Homework 3 : Properties of Stars

(due at the start of class on the 24^th April 2003)

1. Suppose you are a space explorer on board a starship which goes into orbit around a previously uncharted blue star. Your spaceship is orbiting the star at a distance of 3A.U., and you deduce that it will take you half of an Earth year to orbit around the star once. Furthermore, when you deploy a solar panel from the side of your space-craft, you collect 1000 times more energy than when the same solar panel is used to collect Sun-light on Earth. Using this information, deduce

1. a rough estimate for the temperature of the star,

2. the luminosity of the star (you can give you answer in terms of Sun luminosities… i.e., “this star is <your-answer> times more luminous than the Sun”). Show your working.

3. the mass of the star (you can give your answer in terms of Sun Masses). Show your working. [Hint – think about the discussion in class on how we can measure the mass of the Sun. We discussed a formula that will be very useful for this question.]

Do you think this star will suffer a supernova explosion at some point in the future? Will it leave a White Dwarf, a Neutron Star or a Black Hole?

2. The Sun has a total mass of 2´10³⁰kg, of which initially (i.e., at the time of formation) 75% is hydrogen. It “burns” (or more correctly, processes) hydrogen at a rate of about 6´10¹¹kg per second.

1. If you suppose that the Sun processes all of its hydrogen while on the main sequence, calculate the “main-sequence lifetime” of the Sun. Give you answer in terms of years. [Hint – you will need to figure out how many seconds are in a year.]

2. The actual main-sequence lifetime of the Sun is 10 billion years. What is the reason for the difference between this number and the one that you calculated in part (a) above.