Find the orbit of a planet in a grav. field corresponding to the metric
in the Newtonian limit with the initial conditions at t=0, x=R, dx/dt=[itex]\beta[/itex],0=y=z=dy/dt=dz/dt where alpha and beta are cositive constants.
The Levi-Civita connexion and the geodesic equations
The Attempt at a Solution
I calculates the connexion coefficients and wrote down the 4 geodesic equations with the proper time as the parameter:
I can solve the 4th equation of course:
and if I understand correctly, the Newtonian limit means that
But I don't see how that can be applied here to simplify the equations.