Question

A satellite is launched into a circular orbit $1600km$ above the surface of the earth. Find the period of revolution if the radius of the earth is $R=6400km$ and the acceleration due to gravity is $9.8m/se{c}^2.$

Answer 1

Given,

$R=6400km$

$h=1600km$

$g=9.8m/s^2$

Time period , $T=2\pi \sqrt{\frac{(R+h{)}^3}{GM}}$

$T=2\pi \sqrt{\frac{(R+h{)}^3}{g{R}^2}}$ $(GM=g{R}^2)$

$T=2\times 3.14\times \sqrt{\frac{(6400+1600{)}^3\times {10}^9}{9.8\times (6400{)}^2\times {10}^6}}$

$T=7092sec$

$T=1.97hr$