Question

1. Suppose I drop a battleship and paperclip from 300 meters above the Moon's surface. Which one would hit the surface first, or would they hit at the same time? Explain why.

2. We have put our spacecraft into an elliptical orbit around the planet of Proxima Centauri (we'll call it Planet Ten). Assume there are no forces other than Planet Ten's gravity on the spacecraft. Describe how the gravitational potential energy, the kinetic energy, and the total energy of the orbit will change (or not change) as the spacecraft orbits Planet Ten from closest approach to furthest.

Answer 1

1. Gravitational acceleration acts on an object equally irrespective of the mass of the object. The formula for gravitational acceleration is given by:

g = GM/r² where M is the mass of the planet or in this case, the moon and r is the distance of the object from the center of the planetary body.

Thus, the acceleration depends only on the mass of the planetary body. This is why, when we drop both a battleship and a paperclip, they will hit the surface at he same time.

2. Kepler's second law of orbital motion states that an object sweeps out equal areas in equal amounts of time. This means that when the object is closer to the body it is orbiting around, its velocity increase, while at the further reaches of its elliptical orbit, the object slows down. Since kinetic energy is energy possessed by a body by virtue of its motion, the faster the object is, the more kinetic energy it has. Thus, the spacecraft has more kinetic energy when it is closer to the planet. As the space craft moves away from the planetary body, the planet pulls the spacecraft towards it with greater and greater force. This increases the gravitational potential energy of the object increases as it moves away.

The principle of conservation of energy states that the total energy of a closed system is always constant. Since no energy is being added or removed from the system (gravitational potential energy of the spaceship is converted to kinetic energy and vice versa at the closer and farther parts of the orbit respectively), the total energy remains constant.

Thus, to surmise, the total energy remains constant, the kinetic energy is greater at the closest parts of the orbit, while the gravitational potential energy is greatest at the farthest parts of the orbit.