PROBLEM SET #6

ASTR 1200

1. Estimate the radius of the Earth if it were collapsed to the density of a Neutron Star.

2. Why is it that a white dwarf can be formed without the violence of a supernova explosion, but a neutron star cannot?

3. Calculate the thermal luminosity of a neutron star with a 10km radius and a surface temperature of 5000K. Compare to the Sun.

4. An 8km radius neutron star is spinning 1000 times per second. Calculate the speed of a point on its equator. Compare to the speed of light.

5. Given that the Schwarzschild radius for the Sun is 3km, and radius is proportional to mass, calculate the Schwarzschild radius of a 100kg human and a 10¹¹ solar mass galaxy.

6. Using Newton’s Laws, and the formula for the Schwarzschild radius, calculate the acceleration due to gravity at the surface of a one solar mass black hole. Redo for a 10¹² solar mass black hole.