Tidal forces are inversely proportional to the cube of the distance due to the nature of gravitational potential, which is proportional to 1/r, leading to a second derivative of 1/r³. This relationship results in tidal forces being significantly weaker than standard gravitational forces, explaining why the Moon, despite its smaller size, exerts a stronger tidal influence on Earth than the much larger Sun. The forces in a local Cartesian system in free-fall demonstrate that radial forces point outward while perpendicular forces point inward, contributing to this inverse cube relationship. For further information, resources such as specific physics texts and online explanations can provide more detailed insights. Understanding these principles is crucial for grasping the dynamics of tidal forces.
