Question

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius$\mathrm { R } _ { 1 }$ to another of radius is

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

Answer 2

Total energy of the orbiting satellite of mass m having orbital radius r is

$\mathrm { E } = \frac { \mathrm { GMm } } { 2 \mathrm { r } }$where M is the mass of the planet.

Additional kinetic energy required to transfer the satellite from a circular orbit of radius $\mathrm { R } _ { 1 }$to another radius is

$= \frac { \mathrm { GMm } } { 2 } \left( \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right)$