Astronomy 120
HOMEWORK - Chapter 17
The Stars
Use a calculator whenever necessary.
For full credit, always show your work and explain how you got your answer in full, complete sentences on a separate sheet of paper.
Be careful about units!
Please CIRCLE or put a box around your final answer if it is numerical.
If you wish, you may discuss the questions with friends, but please turn in your own hand-written solutions, with questions answered in your own way.
- Chaisson Review and Discussion 17.1
How is parallax used to measure the distances to stars?
2.Chaisson Review and Discussion 17.3
Explain two ways in which a star’s real motion through space translates into motion that is observable from Earth.
- Chaisson Review and Discussion 17.4
How do astronomers go about measuring stellar luminosities?
- Chaisson Review and Discussion 17.5
Describe how astronomers measure stellar radii.
- Chaisson Review and Discussion 17.7
What is the difference between absolute and apparent brightness?
- Chaisson Review and Discussion 17.8
How do astronomers measure stellar temperatures?
- Chaisson Review and Discussion 17.9
Briefly describe how stars are classified according to their spectral characteristics.
- Chaisson Review and Discussion 17.10
Why do some stars have very few hydrogen lines in their spectra?
- Chaisson Review and Discussion 17.12
What is the main sequence? What is common to all stars on the main sequence? What basic property of a star determines where it lies on the main sequence?
- Chaisson Review and Discussion 17.13
How are distances determined by spectroscopic parallax?
- Chaisson Review and Discussion 17.14
Why does the H-R diagram constructed from data on the brightest stars differ so much from the diagram constructed from data on the nearest stars?
- Chaisson Review and Discussion 17.17
How can stellar masses be determined by observing binary-star systems?
- Chaisson Review and Discussion 17.19
In general, is it possible to determine the age of an individual star simply by noting its position on an H-R diagram? Explain.
- 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?
- The main-sequence star Regulus has a mass about five times that of the sun. Use the mass-luminosity relationship to estimate the luminosity of Regulus.
16. 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 . Luminosity is related to flux by the following equation:
whereL 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? (3 points)
b) Sirius is 8.8 ly away (). What is Sirius' luminosity? (3 points)
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....
where Teff is the "effective" or surface temperature and is the Stefan-Boltzman constant. . Assume Sirius has a radius of meters - this is where the flux is measured. (5 points)
17. Stellar parallax allows us to find the distances to stars using simple trigonometry. The figure below shows the geometry.
so that
but the tangent of small angles is approximately equal to the angle itself in radians. So....
,
if R is in A.U.'s and p is in arcsec's, then d is in parsec's and .
the smallest detectable parallax is about 0.001 arcsec; how far would a star with this parallax be? (3 points)
18.The relationship between the apparent and absolute magnitude of a given star is expressed as:
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 #17 had an apparent magnitude of 5, what would its absolute magnitude be? (5 points)
19.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.
20. Invent a new mnemonic for spectral classification. O-B-A-F-G-K-M
(e.g. Oh boy, a furry gorilla kissed mom!).
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 (white main sequence)
4. Capella 45 76 170 5,250 (yellow giant)
5. Rigel 900 74 120,000 11,700 (blue-white super giant)
6. Procyon 11.3 59 7.59 6,670 (yellow main Sequence)
7. Betelgeuse 520 57 110,000 3,100 (red super giant)
8. Altair 16.5 41 12 7,940 (white main sequence)
9. Aldebaran 68 39 500 4,150 (orange-red giant)
10. Spica 220 34 9,000 22,000 (blue-white main sequence)
11. Antares 520 35 20,000 3,200 (red super giant)
12. Pollux 35 2953 4,850 (orange-red giant)
13. Fomalhaut 22.6 2820 9,000 (white main sequence)
14. Deneb 1600 26 110,000 9,200 (white super giant)
15. Regulus 87 24 410 13,000 (blue-white main sequence)
16. Castor 45 2053 10,000 (white main sequence)