Question

The international space station is in a circular orbit 500 km above the Earth.

A) Calculate the acceleration due to the Earth's gravity for this orbit

B) Use this acceleratiom to calculate the speed of the space station

Answer 1

A) The acceleration due to gravity on the surface of a space station is

            g = F/m = GM/R² = (6.67 x 10^-11)(5.98 x 10²⁴ kg)/[500*10^3]² = 1.59e3 m/s²

B) The gravitational attraction must provide the centripetal acceleration for the circular orbit:

            GM_Em/R² = mv²/R,

            v²= GM_E/(R_E + h)

            = (6.67x 10^-11 N · m²/kg²)(5.98 x10²⁴ kg)/(6.38 x10⁶ m + 0.5x 10⁶ m)

= 5.79 x 10^7 m2/s2

v= sqrt (5.79 x 10^7) = 7.61 x 10^3 m/s