It did not really start until May 25 when everybody was in town.
By September, the sessions produced the US Constitution that we know today. It was subsequently sent to the states for ratification. The Bill of Rights, or the first 10 Amendments, were added between 1789-1791.
It was a contentious summer. Let me recommend "Miracle in Philadelphia" to follow the day to day stories.
P.S. You can listen to my show (Canto Talk). This is another good book: