Stellar model 1:
PROBLEM SET
Constant density model
PROBLEM 1.
Show that if the density is constant then  =
PROBLEM 2.
Show that
r
3
m(r) =  4r2dr = 4r  =
3
0
3M
.
4R3
Mr3
.
R3
PROBLEM 3.
written
Show that the equation of hydrostatic equilibrium can be
PROBLEM 4.
Show that the equation in PROBLEM 3 can be written as
R
3
P(R) - P(r) = - G(4r2)dr .
3r
r
R
2
0 - P(r)= - G4 rdr .
3
r
PROBLEM 5.
Show that the equation of PROBLEM 4 results in
P(r) =
2G2(R2 - r2) .
3
PROBLEM 6. Show that the equation in PROBLEM 5 can be written in each
of the two forms
P(r) =
3GM2(R2 - r2)
GM(R2 - r2)
,
or
P(r)
=
.
2R3
8R6
GM
2R
=
3GM2
.
8R4
PROBLEM 7.
Show that Pc =
PROBLEM 8.
Taking the earth to have a constant density, find Pc.
PROBLEM 9.
Taking the sun to have a constant density, find Pc.