An intergalactic spaceship arrives at a distant planet that rotates on its axis with a...

jubateee

jubateee

Answered

2021-12-30

An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 34 hours. The mass of the planet is M=2.71025 kg. The spaceship enters a circular orbit with an orbital period that is equal to the planets

Answer & Explanation

Stella Calderon

Stella Calderon

Expert

2021-12-31Added 35 answers

Time period of planet in its own axis (T) = 34 hours
=122400 seconds
Mass of planet (M)=2.7×1025 kg
let the mass of spaceship = m
Therefore,
velocitytime=circumference of the orbit
using, orbital velocity =GMr
GMrT=2πr
squaring both sides
T2GMr=4π2r2
r3=T2GM4π2
r=[T2GM4π2]13
Substitute the given values in above expression
r=[(122400)26.6710112.710254π2]13
r=88084108.8 m
r=8.81107 m

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