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Mar30-12, 01:26 PM
P: 939
Quote Quote by D H View Post
They're a bit more complex (well, more than a bit more complex) than that. See equation 8.1 in, for example (this is what JPL uses), or see equation 10.12 in
So basically yes, except it's hard to decide what the coefficient in place of 1/2 is because they are using vectors :) The equation in IERS document is pretty simple: first you have the correction from Schwarzschild metric, then two terms which look like v^2/c^2, and then corrections O(c^-4) which contain angular momentum and then it gets properly confusing, but we can drop those for now. The last term looks like some kind of angular momentum correction from the Sun, so lets drop that one too because we don't care about that... Finally, lets just be lazy and say we're on a circular orbit so [itex] \mathbf{r} \cdot \mathbf{\dot{r}} = 0 [/itex] and that it's general relativity so [itex] \gamma = 1 [/itex] and we're left with just
[itex] \Delta |\mathbf{a}| = \frac{GMv^2}{c^2 r^2} [/itex] which is actually twice as big as you'd expect. Is that about right?