PROBLEM SET #5 --Answers

PROBLEM SET #5 --Answers APAS 1200

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?

a)

years

b) years

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?

L=s4pR²T⁴

10000x4x10²⁶=5.7x10^-8x4pR²3000⁴

R=2.6x10¹¹m

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

White Dwarf is one million times denser, thus the radius of the Earth would be the cube root of one million times smaller, or 100 times. This would make it about 40miles across.

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.)

A Type I supernova requires a binary system where mass transfer from one star drives the white dwarf member above the Chandrasekhar Limit. The Sun is not a binary. The stars in Alpha Cen are too far apart for mass transfer.