Problem sheet 2 for Astrophysics I
Due March 4th at the beginning of class or in my mailbox in the physics
office before class. We will have a review on March 4th as well, and then the
midterm on March 7. Sound good!?
1. (a) Calculate the gravitational acceleration of the surface of the Sun. [I
know I gave this to you last time.] (b) The effective temperature of the
Sun is about 5800 K. Compute the radiation pressure at the surface of
the Sun. (c) The solar photosphere has a charateristic length of about
300 km. From the gravitational acceleration and one of the equations of
stellar structure, compute the pressure at this depth. You may simplify
the problem by assuming a constant pressure gradient, and a constant
density of 2 × 10−4 kg/m3 . (d) Compare the radiation pressure and the
gas pressure at the surface of the Sun.
2. Using the “mean” properties of stars derived early in the course (i.e. the
mean temperature based on the total internal energy of the star divided
by its mass, and the mean density from straightforward calculation of the
density):
(a) calculate the ratio between the electron scattering opacity in a star
and the free-free absorption opacity in a star as a function of the stellar
mass and radius.
(b) Next, assume that the mass is proportional to the radius, which is
approximately true over much of the main sequence.
(c) Finally, find the mass of a star, in solar units, for which the two
opacities are equal.
3. A unit conversion problem to give a feel for numerical scales: most nuclear
reactions are presented in units of MeV. The fusion of 4 hydrogen nuclei
into a helium nucleus produces about 26 MeV of energy. Given that the
Sun has a luminosity of 4 × 1026 W, how many fusion reactions take place
per second in the Sun?
4. Calculate the energy generated per unit mass, if helium burning produces
equal amounts (mass fractions) of carbon and oxygen.
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