What is the magnitude of the acceleration due to gravity at this distance? ( 𝑀E = 5.98×1024 kg and 𝑟E = 6.38×106 m )

Question

Synchronous communications satellites are placed in a circular orbit that is 3.59×107 m above the surface of the earth.

Answer 1

m = mass of satellite

 

GmM_E/(R_E + h)² = mg'

 

g' = GM_E/(R_E + h)² = (6.67 x 10^-11)(5.98 x 10²⁴)/(6.38 x 10⁶ + 3.59 x 10⁷)² m/s²

 

g' = 0.223 m/s²