The gravitational potential energy of a planet is the energy that is associated with the gravitational force between the planet and any object near its surface. It is a measure of the work that would be required to move an object from infinity to that specific point in the planet's gravitational field.
The gravitational potential energy of a planet can be calculated using the formula U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance from the planet's surface. Alternatively, it can also be calculated using the formula U = -GMm/r, where G is the universal gravitational constant, M is the mass of the planet, m is the mass of the object, and r is the distance between the object and the planet's center of mass.
Yes, the gravitational potential energy of a planet does vary with height or distance. As an object moves further away from the planet's surface, its gravitational potential energy decreases. This is because the distance between the object and the planet's center of mass increases, resulting in a weaker gravitational force and therefore, less potential energy.
The gravitational potential energy of a planet affects objects on its surface by determining their potential to do work. For example, if an object is at a higher point on the planet, it has more gravitational potential energy and can potentially do more work. This can be seen in the form of potential energy being converted to kinetic energy when an object falls from a higher point to a lower point on the planet's surface.
Yes, the gravitational potential energy of a planet can be negative. This occurs when an object is at a distance less than the planet's radius, resulting in a negative value for the potential energy. However, this negative potential energy does not mean that the object has less energy, it simply means that it is closer to the planet and therefore, has a stronger gravitational attraction.