AST 101 HW000424 due in two weeks

1. If an open cluster contains 1,500 stars and is 30 pc in diameter, what is the average distance between the stars?
2. How massive could a star be that will survive for 5 billion years?
3. The Crab Nebula is now 1.35 pc in radius and is expanding at 1400 km/s. About when did the supernova occur?
4. Suppose that a neutron star has a radius of 10 km and a surface temparature of 10⁶ K. How luminous is it?
5. What evidence do we have that black holes exist?