physics 1
posted by Anonymous on .
A satellite is in a circular orbit about the earth (ME = 5.98 x 1024 kg). The period of the satellite is 1.77 x 104 s. What is the speed at which the satellite travels?

F = G Mm/R^2 = m v^2/R
v^2 R = G M = 6.67*10^11 * 5.98*10^24
v^2 R = 39.9 * 10^13
v T = circumference = 2 pi R
so
R = v T/(2 pi)
R = v [1.77*10^4/(2 pi)]
R = 2.82*10^3 v
so
v^3 (2.82*10^3) = 39.9 * 10^13
v^3 = 14.1 * 10^10 = 141 * 10^9
v = 5.2 * 10^3
v = 5,200 m/s 
v =1.01 m/s