Algebra/differentiation/trig expansions/ small approximation

[vela]

In fact, the book does a similar exercise a few pages on (for timelike geodesics instead of null) and so the equations differ very slightly.

Is this problem considering a null geodesic? I figured it would be a timelike geodesic since you're comparing it to a Newtonian orbit.

I take it M=mass, J=angular momentum, e=eccentricity, and u=1/r. Is that right?

For what it's worth, I don't see how you're supposed to get the expected result without some other assumption that allows you to neglect more terms.

 

[binbagsss]

Is this problem considering a null geodesic? I figured it would be a timelike geodesic since you're comparing it to a Newtonian orbit.

I take it M=mass, J=angular momentum, e=eccentricity, and u=1/r. Is that right?

For what it's worth, I don't see how you're supposed to get the expected result without some other assumption that allows you to neglect more terms.

Apologies yes it's time-like, I said this the wrong way around.
Yes, with $e$ as given by #27.

In justifying neglecting the $u^{3}$ the book gives an idea of figures for the case of the Earth orbitting the Sun, these are:
$2Mu$ ~ $10^{-8}$
$J^{2}u^{2}$~$10^{-8}$
$2MJ^{2}u^{3}$~$10^{-16}$