A communications satellite with a mass of 440 kg is in a circular orbit about the Earth. The radius of the orbit is 2.9×104 km as measured from the center of the Earth.
A) Calculate the weight of the satellite on the surface of the Earth.
B) Calculate the gravitational force exerted on the satellite by the Earth when it is in orbit.
I need help. I've tried w=mg and F=G*(mM/r2).
The radius of the orbit is 2.9×10^4 km. Sorry.
on the surface, W=440kg x 9.8m/s/s
in orbit, the weight is GMm/r^2 where r is the distance from the center ofthe earth
the radius of the orbit, 2.9x10^7 m, is 2.9x10^7/6.4x10^6= 4.53 times the radius of the earth
since the force of gravity decreases as 1/r^2, we can deduce that the force acting on the satellite in orbit is 1/4.53^2 less than on the surface of the earth
therefore, the weight in orbit is 440g/4.53^2 = 210N (compared to 4312 N on the surface)
You are using the correct eqns. In A) W = m*g = 440 kg * 9.80 m/s^2 = 4310N
in B) F = GMm/r^2. = 6.67x10^-11*5.97x10^24kg*440kg/(2.9x10^7m)^2 = 208N
The first part is ok.
w = mg = 440x9.8 = 4312N
But the second part you do this.
since r é about 6.4x10^6m then
F/w = (6.4x10^6/2.9x10^7)² = 0.0487
So F = w x 0.0487 = 4312x0.0487 = 210N