PROBLEM SET #4

ASTR 1040

1. The main-sequence lifetime of the Sun is about 1010 years. What would be the lifetimes of a) a 10-solar mass, 1000 solar luminosity blue giant, and b) an 0.1 solar mass, .001 solar luminosity red dwarf?

2. Calculate the radius of a red supergiant with temperature 3000K and luminosity 10000 solar luminosities. How many planets in our our solar system would be engulfed?

3. Estimate the radius of the Earth if it were collapsed to the density of a White Dwarf.

4. Why will the Sun fail to become a Type I supernova? Why will the binary system Alpha Cen fail to become a Type I supernova? (It is a G2 and K5 star separated by 10AU.)

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

6. 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.

7. 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.

8. 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.