Lecture4 - Tides A tidal force arises from the differential...

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Tides A tidal force arises from the differential gravitational force on different sides of the same object. ¾ E.g. the pull of the Moon is stronger on the side of the Earth that faces it, than on the other side ¾ This causes the oceans to “bulge” The differential force is 3 r dF ¾ This raises a tidal bulge, which itself exerts a force 6 r dF ¾ Thus tidal forces diminish quickly as objects are separated Rotation causes the tidal bulges to advance, and the “frictional” tidal force changes the orbits and induces synchronous rotation ¾ the Moon always show the same face to Earth, because the drag force caused by the tidal bulge has caused the Moon’s rotation period and orbital period to be the same ¾ This effect causes Pluto and Charon to always show the same face to one another (as Earth and Moon will do eventually) ¾ Similarly, Mercury rotates exactly 3 times for every two orbits of the Sun, which ensures Mercury’s tidal bulge always aligns with Sun at perihelion.
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Effects of Tides As a small body approaches a larger one, the tidal forces eventually get strong enough to rip it apart ¾ The Roche limit is the distance at which tidal forces overcome gravitational forces holding a body together. ¾ 3 / 1 m M Roche R r ρ α , where R is the distance between two objects with mass m and M , and ρ is the mass density. α is a constant that varies from ~1.19 to ~2.44, depending on the size and strength of the body. ¾ Of course real moons may be held together by forces other than gravity alone. The flexing caused by tidal forces in an eccentric orbit can
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This note was uploaded on 04/15/2009 for the course PHYS 275 taught by Professor Harris during the Winter '09 term at Waterloo.

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Lecture4 - Tides A tidal force arises from the differential...

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