Question

An artificial satellite circling the Earth completes each orbit in 150 minutes.

(a) Find the altitude of the satellite.
  express in m

(b) What is the value of g at the location of this satellite?
express in m/s²

Answer 1

By using Kepler's orbital formula:

R = [T²GMe/4π²]^(1/3) where T is the period in seconds.

where,

mass of earth (Me) = 5.98 x10^24 kg

Radius of earth (Re) = 6.371x 10^6 m

G = 6.67408 × 10^-11 m³ kg^-1 s^-2

orbital radius = R.

T is the period in seconds (ie T =150x60 = 9000 sec)

substituting the values in orbital equation we get;

orbital radius R = 9.353714 x10^6 m;

therefore, the altitude of the satelite = R - Re

= 2.982x10^6 m.

(b) value of g at the location of this satellite

g = GMe/R²

= 6.67408 × 10^-11 x 5.98 x10^24/ (9.353714 x10^6)²;

= 4.558 m/s²