Question

A satellite of mass 1,470 kg is in circular orbit about Earth. The radius of the orbit of the satellite is equal to two times the radius of Earth.

(a)

How far away (in m) is the satellite from the center of Earth?

_____________ m

(b)

Find the kinetic, potential, and total energies of the satellite. (Give your answers in joules.)

kinetic energy_________ J

potential energy_________ J

total energy___________ J

please show formulas thank you.

Answer 1

mass of satellite=m=1470 kg

radius=r=2*earth radius=2*6371 km

=12742 km

=1.2742*10^7 m

part a:

satellite’s distance from the center of earth=radius of its orbit

=1.2742*10^7 m

part b:

if speed of the satellite is v,

balancing gravitational pull with centripetal force:

G*M*m/r^2=m*v^2/r

where M=mass of earth=5.972*10^24 kg

G=universal gravitational constant=6.674*10^(-11)

then v^2=G*M/r

==>v=sqrt(G*M/r)

=5592.9 m/s

i)

kinetic energy=0.5*m*v^2

=2.3*10^10 J

potential energy=-G*m*M/r

=-4.6*10^10 J

total energy=kinetic energy+potential energy

=-2.3*10^10 J