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

kg/m³

Volume Earth = 6x10²⁴kg/2x10¹⁸kg/m3 = 3x10⁶m³

1.33pr³ = 3x10⁶m³

r = 100m

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

The electron degeneracy of a white dwarf is built up slowly in the center of a star. The only way to reach neutron degeneracy is through the sudden collapse of electron degeneracy.

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

L=sAT⁴=5.7x10^-8x4px(10⁴)²x(5000)⁴=4.5x10¹⁶W

L_ns = 10^-10L_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.

Circumference = 2pr = 50km

At 1000 per second, v = 50,000km/s

V = .16c

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.

R_human = 3000m x 100kg / 2x10³⁰kg = 1.5x10^-25 m

R_galaxy = 3km x 10¹¹ = 3x10¹¹ km

6. Using Newtons 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.

a = 1.5x10¹³x10¹²/10²⁴ = 15m/s² = 1.5 x gravity of Earth