Orbital Velocities

[bknight]

Just needs a little light algebra to get the equation into the right order and away you go.

Yes, you are correct, but I don't remember how to compute
R_a² + R_a * R_p in terms of R_a

In this case, R_a is the unknown x, so a=1, b=R_p and c=-2*GM(R_p)/V_p²

But the left hand side may not be equal to zero
Remember from the original equation
.5V_p² = GM(R_p/(R_a(R_a+R_p))

EDIT:
ax²+bx+c=d

[bknight]

Never mind I get it, thanks for the assistance.