14.18: Tidal Forces
The origin of Earth's ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be the beginning of the proper understanding of the phenomenon. Ocean tides are the result of gravitational tidal forces. These same tidal forces are present in any astronomical body; they are responsible for the internal heat that creates the volcanic activity on Io, one of Jupiter's moons, and the breakup of stars that get too close to black holes.
Newton's law of gravitation states that gravitational force is inversely proportional to the square of the distance between the two-point masses. However, for an extended object like Earth, the gravitational force acting on the side facing the Sun is much higher than the gravitational force acting on the other side. This difference in forces at different locations gives rise to tidal forces, which are inversely proportional to the cube of the distance between the two masses.
Sea levels rise twice a day mainly due to tidal forces acting on the Earth because of the Moon's gravitational force. Though the Sun is 27 million times more massive than the Moon, its distance from the Earth is approximately 390 times more than the distance between the Earth and the Moon. Since the tidal forces are inversely proportional to the cube of the distance, the Sun's tidal force is about half that of the Moon.
Although the Moon is the dominant force that causes tides on the Earth, the Sun still has an effect. The tides vary depending on the orientation of the three bodies. When the Sun, Earth, and Moon are aligned, i.e., on a Full Moon or a New Moon day, the tidal forces add, and the amplitude of tides is maximum. These are called Spring tides. On a Half Moon day, the Moon is perpendicular to the Sun-Earth line. Here, the tides are at their smallest and are called Neap tides.
The rotation of the Earth and the revolution of the Moon further complicates the calculation for the time intervals of tides. However, approximately, the time between consecutive high (or low) tides can be considered to be 12.5 hours.
This text is adapted from Openstax, University Physics Volume 1, Section 13.6: Tidal Forces.