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

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Leigh,

Apparently the assignment is to apply special, but not general
relativity.  I suppose I'd try to solve the equation

    -G M r_vec/r^2 = d(gamma v_vec)/dt

separating out the radial and azimuthal components and performing
something like the usual small amplitude radial oscillation analysis
to find the apsidal angle.

But maybe that isn't saying anything you hadn't already thought of
and the stumbling block lies further along that path.

John Mallinckrodt
Cal Poly Pomona

> 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
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