Energy in two body orbits

I'm trying to derive the energy in an orbit and don't quite understand it (which makes remembering it pretty difficult for exams!)

I've put parts of my notes relating to this below.

My first problem is with the integration (2nd equation to 3rd equation). I've tried using integration by parts, but cannot get this answer. I've tried searching on the internet for the answer, but can't find it.

My next problem is the final step, getting to C=E((m1+m2)/m1m2). It says using eq 33, which is the equation after 'Integrating' (the third equation in the list). I don't understand how this is related at all?

Thanks in advance for any help, this has got me totally confused!

[PLAIN]http://img718.imageshack.us/i/energy1.png[PLAIN]http://img151.imageshack.us/i/energy2.png [Broken]

http://img718.imageshack.us/i/energy1.png
http://img151.imageshack.us/i/energy2.png

Sorry about the links, can't get it to show the pictures in the post

Last edited by a moderator:

It is a matter of algebraic manipulation. The last two equations on the energy1.png page can be combined and to solve for C in terms of m1, m2, and E. Is there a relationship between $$\mu$$, m1, and m2?