A2 Daily A Level Physics question
A satellite moves in a stable circular orbit of radius r around a planet. Its engines are fired briefly to move it into a new stable circular orbit of radius 2r. Which statement correctly describes the change in the satellite's kinetic energy and its total orbital energy?
Answer
The correct answer is B.
For a stable circular orbit, the gravitational force provides the centripetal force: GMm/r² = mv²/r. Rearranging for kinetic energy (E_k = ½mv²) gives E_k = GMm/(2r). Since E_k is proportional to 1/r, doubling the radius r will halve the kinetic energy, so it decreases. The total energy (E_total) is the sum of kinetic energy and gravitational potential energy (E_p = -GMm/r). Therefore, E_total = E_k + E_p = GMm/(2r) - GMm/r = -GMm/(2r). When the radius is doubled to 2r, the new total energy is E'_total = -GMm/(4r). Since -1/4 is a greater number than -1/2, the total energy has increased (become less negative). Moving to a higher orbit requires work to be done on the satellite, which increases its total energy.