Summary: ASTR 3730: Astrophysics 1 Problem Set #5
Due in class Wednesday 3rd December
1) A giant star has a radius of 200 Rsun, with a compact core of mass 0.6 Msun
surrounded by an extended envelope of mass 0.2 Msun.
(i) Estimate the gravitational potential energy of the envelope.
(ii) By applying the Virial Theorem to the envelope (assuming that it is an ideal
gas with g = 5/3) determine the thermal energy U of the gas in the envelope, and
hence estimate the binding energy (equivalently the total energy: gravitational
plus thermal) of the envelope.
(iii) Suppose that the envelope is composed entirely of ionized hydrogen. How
much energy would be liberated if the gas cooled and all the protons and
electrons recombined to form neutral hydrogen (the recombination energy is 13.6
eV per atom)?
2) Consider a transiting hot Jupiter planet orbiting a Solar mass star. The star has
a radius of 7 x 1010
cm, while the planet has a radius of 8.5 x 109
(i) Sketch the lightcurve (flux vs time) that you would expect to see during the
(ii) Calculate the maximum depth of the transit, expressed as a percentage of the