Homework Handout #3

3.01:  What is the luminosity of a star with absolute visual magnitude MV = 3.49 and bolometric correction BC = -0.11, in units of the solar luminosity?

3.02:  Using the information in Table A4-3 of the book, and assuming the star is Luminosity Class V, what is the approximate spectral type of the star mentioned in the previous problem?  At what wavelength would its spectrum peak if it were a perfect blackbody?

3.03:  (a) Derive the Rayleigh-Jeans Law from the expression for Bn given in the lecture notes, by using the approximation hn << kT. (The first-order expansion ex = 1 + x + ... will be useful.)  Notice that Planck's constant is not present in your answer.  The Rayleigh-Jeans Law is a classical result, which gives rise to the ultraviolet catastrophe that we mentioned in lecture.  (b) Derive the expression for the behavior of the Planck function in the Wien Limit, given in the lecture notes, using the approximation hn >> kT.

3.04: Consider a star consisting of a spherical blackbody with a surface temperature of 28,000 K and a radius of 5.16 x 109 m.  Let the star be located at a distance of 180 pc from Earth.  Determine the following for the star:
(a) Luminosity.
(b) Absolute bolometric magnitude.
(c) Apparent boloemtric magnitude.
(d) Distance modulus.
(e) Radiant flux at the star's surface.
(f) Radiant flux at Earth.