Fall 2002                  Special Topics: Astrophysics (Phys 493)

Dr. I. Fernini

                                        Homework # 5

       

Due in the first lecture after Eid Vacation - Late HW won't be accepted anymore.

 

Problem 1:

 

Estimate the radii of both a main-sequence M star (M V) and a red supergiant (M I) using information from the H-R diagram in the book (chapter 13).

 

 

Problem 2:

 

Using the H-R diagram in Figure 13-7 and the relationship between temperature and spectral type in Figure 13-6, estimate how many times larger is Betelgeuse than

(a)                 the star Antares

(b)                the star β Crucis

(c)                 the star α   Centauri

 

 

Problem 3:

 

When the observed masses and luminosities for stars in binary systems are graphed, we obtain  the correlation called the mass-luminosity relationship (or M-L relation). Eddington (1924) calculated that the mass and luminosity of normal stars like the Sun are related by:

 

                                                             L/L_O  = (M/M_O)^α   

 

L_O represents the Sun’s luminosity, M_O the Sun’s mass, and α  the slope of the curve representing the relation.

 

For general use, an adequate form of the M-L relation is :

 

                          L/L_O  = (M/M_O)^4.0              for stars of mass M > 0.43 M_O

 

                  L/L_O  = 0.23 (M/M_O)^2.3     for stars of mass   M < 0.43 M_O

 

(a)  Use the mass-luminosity relation to compute the luminosity range of stars from the observed mass range of  0.085 M_O to 100 M_O.

(b)   What is the mass of a star that is 0.1 the luminosity of the Sun?

(c)  What is the mass of a star that is 1000 times the luminosity of the Sun?