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Gravitational potential energy represents the energy that an object possesses due to its position in a gravitational field. In simpler terms, it's the energy stored because of an object's height above a planet's surface. When an object is infinitely far from a massive body, like a planet, it has zero gravitational potential energy, as there is no gravitational pull affecting it at this extreme distance.
In our exercise, the meteorite's initial position is considered infinitely far from Planet Roton. Therefore, its gravitational potential energy starts at zero. As the meteorite falls toward the planet, the gravitational force pulls it closer, converting potential energy into kinetic energy.
The gravitational potential energy upon reaching the planet's surface is crucial for determining how much total energy is available to be converted into velocity. The formula used to calculate this energy is:

• \( U = -\frac{G M m}{r} \)

where \(U\) is the gravitational potential energy, \(G\) is the gravitational constant, \(M\) is the planet's mass, \(m\) is the meteorite's mass, and \(r\) is the radius of the planet.

Kinetic energy is the energy an object possesses due to its motion. When a meteorite starts falling towards Planet Roton, it gains speed, and thus, kinetic energy. This happens because the initial potential energy it had at an infinite distance is converted into kinetic energy as it accelerates under the influence of gravity.
The formula for kinetic energy is:

• \( KE = \frac{1}{2} mv^2 \)

where \(KE\) represents kinetic energy, \(m\) is the mass of the object (in this case, the meteorite), and \(v\) is its velocity upon impact with the planet's surface.
The process of converting gravitational potential energy to kinetic energy demonstrates the conservation of energy principle at work. In the problem, since the meteorite starts from rest, it has no initial kinetic energy. By the time it impacts the surface, all the lost potential energy has become kinetic energy, determining the final speed needed.

Gravitational force is the attraction between masses. Every object with mass exerts a gravitational pull on every other mass. This force is what causes the meteorite to fall towards Planet Roton. It is always directed toward the center of mass of the objects involved.
The gravitational force can be calculated using Newton's law of universal gravitation:

• \( F = \frac{G M m}{r^2} \)

where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(M\) is the mass of the planet, \(m\) is the mass of the meteorite, and \(r\) is the distance between the centers of the two objects.
This force is responsible for the meteorite's acceleration as it falls toward the planet. As the meteorite gets closer, it experiences a stronger gravitational pull, contributing to its increase in speed and kinetic energy.

Free fall is the condition under which an object moves freely under the influence of gravity alone, without any resistance from air or other forces. In our exercise, free fall describes the meteorite's journey towards Planet Roton. Since we assume the planet is airless, no air resistance acts on the meteorite, making it an ideal scenario to apply the conservation of energy principles.
In free fall, the only force acting on the falling object is gravity. This causes the object to continuously accelerate, increasing its speed until it reaches the planet's surface. This acceleration due to gravity is constant, which in the context of the exercise ensures that all potential energy converts into kinetic energy as calculated.
By understanding free fall, we observe how gravity leads to an increase in an object's velocity when falling near a large mass like a planet, perfectly illustrating how a meteorite can gain high speeds upon impact, as calculated in our solution.