- #1

tdotson

My problem involves the precession of the perihelion of Mecury

F sub g = - (GMm)/r^2 * (1 + a/r) where a << r

I proved in previous parts d^2r/dt^2 - r*(dtheta/dt)^2 =

-GM/r^2 * (1 + a/r) [eqn 1] and r* d^2theta/dt^2 + 2*dr/dt*dtheta/dt = 0

I also used u(theta) = 1/r(t) to turn eqn 1 to d^2u/dtheta^2 +

u(1-GMa/l^2) = GM/l^2 where l = L/m.

Where I'm stuck is showing the solution is u(theta) = u(sub 0) *

(1+ ecos(n(theta - theta (sub 0))) where e and theta (sub 0) are constants of integration and u(sub 0) and n are in terms of a, G, M and l. I've tried many times but can't get it to work out.

F sub g = - (GMm)/r^2 * (1 + a/r) where a << r

I proved in previous parts d^2r/dt^2 - r*(dtheta/dt)^2 =

-GM/r^2 * (1 + a/r) [eqn 1] and r* d^2theta/dt^2 + 2*dr/dt*dtheta/dt = 0

I also used u(theta) = 1/r(t) to turn eqn 1 to d^2u/dtheta^2 +

u(1-GMa/l^2) = GM/l^2 where l = L/m.

Where I'm stuck is showing the solution is u(theta) = u(sub 0) *

(1+ ecos(n(theta - theta (sub 0))) where e and theta (sub 0) are constants of integration and u(sub 0) and n are in terms of a, G, M and l. I've tried many times but can't get it to work out.

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