bcrelling said:
Thanks man, it'll take me a while to digest it all.
BTW, I think I stumbled upon an aditional proof that gravitaty does increase for moving objects.
Consider the perihelion orbit of Mercury, its trajectory can be explaned that as mercury nears the Sun, its velocity increases and hence is mass and gravity also increase. This would cause a sling shot effect putting the eliptical orbit on a new trajector every time it passes.
I've seen this claim before, and it baffles me. Where did you read it?
Working things out for myself, I get a totally different answer.
Start with Newton's equations
F = GmM/r^2 = mv^2/r
If we substitute the "relativistic mass" blindly in for m on both sides of the equation, we conclude that nothing happens!
This is obvious and sensible - it says that things fall at the same rate, regardlelss of mass. If the mass of our particle changes with its velocity, it doesn't matter as long as our quasi-Newtonian-made-up-on-the-spot "gravitational mass" matches our quasi-Newtonian-made-up-on-the-spot "inertial mass".
If we substitute it on one side, and not the other, we are violating the conservation of momentum, the principle that every action has an equal and opposite reaction.
I don't think this even turns out to correctly predict the magniutde of the precession even if we take it seriously, and it's really ugly. As well as poorly motivated.
As far as the GR explanation goes, the majority of the precession can be explained by the PPN parameter gamma, which as other posters have remarked is due to the distortion of space.
There is also an affect from the PPN parameter beta, this effect actually goes in the opposite direction from the gamma effect.
This makes precession a more complex topic than light bending, or the Shapiro effect, both of which depend only on \gamma and not \beta
I.e. from MTW's gravitation, pg 1110
\delta \phi_0 = \frac {\left( 2 - \beta + 2\gamma \right) }{3} \frac {6 \pi M_{sun}}{a \left( 1 - e^2 \right) }
Here \beta = \gamma = 1 are PPN parameters
M_{sun} is the mass of the sun
a is the semi-major axis of the orbit
e is the eccentricity.
\delta \phi_0 is the perihelion shift.
So we see that \gamma over-explains the precession, and \beta fights this over-explanation, giving the right answer.
\gamma models spatially curvature. \beta is a second order term in the expression for gravitational time dilation, i.e.
g_{00} = (1 - 2M/r + 2 \beta M^2 / r^2 )
It might be instructive to sketch how we actually find the orbits in GR:
We start with the metric in the equatorial plane (we can use the whole metric if we want, but we don't need the non-equatorial terms, it's slightly simpler without them).
<br />
ds^2 = -f(r)\, dt^2 + g(r)\, dr^2 + h(r)\, d\phi^2<br />
We can work it out in a couple of different coordinate systems, the PPN system uses
f = c^2 \left( 1 - \frac{2GM}{c^2 r} + \frac{2 G^2 M^2}{c^4 r^2} \right) \quad g = \left( 1 + \frac{2GM}{c^2 r} \right) \quad h = r^2 \left( 1 + \frac{2GM}{c^2 r} \right)<br />
standard Schwarzschild is
f = c^2(1 -\frac{2 G M}{c^2 r}) \quad g = 1 / (1 -\frac{2 G M}{c^2 r}) \quad h = r^2
In either case, we apply the geodesic equations,
http://en.wikipedia.org/wiki/Solving_the_geodesic_equations
The radial term gives us:
<br />
\frac{d^2r}{d \tau^2} + \Gamma^r{}_{tt} \left( \frac{dt}{d \tau} \right) ^2 + \Gamma^r{}_{rr} \left( \frac{d r}{d \tau} \right)^2 + \Gamma^r{}_{\phi \phi} \left( \frac{d \phi }{d \tau} \right)^2 = 0<br />
We need two more equations (this is one of three geodesic equations we need to solve, the one that's formally similar to the Newtonian radial force equation.)
The funky-looking Chrsitoffel symbols are well defined in the literature - they're a pain to compute by hand, but you can compute them directly from the metric coefficeints.
In particular
\Gamma^r{}_{tt} = \frac{(\frac{df}{dr})}{ 2g} \quad \Gamma^r{}_{rr} = \frac{(\frac{dg}{dr})}{ 2g} \quad \Gamma^r{}_{\phi \phi} = - \frac{(\frac{dh}{dr})}{ 2g}
