://www-astronomy.mps.ohio-state.edu/~ryden/ast161_4/notes19.html )that claims that the day has lengthened by about an hour in the last 240 million years, and that the Moon is getting some 3.8 meters farther away each century. The phrase this source uses for the process is "tidal braking".

Mike W.

(published on 10/22/2007)

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