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.
3 Answers
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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, 2.9×10^7 m, is 2.9×10^7/6.4×10^6= 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)
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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. = 6.67×10^-11*5.97×10^24kg*440kg/(2.9×10^7m)^2 = 208N
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The first part is ok.
w = mg = 440×9.8 = 4312N
But the second part you do this.
w=G(mM/r²) eq(01)
and
F=G(mM/(2.9×10^7)² eq(02)
since r é about 6.4×10^6m then
F/w = (6.4×10^6/2.9×10^7)² = 0.0487
So F = w x 0.0487 = 4312×0.0487 = 210N
see you
