A spacecraft (mass = m₁) orbits a planet (mass = m₂) in a circular orbit (radius = r). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible? A)Gm₁m₂/(4r) B)Gm₁m₂/R C)Gm₁m₂/(2R) D)Gm₁m₂/(3R) E)2Gm₁m₂/(5R)

Question

Quizplus · Accepted Answer

The minimum energy required to send the spacecraft to a distant point in space where the gravitational force on it by the planet is negligible is equal to the energy required to overcome the planet's gravitational attraction and move the spacecraft from its initial circular orbit to an infinite distance away from the planet. This is equal to the difference in potential energy of the spacecraft between these two points, which is equal to the initial potential energy minus the final potential energy. The initial potential energy of the spacecraft in its circular orbit is equal to -Gm₁m₂/r, and the final potential energy when the spacecraft is at an infinite distance from the planet is equal to zero. Therefore, the minimum energy required is equal to the initial potential energy, which simplifies to Gm₁m₂/(2R). The correct answer is therefore C.

A Spacecraft (Mass = M1) Orbits a Planet (Mass =

A Spacecraft (Mass = M₁) Orbits a Planet (Mass =