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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 obtainthe 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/LO= (M/MO)α ††

LO represents the Sunís luminosity, MO the Sunís mass, and αthe slope of the curve representing the relation.

 

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

 

††††††††††††††††††††††††† L/LO= (M/MO)4.0††††††††††††for stars of mass M > 0.43 MO

 

††††††††††††††††† L/LO= 0.23 (M/MO)2.3†††† for stars of mass†† M < 0.43 MO

 

(a)  Use the mass-luminosity relation to compute the luminosity range of stars from the observed mass range of0.085 MO to 100 MO.

(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?