Summary: ASTR 3730: Astrophysics 1 ­ Problem Set #5
Solutions
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.
Solution: For an estimate, it suffices to calculate the gravitational potential
energy by assuming that the gravity is dominated by the core, and that the
characteristic radius of gas in the envelope is just the stellar radius:

W ª -
GMcore Menv
R
= -2.3¥1045
erg
(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.
Solution: For g = 5/3, the virial theorem is:

Source: Armitage, Phil - Department of Astrophysical and Planetary Sciences, University of Colorado at Boulder

Collections: Physics