Chapter 13, Problem 49EAP

Lost in the Glare. This exercise helps you consider how much harder it would be for an alien astronomer to detect the light from planets in our solar system than to detect the light from the Sun itself.

1. Calculate the fraction of the total emitted sunlight that reaches Earth. (Hint: Imagine a sphere around the Sun the size of Earth’s orbit  $\left[\text{area=4}\pi a^2\right]$ , then calculate the fraction of that area taken up by the disk of Earth  $\left[\text{area=}\pi r^2{}_{\text{Earth}}\right]$ .
2. Earth reflects 29% of the Sun’s light. Based on this fact and your answer to part a, find the ratio of the total amount of light emitted by the Sun to the amount reflected by Earth. What does this tell you about the difficulty of detecting a planet like Earth around another star? How would a “star shade” like that discussed in Section 13.4 help?
3. Would detecting Jupiter be easier or harder than detecting Earth? Comment on whether you think Jupiter’s larger size or greater distance has a stronger effect on its detectability. You may neglect any difference in reflectivity between Earth and Jupiter.