1) Two trigonometric distance determination techniques weıve used in class involve angular diameter and parallax.

a) (7 pts) Suppose I place meter stick A at a distance of 120 meters away from you. With an angular measuring device, you find that it has an angular size of about 30 arcminutes (about the angular size of the Moon as seen from Earth) Meter stick B (same size as stick A, of course) is placed at some unknown distance from you and is measured to have an angular size of 60 arcminutes. How far away is stick B? Justify your answer with a simple diagram and/or by showing your work.

b) (7 pts) Suppose Astronomers were to set up a parallax observatory on Mars, which orbits the Sun at a distance of 1.4 AU (130 million miles) compared to the Earthıs orbital distance of 1.0 AU (93 million miles). Using Marsı orbit as a baseline instead of Earthıs orbit, would our ability to measure stellar parallax change for better or worse (or neither)? Explain.

2) The parallax method of distance determination is only useful for stars within a certain distance from Earth.

a) (7 pts) Explain why the parallax is limited in this way.

b) (7 pts) Explain why this limitation led scientists to be extremely skeptical of the Copernican (heliocentric) model of the solar system after it was introduced.

3) Below is the spectrum of Arcturus, plotted on the same graph as a spectrum of our own Sun for comparison purposes. Note that the Sun peaks in the middle of the visible region of the spectrum, which gives it a yellowish color. Arcturus, with its cooler surface temperature, peaks at a somewhat longer wavelength.

a) (7 pts) Explain why stars like Arcturus, which are cooler than the Sun, tend to have their peak wavelength at longer wavelengths.

b) (7 pts) If we were to observe using some kind of red filter that only enabled us to see the red wavelengths of light being emitted by each star, which would appear brighter? Explain your answer.

4) The law of scattering says that shorter wavelengths of light tend to be scattered more effectively by gas and dust than longer wavelengths. Use this principle to explain why the sky is blue and why the Sun appears to be red during sunset (much more red than when it is directly overhead...explain the color difference).

5) Two stars, A and B, both of the same temperature and the same abundance of Calcium, resulting in the Calcium absorption line pattern you see below for both stars. Assume neither star has a significant rotation speed in this problem, and assume both stars have the same mass. Assume both lines have the same strength.

a) (8 pts) Which of these two stars is probably larger in size (A, B, same size)? Justify your answer completely. In other words, ³Star A is smaller because the lines are deeper/same strength/wider.² is an example of insufficient reasoning. Why can you tell anything about the size of the star based on the spectral lines? Explain that.

b) (6 pts) Assume that star A is at rest relative to the Earth. The radial velocity of star B is (toward Earth, away from Earth, zero). Justify your answer.

6) Explain why the temperature of a star has an effect on the strength of the spectral lines in that starıs spectrum. Specifically, state why spectral line strength for certain elements gets weaker at very low temperatures *and* at very high temperatures.

7) Limb darkening is a phenomenon seen in the photosphere of the Sun, and its existence tells us something about the temperature structure of the photosphere.

a) (8 pts) Explain what limb darkening is, why we see it, and what it tells us about the temperature structure of the photosphere (i.e. is it hotter near the surface or deep inside?).

b) (6 pts) Suppose the gas throughout the photosphere has a constant temperature. Would we still see limb darkening? Would we see limb brightening? Explain.

8) We know that the corona is a region of extremely hot gas surrounding the Sun, and gas in the corona often reaches temperatures of several million degrees.

a) (6 pts) Explain why the corona is so hot relative to, say, the photosphere of the Sun, which is only about 6000K.

b) (8 pts) Explain how the observation of ionization species in the Sunıs corona is evidence of its temperature structure. As part of your answer, explain what an ionization species is and why a given species is indicative of the temperature.