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.
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).
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
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/LO† = (M/MO)α ††
LO represents the Sunís luminosity, MO the Sunís mass, and α† the 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 of† 0.085 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?