A rocket coasts in an elliptical orbit about Earth. To attain escape velocity using the least amount of fuel in a brief firing time, should it fire off at the apogee, or at the perigee? (Hint: Let Fd = ∆ KE guide your thinking.)
A)perigee, where it is closest and fastest
B)apogee, where it is farthest and slowest
C)same at either location
D)same at any location

Question

Quizplus · Accepted Answer

Firing at perigee, where the rocket is closest to Earth and moving fastest, takes advantage of the Oberth effect. This effect states that a rocket engine is most efficient when the rocket is moving at high speed because the propellant has more usable energy due to its higher kinetic energy. Thus, firing at perigee, where velocity is greatest, maximizes the energy gained from a brief burst of fuel, making it the best choice for achieving escape velocity with the least amount of fuel.

A Rocket Coasts in an Elliptical Orbit About Earth