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=2.7⋅1025 kg. The spaceship enters a circular orbit with an orbital period that is equal to the planets

Question

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=2.7⋅1025 kg. The spaceship enters a circular orbit with an orbital period that is equal to the planets

Stella Calderon · Accepted Answer

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,  velocity⋅time=circumference of the orbit  using, orbital velocity =GMr  GMr⋅T=2πr  squaring both sides  T2⋅GMr=4π2⋅r2  r3=T2⋅GM4π2  r=[T2⋅GM4π2]13  Substitute the given values in above expression  r=[(122400)2⋅6.67⋅10−11⋅2.7⋅10254⋅π2]13  r=88084108.8 m  r=8.81⋅107 m