Download Due: January 14, 2014 Name: White dwarfs are “has been

Homework Chapters 13-14
ASTRON 311 Introduction to Astronomy
Due: January 14, 2014
Prof. Menningen
p. 1/2
Name: ______________________________________
1.
Spectral classification of a star into the lettered categories, O, B, A, F, G, K, M, is carried out by
a. finding the wavelength of peak emission in the continuum spectrum of the star.
b. determining the total energy emitted at all wavelengths by the star, taking account of the full spread of
wavelengths and their distances, to place the star into its luminosity class.
c. determining the relative mass through the study of binary star motions to place the star into its proper
mass classification.
d. examining the relative depths of absorption lines from various neutral and ionized atoms in a
stellar spectrum.
2.
Using the mass-luminosity relationship for main sequence stars shown in Fig. 13.21, which of the following is the
correct sequence of stars in increasing order of mass?
a. Barnard's Star, Sirius, the Sun, Spica
b. Spica, Barnard's Star, the Sun, Sirius
c. Spica, Sirius, the Sun, Barnard's Star
d. Barnard's Star, the Sun, Sirius, Spica
3.
How do white dwarfs differ from brown dwarfs? Which are more massive? Which are larger in radius? Which are
denser?
White dwarfs are “has been” (dead stars), whereas brown dwarfs are “never was” objects
(their masses are too small to initiate nuclear fusion). White dwarfs are more massive, smaller
in radius, and much denser than brown dwarfs.
4.
Stars A and B are both equally bright as seen from Earth, but A is 60 pc away while B is 15 pc away. Which star has
the greater luminosity? How many times greater is it?
Use the ratio similar to the one on page 365 of your text or Box 19-2 of the handout:
2
2
LA  d A  bA  60 pc  b
 

  16
LB  d B  bB  15 pc  b
LA  16 LB
5.
Star A has a brightness of 1.04×10−7 W/m2 and is known by parallax to be 8.57 ly away. Star B is 233 times less
luminous than Star A and has a brightness of 1.87×10−11 W/m2. How far away is Star B? Show your work!
Use the equation on p. 344 or the ratio p. 365 that relates brightness to luminosity and distance.
dB

dA
LB 4 BB
LA 4 BA

LB BA

LA BB
 2331 LA  1.04 107 W/m2 

LA 1.87 1011 W/m 2

 4.89
d B  4.89 d A  4.89  8.57 ly   41.9 ly
6.
Try the H-R Diagram Interactive under chapter 12 of your textbook companion web site. Set the speed slide bar to
"automatic" and determine the mass of a star that has a surface temperature of about 12,500 K (a) If you observe a
star cluster where no star has a surface temperature that exceeds 12,500 K, about how old is the cluster? You can use
the star Birth/Death slide bar after the star has been created for assistance in finding the answer. (b) About how much
more time does the Sun spend on the main sequence compared with a main sequence star of temperature 12,500 K?
(a) The star with a surface temperature of 12,500 K is about 1.5 solar masses and spends about
1.5 billion years on the main sequence. Thus the cluster is about 1.5 billion years old.
(b)
The Sun spends about 5.5 billion years on the main sequence, about 3.7 times longer than
the 1.5 solar mass star.
Homework Chapters 13-14
ASTRON 311 Introduction to Astronomy
Prof. Menningen
p. 2/2
7.
How does the temperature of an interstellar cloud affect its ability to form stars?
a. Higher temperatures inhibit star formation.
b. Star formation is independent of the temperature of the cloud.
c. Higher temperatures help star formation.
d. Star formation is so complicated that it is not possible to say how one quantity, such as temperature,
affects it.
8.
A protostar of about 1 solar mass is gradually contracting and becoming hotter. This will cause its position on the
Hertzsprung-Russell diagram to shift slowly
a. upward and toward the left.
b. downward and toward the left.
c. downward and toward the right.
d. upward and toward the right.
9.
Describe the energy source that causes a protostar to shine. How does this source differ from the energy source inside
a main-sequence star?
The energy radiated from a protostar comes from gravitational potential energy that is
converted to kinetic and then thermal energy when the matter within the protostar falls toward
the core. The energy radiated by a main-sequence star comes from nuclear fusion.
10.
At one stage during its birth, the protosun had a luminosity of 1000L and a surface temperature of about 1000 K. At
this time, what was its radius? Express your answer in three ways: as a multiple of the Sun's present-day radius, in
kilometers, and in astronomical units.
2
L 
 R  T 
and T*

4
We make use of the equation given in the box on page 346:  *    *   *  , where the subscript
 L   R  T 
indicates values for the protosun. We are told that
Solve for R* R :
( L* / L )
R*


R
(T*/T ) 4
1000
 0.1724 
4
L*
 1000
L
T
1000
 0.1724 .
5800
 1060
The radius of the protosun was about 1100 times larger than that of the present Sun. In terms of
kilometers this is 1060  6.96  105 = 7.4  108 km, or in terms of AU, this is
7.4 108 km 
1 AU
 4.9 AU almost out to the orbit of Jupiter (5.2 AU)!
1.496 108 km
11.
What particular feature of stellar behavior is associated with the fact that a star is on the main sequence in the
Hertzsprung-Russell diagram?
a. The star is generating internal energy by hydrogen fusion in its core.
b. The star is slowly shrinking, thereby releasing gravitational potential energy.
c. The star is generating energy by helium fusion in its core, having stopped hydrogen "burning."
d. The star has ceased nuclear "burning" and is simply cooling down by emitting radiation.
12.
The two stars that make up a binary star have estimated masses of 0.99M
Find the average separation between the two stars in kilometers.
and 0.62M
and a period of 8.0 hours.
The period is 8 hours or 1/3 day. The total mass is 0.99M  0.62M =1.61M .
From Newton’s form of Kepler’s third law (p. 357) (m + M)P2 = a3 or
2
 1 day
1 yr 
6
3
a   m  M  P  1.61 solar masses  

  1.34  10 AU
3
orbits
365
day


3
2
a  3 1.34  106 AU3  1.10  102 AU  1.496  108 km/AU  1.65  106 km