You are visiting a newly discovered exoplanet (mass M and radius R ) that comple

Question

You are visiting a newly discovered exoplanet (mass M and radius R) that completes one rotation about its axis every 12 hours (Earth hours). You place your spaceship in a geostationary orbit at an altitude h = 7R above the planet's surface. While in orbit you decided to beam down to the planet to investigate the surface. While on the surface you perform a simple kinematics experiment and discover that the gravitational acceleration at the surface is ap = 0.80g, where g is the gravitational acceleration on the Earth's surface. You can assume that the exoplanet is a uniform sphere, and that your spaceship's orbit is circular.

Note: A geostationary orbit is a special type of geosynchronous orbit where the satellite/spaceship remains at the same position above the equator throughout its orbit. Technically the prefix "geo" indicates the Earth, but we'll go ahead and use the term here in reference to this new planet.

(a) What is the radius of the planet?
R =  km

(b) What is the mass of the planet?
M =  kg

Explanation / Answer

radius of geostationary orbit = (time period^2 * G * mass of planet / (4 * pi^2))^(1/3)

12 hours = 43200 sec

7R = (43200^2 * 6.648 * 10^-11 * mass of planet / (4 * pi^2))^(1/3)

acceleration due to gravity = G * mass of planet / radius^2

0.8 * 9.8 = 6.648 * 10^-11 * mass of planet / R^2

on solving we'll get

R = 1.08051 * 10^6 m or 1.08051 * 10^3 km

M = 1.37684 * 10^23 kg

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