Download Astronomy 120

Astronomy 120
HOMEWORK - Chapter 13
The Stars as Suns
Use a calculator whenever necessary.
For full credit, always show your work and explain how you got your answer.
Be careful about units!
Please CIRCLE or put a box around your final answer if it is numerical.
1. Zeilik Study Exercise 13.1
In the winter sky, you see the following stars: Capella (yellowish), Betelgeuse (reddish), and
Sirius (bluish). List these stars in order of increasing surface temperature. Estimate the
surface temperature of Betelgeuse and of Sirius.
2. Zeilik Study Exercise 13.9
Jupiter is about 5 times as far from the sun as the earth is (  5 A.U.’s compared to 1 A.U. ).
By how much less is the sun’s flux at Jupiter compared to that at the earth?
3. Zeilik Study Exercise 13.3
What limits the accuracy of ground-based heliocentric parallax measurements?
4. Zeilik Study Exercise 13.4
Refer to Figure 13.15 to answer the following questions.
(a) Capella and the sun have roughly the same surface temperature. Which star is larger?
(b) Regulus and Capella have about the same luminosity. Which star is larger?
(c) Vega and Sirius have about the same surface temperature. Which star is more luminous?
(d) Which star would appear redder, Vega or Pollux?
5. Zeilik Study Exercise 13.6
What procedure does an astronomer follow to find out a star’s density? Hint: Divide mass by
volume to get density.
6. Zeilik Study Exercise 13.7
Consider a binary star system that does not eclipse and in which one star is much brighter
than the other. Then the absorption lines from the fainter star do not appear in the spectrum,
but those of the brighter one do. Describe how the Doppler shift would appear from the
orbital motion of the stars.
7. Zeilik Study Exercise 13.8
The star Regulus has a mass about five times that of the sun. Use the mass-luminosity
relationship to estimate the luminosity of Regulus.
8. Zeilik Study Exercise 13.2
Consider stars with the following spectral types: M I, G III, and A V. Which star is the
largest? Which is the most luminous?
9. The Sun produces energy primarily via the proton-proton chain. We can figure out how much
energy one such reaction will release by using the famous Einstein relation:
E  mc 2
where E is the energy in Joule's
m is the mass in kilograms
c is the speed of light in meters per second
c  2.9979  108 m s
The mass in this equation refers to the difference in mass between
4 protons  4 electrons  6.694  10 27 kg , and a helium nucleus ( 2 protons  2 electrons )
 6.644  10 27 kg .
a) Find the difference in mass and then the energy released.
b) if the Sun emits 3.9  10 26 Joules per second, how many of these reactions must occur
per second?
10. The flux we receive from the Sun is about 1370 Watts per square meter. (A watt is a unit of
power which is equivalent to 1 Joule per second). Sirius sends us a flux of about
1  10 7 W m 2 . Luminosity is related to flux by the following equation:
L  4r 2  F
where L is the luminosity in Watts
r is the distance in meters
F is the flux in W/m2
a) The Sun is 1.49598 x 1011 m away, what is the Sun's luminosity?
b) Sirius is 8.8 ly away (1 ly = 9.46053  1015 m ). What is Sirius' luminosity?
c) If Sirius had a surface temperature of 15,000 K, what would its luminosity be then? We
need to remember that flux has a temperature dependence through the equation....
F  Teff 4
where Teff is the "effective" or surface temperature and  is the Stefan-Boltzman constant.
  56697
.
 108 W 2 4 . Assume Sirius has a radius of 8  10 8 meters - this is where
m K
the flux is measured.
11. Stellar parallax allows us to find the distances to stars using simple trigonometry. The figure
below shows the geometry.
Earth
R
p
Sun
d
tan p 
R
d
so that
d
R
tan p
but the tangent of small angles is approximately equal to the angle itself in radians. So....
d
R
,
p
if R is in A.U.'s and p is in arcsec's, then d is in parsec's and 1 pc = 326
. ly . See Focus 13.2
(Zeilik, p. 286).
the smallest detectable parallax is about 0.001 arcsec; how far would a star with this
parallax be?
12. The relationship between the apparent and absolute magnitude of a given star is expressed as:
m  M  5log d  5
where m is the star's apparent magnitude, M is the star's absolute magnitude and d is the
distance to the star in parsec's.
If the star in problem #11 had an apparent magnitude of 5, what would its absolute
magnitude be?
13. On the Hertzsprung-Russell (HR) diagram on the back of this page, plot points representing
the Luminosity and Surface Temperature of each of the 16 brightest stars (in the northern
hemisphere) on your list. (The values of luminosity (in units of the Sun's luminosity) and the
surface temperature are given in your list of stars.) Write the name of each star next to its
location on the HR diagram.
14. Invent a new mnemonic for spectral classification. O-B-A-F-G-K-M
(e.g. Oh boy, a furry gorilla kissed mom!).
HERTZSPRUNG – RUSSELL DIAGRAM
106
105
104
103
102
10
1
10-1
30
25
20
15
10
9
8
7
6
SURFACE TEMPERATURE (103 K)
5
4
3
2
16 BRIGHTEST STARS
(VISIBLE FROM NORTH OF THE TROPICS)
___________________________________________________________________________
STAR
DISTANCE APPARENT LUMINOSITY Tsurf(oK)
TYPE
(light years) BRIGHTNESS (Sun = 1)
(Compared to
the sun if it
were 32.6 ly
distant
___________________________________________________________________________
1. Sirius
8.7
310
38
9,700 (white main
sequence)
2. Arcturus
36
86
200
4,600 (orange-red giant)
3. Vega
26.5
80
97
10,000
4. Capella
45
76
170
5,250
900
74
120,000
11,700
5. Rigel
6. Procyon
7. Betelgeuse
11.3
520
59
7.59
6,670
57
110,000
3,100
(white main
sequence)
(yellow giant)
(blue-white super
giant)
(yellow main
Sequence)
(red super giant)
8. Altair
16.5
41
12
7,940
9. Aldebaran
68
39
500
4,150
10. Spica
220
34
9,000
22,000
11. Antares
520
35
20,000
3,200
(blue-white main
sequence)
(red super giant)
12. Pollux
35
29
53
4,850
(orange-red giant)
13. Fomalhaut
22.6
28
20
9,000
1600
26
110,000
9,200
(white main
sequence)
(white super giant)
15. Regulus
87
24
410
13,000
16. Castor
45
20
53
10,000
14. Deneb
(white main
sequence)
(orange-red giant)
(blue-white main
sequence)
(white main
sequence)