Chapter 13, Problem 50EAP

Transit of TrES-1. The planet TrES-1, orbiting a distant star, has been detected by both the transit and the Doppler method, so we can calculate its density and get an idea of what kind of planet it is.

1. Using the method of Mathematical Insight 13.3, calculate the radius of the transiting planet. The planetary transits block 2% of the star’s light. The star TrES-1 has a radius of about 85% of our Sun’s radius.
2. The mass of the planet is approximately 0.75 times the mass of Jupiter, and Jupiter’s mass is about  $1.9\times {10}^{27}$ kilograms. Calculate the average density of the planet. Give your answer in grams per cubic centimeter. Compare this density to the average densities of Saturn (0.7 g/cm3) and Earth (5.5 g/cm3). Is the planet likely to be terrestrial or jovian in nature? Explain. (Hint: To find the volume of the planet, use the formula for the volume of a sphere:  $V=\frac{4}{3}\pi r^3$ . Be careful with unit conversions.)