4

(c) v =3869.1 m / s (d) v =4783.83 m / s Step-by-step explanation Step 1: For a satellite to be in orbit, the gravitational force must be balanced with the cetrifugal force. r 2 GMm = rmv 2 Where m is the mass of satellite, M is the mass of earth, v is velocity of the satelite and r is orbit radius v = rGM Substituting, G =6.67×10 −11 m 3 / kgs 2 and M =5.97×10 24 kg r =2.66×10 5 m v = 2.66×10 5 6.67×10 −11 ×5.97×10 24 v =3869.1 m / s Step 2: Moon is a natural satellite of the earth and it to be in orbit, the gravitational force must be balanced with the cetrifugal force. r 2 GMm = rmv 2 Where m is the mass of moon, M is the mass of earth, v is velocity of the moon and r is orbit radius v = rGM Substituting, G =6.67×10 −11 m 3 / kgs 2 and M =5.97×10 24 kg r =1.74×10 5 m v = 1.74×10 5 6.67×10 −11 ×5.97×10 24 v =4783.83 m / s