Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 8: Survey of SolarSystems

Problems

1
(a) By what factor would the Sun be shrunk to be the size of a large beach ball, 1 meter in diameter? (b) Calculate the distances and diameters of Mercury, Earth, Ceres, Jupiter, Neptune and Pluto if the whole Solar System were shrunk. (b) and their masses be if their density stayed the same?
2
Calculate the densities of Venus and Jupiter (use the masses and radii given in the appendix). How do these numbers compare with the density of rock (about 3 grams per cm3) and water (1 gram per cm3)? (Note: Be sure to convert kilometers to centimeters and kilograms to grams if you are expressing your answer in grams per cm3.)
3
Look up the mass and radius of Mercury and Jupiter and calculate their escape velocities, using the expression in chapter 3. Does this help you see why the one body has an atmosphere but the other doesn't? (Note: Be sure to convert kilometers to meters or the appropriate unit.)
4
Look up the mass and radius of Neptune and Mars and calculate their escape velocities, using the expression in chapter 3. Compare both with that of the Earth (see section 3.8). What is different about the atmospheres of these three planets? (Note: Be sure to convert kilometers to meters or the appropriate unit.)
5
(8.3/2.3) Kepler 30-b is an exoplanet orbiting a star of about 1 solar mass. Its orbital period is nearly 29 days. Calculate the semimajor axis of its orbit in AU. (Use Kepler's laws.)
6
Calculate the maximum Doppler shift that could be observed for the planet in question 5.
7
Using the modified form of Kepler's laws given in figure 8.7, calculate the orbital period for Gliese 851d, an exoplanet with a mass about 7.1 times the mass of Earth. The star Gliese 851 is a red dwarf with a mass of 0.31 solar masses and the planet orbits with a semimajor axis of 0.22 AU. (Remember to convert distances to meters and masses to kilograms when using the equation.)
8
Imagine an alien is detecting the Earth as it transits our Sun. Compute the ratio of the areas of the Earth's disk and the Sun's to roughly estimate what percentage of the Sun's light the Earth blocks mid-transit. What percentage would Jupiter block?
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