AST 307 · Introductory Astronomy Fall 2003

Exam #2 Sample Questions

1. The Sun has a surface temperature of about 6000 K and is brightest at a wavelength of about 0.5 um (in the middle of the visible part of the spectrum). The Earth has a surface temperature of about 300 K.
At about what wavelength does the Earth emit most brightly?

How does the power emitted by each square meter of the Earth compare to the power emitted by each square meter of the Sun?

2. If a star has a parallax of 0.01 arcsec, what is its distance in pc?

If that star has a companion star 0.1 arcsec from it in the sky, what is the distance between the two stars in AU? Assume they have the same distance from us.

3. Explain the formula L = 4 pi d^2 x F. (That is, say what the letters in this formula stand for and explain where the formula came from.)

4. Why can't we measure the masses of all stars, even nearby ones?

5. Why isn't it very practical to calculate the temperature of a star from its size and luminosity?

6. Hydrogen absorption lines are strongest in stars with atmospheric temperatures of about 10,000 K, and are weaker in both cooler and hotter stars. Explain what makes the hydrogen lines weaker in cooler stars.
(If you don't know the answer, instead say why they are weaker in hotter stars for part credit.)

7. Give an argument showing that stars in the upper right of the Hertzsprung-Russell diagram must have large diameters. (Say what the axes of the diagram are, so what it means that a star is in the upper right, and then argue that it must therefore be large.)

8. I found two stars in the sky. They have the same temperatures, but star A is a main sequence star and star B is a giant star with 10 times the radius of star A.

How do their luminosities compare? (Which is more luminous, and how many times more luminous is it?)

If the two stars appear equally bright (they have the same flux), how do their distances compare? (Be quantitative.)

9. How does gas pressure depend on the number of atoms in a box? Why does it vary in this way?

How does gas pressure depend on the speed of atoms in a box? Why does it vary in this way?

10. Why does a protostar contract, and what causes it to stop contracting when it becomes a main sequence star?

11. Why doesn't a white dwarf contract as it cools?

12. The wavelength of the hydrogen Balmer alpha line is 656.3 nm. In a distant galaxy it appears at 662.9 nm. Is that galaxy approaching or receding, and how fast?

13. How would an astronomer measure a star's F, d, L, M, T?

14. If a star increased in temperature without changing its size, how would it move on the HR diagram?

15. Be able to sketch an HR diagram, showing the locations of the main sequence, red giant, and white dwarf stars.

16. Describe the standard candle method of measuring distances.

17. How does pressure depend on the temperature of the gas in a box?   Why?

18. When a star is in hydrostatic [or thermal] equilibrium, what two influences balance, and what stays constant as a result?

19. Describe what is happening at the center of a star in each of these phases: protostar, main sequence, going from main sequence to red giant.

20. Describe how a white dwarf moves on the H-R diagram as it ages, and explain why it changes as it does.

21. The peak of the spectrum of a 1000 K blackbody is at a wavelength of 2.9um. Sketch the spectrum of light emitted by a (blackbody) rock at a temperature of 1000 K. On the same plot, sketch the spectrum of the same rock but heated only to 500 K. Label each axis with the name of the quantity that varies along that axis and put numbers on the horizontal axis. You don't have to show the shapes of the spectra very accurately, but draw your plot accurately enough to show which curve is higher at each wavelength, and put the peaks at the right wavelengths.

22. Sketch the visible wavelength spectrum of a tube of glowing hydrogen gas at rest relative to the observer. Label the axes, but you don't have to include any numbers. Sketch with a dotted line the spectrum of a tube of glowing hydrogen moving toward the observer at 1/10 the speed of light. Bonus: on your sketch show the right number of visible wavelength lines for hydrogen and roughly how they are arranged in wavelength.

23. What do we mean by the frequency of light? That is, what is it that is changing or coming past you at that frequency? In words, explain why the frequency of a wave varies inversely with wavelength.
When light enters glass, its speed decreases while its frequency stays constant. How must its wavelength change? Why does wavelength depend on speed in this way?

24. Give a qualitative explanation why the pressure of gas in a box increases as the temperature of the gas increases. You don't have to explain why pressure depends on temperature in exactly the way it does, only why it increases with temperature. (There are two reasons.) Saying that the ideal gas law says this is not sufficient.
If the temperature of the atmosphere of a planet increased, but exactly the same number of atoms and molecules stayed in the atmosphere, the pressure at the surface of the planet would change very little. Use the equation of hydrostatic equilibrium to explain why.

25. a) If a star has the same surface temperature as the Sun, but twice the radius, how does its luminosity compare to that of the Sun? That is, what is its luminosity in solar units?
b) If instead a star has the same radius as the Sun, but one half the temperature, what is its luminosity?
c) Which of these two stars lies the closest to the main sequence on a Hertzsprung-Russell diagram?
d) For a star to have the same luminosity as the Sun with 1/2 the Sun's temperature, what radius would it have to have?

26. Where do red giants come from? That is, what sort of a star evolves into a red giant or leaves behind a red giant when it dies? Describe briefly how the conditions at the center of a star change as it becomes a red giant.

Where do white dwarfs come from? That is, what sort of a star evolves into a white dwarf or leaves behind a white dwarf when it dies? Describe briefly one way a white dwarf might be destroyed or changed into something else.

5 November 2003
Astronomy Program · The University of Texas at Austin · Austin, Texas 78712
prospective student inquiries: studentinfo@astro.as.utexas.edu