Chapter 13, Problem 13.84PP

EXOPLANETS. As planets with a wide variety of properties are being discovered outside our solar system, astrobiologists are considering whether and how life could evolve on planets that might be very different from earth. One recently discovered extrasolar planet, or exoplanet, orbits a star whose mass is 0.70 times the mass of our sun. This planet has been found to have 2.3 times the earth’s diameter and 7.9 times the earth’s mass. For planets in this size range, computer models indicate a relationship between the planet’s density and composition:

Density Compared with That of the Earth	Composition
2-3 times	Mostly iron
0.9-2 times	Iron core with a rock mantle
0.4-0.9 times	Iron core with a rock mantle and some lighter elements, such as (water) ice
< 0.4 times	Hydrogen and/or helium gas

Based on S. Seager et al., “Mass-Radius Relationships for Solid Exoplanets”; arXiv:0707.2895 [astro-ph].

13.82 Based on these data, what is the most likely composition of this planet? (a) Mostly iron; (b) iron and rock; (c) iron and rock with some lighter elements; (d) hydrogen and helium gases.

13.83 How many times the acceleration due to gravity g near the earth’s surface is the acceleration due to gravity near the surface of this exoplanet? (a) About 0.29g; (b) about 0.65g; (c) about 1.5g; (d) about 7.9 g.

13.84 Observations of this planet over time show that it is in a nearly circular orbit around its star and completes one orbit in only 9.5 days. How many times the orbital radius r of the earth around our sun is this exoplanet’s orbital radius around its sun? Assume that the earth is also in a nearly circular orbit. (a) 0.026r; (b) 0.078r; (c) 0.70r; (d) 2.3r.