Question

An earth satellite remains in orbit at a distance of 1.7100×104 km from the center of the earth. The Universal Gravitational Constant is 6.67×10−11 N⋅m2/kg2 and the mass of the earth is 5.98×1024 kg. Part A What speed (in m/s) would the satellite have to maintain? Express your answer using three significant figures. Credit: 3 pts.

Answer 1

Gravitational force between 2 objects=GMm/r^2, where G is universal gravitational constant, M and m are masses and r is distance between the masses.

Also, for circular motion, centripetal force=m(v^2)/r, where m is mass, v is velocity and r is radius of the circular trajectory.

Now, gravitational force provides the necessary centripetal force.

So,GMm/r^2=m(v^2)/r

=>GM/r^2 = (v^2)/r

v=[GM/r]^0.5

For the given problem, G=6.67*10^-11 Nm2/kg2, M=mass of earth = 5.98*10^24 kg and r=1.71*10^4 m.

So,v=[ (6.67*10^-11)*(5.98*10^24) / (1.71*10^4)] ^0.5 = 152726.87 m/s = 153000 m/s(using 3 significant digits)