Question

A satellite of mass m is orbiting around the earth in a circular orbit with velocity v. What will be its total energy?

Answer 1

mv^2/r= GMm/ r^2
KE= mv^2/2= GM/2r
PE= -GMm/r
TE= PE+KE
TE= -GMm/2r

Answer 2

otal energy of the satellite=kinetic energy + Potential energy

=½mV2 - GMm/ h --(1)

here M is the mass of earth and h is the height of satellite from the center of the earth

Now Centripetal force=Gravitational force

mv2 / h=GMm/ h2

multiplying both sides by h we get

mv2=GMm/ h

substituting value of GMm/ h in eq(1) we get

Total Energy=½mV2 - mv2

Total energy=-(1/2)mv2

negative sign indicates binding energy