Question

A satellite travels around Earth in uniform circular motion, at a height of 35,800 km above Earth's atoms. The satellite has a mass of 580 kg. a) what is the gravitational force exerted on the satellite by Earth? b) How fast must the satellite be moving to retain this orbit (relative to the center of Earth)

Answer 1

Gravitaionla force on the satellite at a distance
           35800*10^3 m + 6371*10^3 m = 42171000 m

   F = GMm/r^2 = mg
          = GM/r^2
          = 6.754*10^-11*6*10^24 /(42171000)^2
          = 227.8686123279 *10^-3 N
  

   orbital speed of the satellite is
       V = sqrt(G*M/R)
          = sqrt(6.754*10^-11*6*10^24/6371000)
          = 7975.4 m/s
satellite should move with speed 7975.4 m/s to retain in the orbit.