Question

How fast is a satellite moving if it is in a circular orbit whose radius is 22000 km? G = 6.67 x 10-11 Nm2/kg2, and the mass of the earth is 5.98 x 1024 kg.

Answer 1

The gravitational force between earth and satellite is given by

F_g=(G.M.m)/r²

Where G is gravitational constant

M is mass of earth

m is the mass of satellite

r is the radius of circular orbit.

And centripetal force acting on satellite is given by

F_c=mv²/r

where v is velocity of satellite m mass of satellite and r radius of orbit

F_g=F_c

(GMm)/r²=mv²/r

V=(GM/r)^1/2

Substituting values we get

V=(6.67×10^-11×5.98×10²⁴/22000)^1/2

V=1.3×10⁵ m/sec

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