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What did you get when you integrated?

here is a picture of it

I'm not sure. Alpha is going to be a function of r(t) and r(t+dt).

alpha=omega*t

That one should be helpfull...

Alpha, as an angle, should be the radial angle if it's omega*t.
|dw:1352577895185:dw|

but that gives me:

but I want to find T as a function of r. How does this help?

Sorry, sorry. I missed an r term. One second.

like that?

Yep. Looks okay to me.

It seems that we only used mathematics but not Kepler´s second law.

... ah so we used that to claim that omega is constant!

It's not that. It's that we made a simplification based on our understanding of the problem.

Where did we simplify?