 
Summary: ASTR 3730: Astrophysics 1 Problem Set #4 Solutions
1) A simple model of a star has mass M, radius R, and density given as a function
of radius by (as in the previous problem):
r(r) = rc 1
r
R
È
ÎÍ
°.
If the central pressure in the star is Pc, and the pressure at r = R is P = 0, integrate
the equation of hydrostatic equilibrium to find an expression for the pressure as
a function of radius [you will need to use the expression for m(r) derived last
time in the hydrostatic equilibrium equation].
Solution: We need to make use of two equations:
dP
dr
= 
