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 15 hours (Earth hours). You place your spaceship in a geostationary orbit at an altitude h = 5R 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 isap = 0.60g, 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.

(a) What is the radius of the planet?

(b) What is the mass of the planet?

Explanation / Answer

here,

let the mass of the planet be M and the radius of the planet be R

at altitude h = 5 * R

R' = 6 * R

time period , t = 15 hours = 15 * 3600

t = sqrt( 4*pi^2 * R^3 /( G * M))

15* 3600 = sqrt(4*pi^2 * R^3 /( 6.67 * 10^-11 * M) ) ......(1)

accelration due to gravity = 0.6 * g

G * M/R^2 = 0.6 * 9.8

6.67 * 10^-11 * M /R^2 = 0.6 * 9.8 .......(2)

from equation(1) nd (2)

M = 1.66 * 10^28 kg

R= 4.34 * 10^8 m

(a)

the radius of the planet is 4.34 * 10^8 m

(b)

the mass of the planet is 1.66 * 10^28 kg

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