5. Drs. Harden, Petrie, and Rozyczka have discovered a Cepheid in a distant galaxy, and want to determine exactly how distant that galaxy is. They have measured the Cepheid's period and brightness. Can they determine its distance?
a. yes, by using the period-luminosity relation to find the luminosity, and with the luminosity and brightness they can find the distance
b. yes, by measuring its trigonometric parallax
c. yes, by measuring the Doppler shift of its spectrum
d. no, they would need to know its radius to do that

Cepheids are important because their periods and luminosities are related. Once you know the apparent brightness and the luminosity of a star, you can find its distance using the inverse-square law. Cepheids are quite bright, and therefore well-suited to measuring the distances to other galaxies. Trigonometric parallax will not work for measuring distances outside our galaxy, and the Doppler shift of the spectrum would tell you the Cepheid's velocity, not its distance from us.

6. The wavelength of blue light is about half that of red light. The frequency of blue light is ______________ that of red light, and the energy of a blue light photon is ______________ that of a red light photon.
a. half, half
b. two times, four times
c. two times, two times
d. four times, four times

This is a "Q" class, so we had to have some math. The relevant equations here are: c = lambda * f and E = h * f

7. The Keck telescope has four times the diameter of the Hubble Space Telescope. Ignoring the effects of Earth's atmosphere, the Keck telescope has _____________ angular resolution and _____________ the light-collecting power of the Hubble Space Telescope.
a. one fourth as good; one sixteenth
b. one half as good; four times
c. four times better; sixteen times
d. four times better; four times

More math. Angular resolution is better in a larger telescope, and improves linearly with the diameter of the telescope (i.e. a telescope twice as large will have angular resolution twice as good). Light-gathering power is proportional to the area of the telescope, which is pi * r².

8. Mars orbits the sun at a distance of approximately 1.5 AU. What is its orbital period in years?
a. the cube root of 1.5, which is about 1.14
b. the square root of 1.5, which is about 1.22
c. the cube root of 1.5 squared, which is about 1.31
d. the square root of 1.5 cubed, which is about 1.84

This question is about Kepler's third law, relating the period of a planet's orbit in years to its distance from the sun in AU's.