Question

Find the ratio of kinetic energy required to be given to the satellite to escape earth's

Answer 1

The energy needed to raise the satellite to a height 'h' is

Δv=vA−vBΔv=vA−vB

=−GMmR+h−(−GMmR)=−GMmR+h−(−GMmR)

=GMmhR(R+h)=GMmhR(R+h)

=GMmhR2(1+hR)GMR2=GMmhR2(1+hR)GMR2=g=g

=mgh(1+hR)=mgh(1+hR)=E1=E1

E2=E2= energy of the satellite

=12=12mv20(v0−mv02(v0−orbital velocity )

r- distance of satellite from center of earth

=12=12m(GMr)m(GMr)

=12=12m(GMR+h)m(GMR+h)

=12=12m(GMR2)R(1+hR)m(GMR2)R(1+hR)

E2=mgR2(1+hR)E2=mgR2(1+hR)

∴E1E2∴E1E2=2hR