In physics, gravitational potential energy can be negative depending on the reference point chosen. GPE is often calculated relative to a specific level, typically the ground or the lowest point in the problem. In scenarios where an object is below this reference level, its GPE is considered negative. This concept is especially relevant in astronomical contexts. For example, the GPE of an object within a gravitational well (like a satellite in orbit around Earth) is negative, reflecting the energy required to move it from that point to an infinitely distant point where the gravitational influence is zero.

When an object is in free fall, its gravitational potential energy is converted into kinetic energy. As the object falls, it loses height and thus loses GPE, but this loss is compensated by a gain in kinetic energy due to increased velocity. This conversion is a manifestation of the principle of conservation of energy, where the total energy (kinetic + potential) remains constant. At any point during the fall, the sum of the kinetic and potential energy equals the initial potential energy at the starting height, assuming no other forces (like air resistance) are doing work on the object.

In hydroelectric power plants, gravitational potential energy plays a crucial role. Water stored in a reservoir at a certain height possesses significant GPE. When the water is released and flows down through turbines, this GPE is converted into kinetic energy, which then drives the turbines to generate electricity. The amount of energy produced depends on the mass of the water and the height from which it falls, illustrating the practical application of the GPE = mgh formula. Efficient hydroelectric power generation relies on maximising this conversion of gravitational potential energy into kinetic and subsequently electrical energy.

Gravitational potential energy (GPE) at high altitudes continues to increase, but not at a constant rate as it does near the Earth's surface. The formula GPE = mgh assumes a uniform gravitational field, which is a good approximation for small heights above the Earth's surface. However, at very high altitudes, the gravitational field strength (g) decreases with distance from the Earth's centre according to the inverse-square law. Consequently, the increase in GPE becomes progressively less for the same increase in height as you move further from the Earth, leading to a non-linear relationship between GPE and altitude at these extreme heights.

In orbital mechanics, gravitational potential energy is a key concept in understanding the motion of satellites and other celestial bodies. A satellite in orbit around the Earth has both kinetic and potential energy. The potential energy is due to its position in the Earth's gravitational field, while the kinetic energy arises from its velocity. The balance of these two forms of energy keeps the satellite in orbit. At higher orbits, the satellite has less kinetic energy but more potential energy. This balance is crucial in calculating the necessary velocity and altitude for a satellite to maintain a stable orbit, applying the principles of GPE in an astronomical context.