Randall D. Knight — Newton's Theory of Gravity: Problem 25

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be \(1.8 \times 10^7 \text{ m}\) and its rotation period to be \(22.3 \text{ hours}\). You have previously determined that the planet orbits \(2.2 \times 10^{11} \text{ m}\) from its star with a period of \(402 \text{ earth days}\). Once on the surface you find that the free-fall acceleration is \(12.2 \text{ m/s}^2\). What is the mass of (a) the planet and (b) the star?