Confusion around the tidal force and the centrifugal force

TL;DR

This paper clarifies the correct understanding of tidal forces caused by non-uniform gravity and explains why inertial forces like the centrifugal force are often mistakenly invoked in explanations.

Contribution

It provides a clear distinction between the true origin of tidal forces and common misconceptions involving centrifugal forces.

Findings

Tidal force arises from gravitational non-uniformity, not inertial effects.

Misinterpretation of centrifugal force can lead to misconceptions about tidal phenomena.

Proper treatment clarifies the physical origin of tidal forces.

Abstract

We discuss the tidal force, whose notion is sometimes misunderstood in the public domain literature. We discuss the tidal force exerted by a secondary point mass on an extended primary body such as the Earth. The tidal force arises because the gravitational force exerted on the extended body by the secondary mass is not uniform across the primary. In the derivation of the tidal force, the non-uniformity of the gravity is essential, and inertial forces such as the centrifugal force are not needed. Nevertheless, it is often asserted that the tidal force can be explained by the centrifugal force. If we literally take into account the centrifugal force, it would mislead us. We therefore also discuss the proper treatment of the centrifugal force.