Yo buddy! You're overthinking this a little, well, I think, either ways. yeah. We can go about all these fancy equations/etc, but, in the end there is another way: just consider conservation of energy.
I've never done rotational dynamics for stars/etc. Well, I have, and I know all this other stuff you're talking about. But, the first method that hit my head was just using conservation of energy, it's a lot simpler.
It's in eccentric elliptic orbit: it is still in orbit. The circular centripetal force at this point must be enough such that it provides acceleration to continue the orbit. Hence, use centripetal force to create an energy equation for initial kinetic energy, i.e. the non relativistic version (v<<c)
So, with initial energy, our gravitational potential equation, and a change in radius, you should be able to take it from there
If that isn't a satisfying answer, I'll grudgingly have to go whip out my old physics book and figure this out the more complicated way :_;
Also, I'll just quickly give a hint: your order of magnitude is off, i.e. by a factor of three I think.