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 × 10⁷ m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 1.8 × 10¹¹ m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 59.7 m/s². What are the mass of (a) the planet and (b) the star? (G = 6.67 × 10^-11 N ∙ m²/kg².) A) (a) 7.2 kg × 10²⁵ kg, (b) 2.9 kg × 10³⁰ kg B) (a) 1.3 kg × 10²⁶ kg, (b) 2.9 kg × 10³⁰ kg C) (a) 7.2 kg × 10²⁵ kg, (b) 1.7 kg × 10³⁰ kg D) (a) 1.3 kg × 10²⁶ kg, (b) 1.7 kg × 10³⁰ kg

Question

Quizplus · Accepted Answer

The mass of the planet can be calculated using the formula for gravitational acceleration: $ g = \frac{G \cdot M}{R^2} $. Solving for $ M $ gives the mass of the planet as approximately $ 7.2 \times 10^{25} $ kg. The mass of the star can be calculated using Kepler's third law: $ T^2 = \frac{4\pi^2}{G(M+m)}a^3 $, where $ M $ is the mass of the star and $ m $ is negligible. Solving for $ M $ gives approximately $ 2.9 \times 10^{30} $ kg.

You Are the Science Officer on a Visit to a Distant