1) Star Alpha has a larger parallax angle than Star Beta but the same apparent luminosity. The two stars are known to have the same size (radius) based on their spectral line widths. Which of the two stars will show evidence of higher ionization species in its spectrum? Explain.

2) When we measure the spectrum of light coming from our Sun, the actual peak wavelength of the continuous radiation varies depending upon what part of the Sun we are looking at. Near the limb of the Sun, the peak is close to the red end of the visible spectrum. Near the center of the visible disk, the peak is close to the middle of the visible spectrum.

a) (7 pts) Explain why the Sun appears to have slightly different colors depending upon which part of the visible disk we observe.

b) (7 pts) Explain why the peak wavelength shifts to a shorter value when we look at a gas that has a higher temperature.

3) Based on information in the graph below, determine the size (relative to the size of the Sun) of stars A and B. Show your work.

4) One ingredient in the nuclear fusion process in the Sun is Helium-3. The presence or absence of this nucleus can greatly affect nuclear fusion.

a) (10 pts) In 1-2 sentences, briefly state the "solar neutrino problem", then explain how Helium-3 can be used to help provide a solution for the solar neutrino problem.

b) (4 pts) If Helium-3 is affecting the Sunıs core as some Astronomers think, how might this result in long-term warming or cooling of the Earth?

5) High temperature is an important ingredient in many astronomical situations, like fusion, ionization, excitation, emission, absorption, motion and so on.

a) (7 pts) Explain why high temperatures are needed in order to excite Hydrogen atoms to absorb and subsequently emit photons.

b) (7 pts) Explain why high temperatures are seen in the low density gas of the corona.

6) Astronomers make careful observations of star Alpha and star Beta to determine their properties. Both stars are determined to have the same spectral line widths in their continuous spectrum, but Star Alphaıs continuous spectrum peaks at a much shorter wavelength than star Beta.

a) (2 pts) Which of these two stars has a higher absolute luminosity (or are they probably about the same)?

b) (12 pts) Justify your answer to part (a). As part of your answer, explain why line width relates to stellar size.

7) Energy transport in the Sunıs interior occurs in two different ways, via radiation and convection.

a) (8 pts) Explain why energy is transported via light in the radiative zone and via mechanical motion of atoms in the convective zone.

b) (6 pts) If the core temperature of the Sun were increased, would the boundary of the convective zone move inward toward the core or outward toward the surface? Explain.

8) Currently the number of stars for which Astronomers can measure parallax angles is only a very small fraction of the total number of stars in the galaxy. Suppose we set up an Astronomical parallax observatory on the surface of Mars, which orbits at an average distance of 130 million miles from the Sun (as opposed to Earthıs 93 million miles). Would the number of stars with measurable parallax angles by larger or smaller compared with what we can see from Earth? As part of your explanation for this answer, explain the relationship between parallax angle and the changed variable in the parallax equation.