A particle of unit mass moves in a plane under a central force lamda^2 / r^5 where lamda is a constant.
Explain why (r dot)^2 + r^2.(theta dot)^2 - lamda^2 / (2r^4) = constant
done this part
The particle is projected from a point P at which r = a with speed lamda / (root2 a^2). Find a differential equation for r as a function of the polar angle theta along the orbit, and show that the orbit is a circle through O.
I'm not entirely sure how to start this part
my initial thought was to put the IC's into the above equation. But this simply gives me a constant of zero and then I cant see how to progress from there..