Homework 2
Textbook Problems: 10.3,10.4,10.7,10.13,10.14
Due: 10/28/2009
Estimate the ratio of radiation pressure to gas pressure in the core of the
Sun. Assume that the core of the Sun has temperature T = 15.5 million K,
density 150 grams per cubic centimeter, and has composition 90 % hydrogen
and 10 % helium by number. For what temperature would radition pressure and
gas pressure be of the same size in the core of the Sun?
For a star with mass M*, radius R*, and density profile,
as
density = (central density) x (1-r/R*)
where r is the radial coordinate, find
- m(r), that is, how the mass contained within radius r depends on r;
- express the total mass of the star in terms of the central density and
R*;
- solve for the pressure profile P(r) in the star assuming that the pressure
of the star goes to 0 at its surface.
Consider a star with radius R* with constant density. Assume that
the star is pure hydrogen and obeys the ideal gas law (for the pressure).
- Solve for the pressure profile P(r) under the assumption that the pressure
goes to 0 at its surface.
- Using the pressure profile P(r) and the assumption of contant density, find
the temperature profile T(r).
- Assume that the nuclear energy generation
rate scales with temperature as T4, as typical for the proton-proton
chain at the center of the Sun.
At what radius does the nuclear energy generation rate fall to 10 % of its
values at the center of the star? What fraction of the volume of the star does
the nuclear energy generation region occupy?