Question

(a)what is the magnitude of the gravitational force of the earth on a surveillance satellite of mass 1040kg that is in a grazing circular orbit 100 km above the surface of the earth.

(b)find the magnitude of the acceleration of the satellite in such a grazing orbit.

(c)determine the speed of the satellite.
take the mass and radius of the earth as 5980000000000000000000000 kg and 6370000m respectively

Answer 1

The gravitational constant
G =6.67•10⁻¹¹ N•m²/kg²,
h=100000 m
m=1040 kg
Earth’s mass is M = 5.98•10²⁴kg,
Earth’s radius is R = 6.37 •10⁶ m.

(a) F =G•m •M/(R+h)²
(b) a= G• M/(R+h)²
(c) mv²/(R+h) = G•m •M/(R+h)²
v=sqrt (G•M/(R+h))

Answer 2

2.232667747500