Calculate the weight of the satellite on the surface of the Earth?

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.

w=______N

B) Calculate the gravitational force exerted on the satellite by the Earth when it is in orbit.

F=______N

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.

w=G(mM/r²) eq(01)

and

F=G(mM/(2.9x10^7)² eq(02)

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

see you