question archive An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 37 hours
An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 37 hours
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An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 37 hours. The spaceship enters a geosynchronous orbit at a distance of R = 5.7 • 108 m.
From the given information, write an equation for the mass of the planet.
Calculate the mass of the planet in kilograms.
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For geosynchronous orbit Centripetal Force is equal to Gravitational Force
Gravitational Force = Centripetal Force
GMm/R2 = mv2 / R
GM/R = v2
we know that
time period T = time taken to complete a cycle around M so
T = 2πR/v
v =2πR/T put this v value above
GM/R = v2 = (2πR/T )^2
GM /R = 4π2R2 /T2
from here
M = 4π2R3 /T2G
now just plug the values
T = 37 *60*60 = 133200 sec
R = 5.7*10^8 m
M =
kg answer
