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/LO
= (M/MO)α
LO represents the Sun’s luminosity, MO
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/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?