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[Phys-L] Re: Help on a problem from Goldstein



At 11:08 AM 4/12/2005, Leigh Palmer wrote:
Problem 13 from Chapter 6 of Goldstein's "Classical Mechanics" reads:

Show that the relativistic motion of a particle in an attractive
inverse square law of force is a precessing ellipse. Compute the
precession of the perihelion of Mercury resulting from this
effect. ( The answer, about 7" per century, is much smaller than
the actual precession of 40" per century which can be accounted
for correctly only by general relativity.)

Can someone kickstart my brain with a hint as to what approach I should
consider to solve this problem?

Thanks,

Leigh

A somewhat similar problem is sometimes offered: [Phys 4222 UFlorida]

"Suppose that the sun were surrounded by a dust cloud of
uniform density which extended at least as far as the orbital radius of
the Earth. The
effect of the dust cloud is to modify the gravitational force experienced
by the Earth,
so that the potential energy of the Earth is (neglecting the effects of the
planets)
U(r) = -GMm/r + 1/2 kr^2
where M is the mass of the sun, m is the mass of the Earth, G is the
gravitational
constant, and k = 4 pi rho mG/3 (note that k > 0, so this additional term
is attractive).
The effect of the dust cloud is to cause elliptical orbits about the sun to
precess slowly."


Does this provide any traction, I wonder?




Brian Whatcott Altus OK Eureka!
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