1. The Sun's radius is about 7x105 km.
a. How long would it take a photon produced at the center of the core to exit from the Sun's surface if it could freely escape?
b. In reality, do you expect a photon's escape to take a longer or shorter time that what you calculated in part (a)? Explain your answer.
2. An exoplanetary system has two known planets. Planet X orbits in 290 days and Planet Y orbits in 145 days.
a. Which planet is closest to its host star?
b. If the star has the same mass as the Sun, what is the semi-major axis of the orbits for Planets X and Y?
3. An exoplanet's transit depth can be calculated by finding the fraction of light blocked by the planet; that is, the ratio of the area of the planet projected on the sky (a circle) to the area of the star (also a circle).
If a transit depth of 0.00001 (or 0.001% decrease in brightness) can be detected with the Kepler spacecraft, what is the radius of the smallest planet that could be detected around a star with a radius of 0.3 Rsun? (For reference, the Earth is about 0.001 Rsun.)