You can't really do it analytically. __doPostBack
could be arbitrarily complex.
What you should do instead is install Firebug (assuming you are using Firefox), activate the Network tab, press "Persist", and then click that button. The Network tab will show you the actual network traffic, and you can deduce the real URLs from that. In fact, you can just right-click on the particular network request that interests you and select "Copy as cURL" and it will put the curl instructions -- complete with things like cookies and headers -- in your paste buffer.
There is a similar function built-in to Chrome.