USAAAO — 2020 First Round

In a particular compact binary system consisting of a black hole and a main sequence star, the black hole has a mass of 23.2 M☉ and the main sequence star has mass of 15.6 M☉. The two stars are separated by 1 AU. A clump of gas of mass 1 M☉ detaches from the main sequence star. When the gas is 1000 km from the black hole, what is its total energy? Neglect viscous forces. [Distance updated from the original exam’s 1 km, which lies inside the black hole’s event horizon.]