Two-body problem given as
where the moment of the momentum vector mh
The vector solution to the above equation may be obtained by first taking the cross-product with the constant h and integrating once with respect to time. This yields
The final solution to the equation is then obtained by taking the dot product of above equation with r, is
The Attempt at a Solution
I have no idea what the author is doing. How does cross product with the momentum and then dot product with r solve the equation?
I try following his step but I get a different integration result
I have no idea how his integration w.r.t. time for the GM/r2 reduces it to GM/r and how to cross product GM/r2 with h since they are unknown variables?