Problem: An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 45 hours. The spaceship enters a geosynchronous orbit at a distance of R = 8.7 × 108 m Part (a) From the given information, write an equation for the mass of the planet. Part (b) Calculate the mass of the planet in kilograms. 

FREE Expert Solution

Centripetal forces are equal to gravitational forces. 

ΣFC=maC

(a)

Centripetal force:

FC=GMmR2

Centripetal acceleration:

aC=v2R

Substituting:

GMmR2=mv2Rv=GMR

The velocity, v is:

v=2πRT

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Problem Details

An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 45 hours. The spaceship enters a geosynchronous orbit at a distance of R = 8.7 × 108

Part (a) From the given information, write an equation for the mass of the planet. 

Part (b) Calculate the mass of the planet in kilograms.