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Rotational Equilibrium and Dynamics;The moons gravitational influence on the earth causes the tides, which dissipate the kinetic energy of the earth-moon system. As a consequence the earth’s rotation is slowing and the moon is moving away from the earth at a rate of 3.84 cm each year (same speed your fingernails grow at). At some point in the earths future it is possible that the moons orbit will correspond to the time it takes the earth to rotate – in other words a day will equal a lunar month – and the moon will be in geostationary orbit (the moon will only be visible from one side of the earth). By conserving angular momentum find how far into the future (in years) that this will occur (assuming the sun doesn’t go supernovae before then). The moment of inertia of the earth is 8.008 x 1037 kg m2, the mass of the earth is 5.972 x 1024 kg, the mass of the moon is 7.347 x 1022 kg, and the angular momentum of the earth and moon combined is 3.468 x 1034 kg m2 s-1. The distance from the earth to the moon is currently 3.84 x 108 m, although this will increase with time. Assume a circular orbit throughout.
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