Tidal acceleration

Tidal acceleration is a complex physical process involving the gravitational forces between a planet and its orbiting satellite. In the Earth-Moon system, this interaction causes the Moon to move into a higher orbit while simultaneously slowing Earth's rotation. This phenomenon is a type of secular perturbation, which is a change in an orbit that increases continuously over time rather than oscillating periodically. Unlike many gravitational interactions that cause planets to wobble back and forth, tidal acceleration involves friction. This friction causes a permanent loss of energy from the system, which is converted into heat.

The mechanism begins with the Moon's gravitational pull on Earth. This gravity creates tidal bulges in Earth's oceans and a smaller effect in the solid crust. Because Earth rotates much faster than the Moon orbits, the planet's spin carries these bulges ahead of the Moon's position. This offset creates a gravitational torque, which is a twisting force. This torque exerts a push on the Moon, boosting it into a higher, more distant orbit. As the Moon moves outward, its orbital speed and angular rate decrease, meaning it takes longer to complete an orbit.

At the same time, this process results in tidal braking for the primary planet. As the tidal bulge pulls on the Moon, the Moon pulls back on the bulge. This interaction transfers angular momentum from Earth's rotation to the Moon's orbit. Consequently, Earth's rotation slows down over vast periods of time. This effect is measured by the increasing length of the mean solar day. Current observations show that the day lengthens by just under 2 milliseconds every 100 years.

Scientists have been studying these subtle changes for centuries. In 1695, Edmond Halley first suggested that the Moon's motion was changing by comparing it to ancient eclipse observations. However, he lacked the data to explain why. In 1749, Richard Dunthorne provided the first quantitative estimate, calculating a rate of +10 arcseconds in lunar longitude per century. In 1786, Pierre-Simon Laplace proposed a theory involving Earth's orbital eccentricity. But in 1854, John Couch Adams discovered an error in Laplace's math. Adams showed that Laplace's theory only accounted for about half of the observed acceleration, sparking a major astronomical controversy.

Modern science identifies three distinct factors that contribute to the observed lunar acceleration. First, there are perturbational changes in the eccentricity of Earth's orbit around the Sun. Second, there is a real retardation of the Moon's angular orbital motion due to the exchange of angular momentum. Third, there is an apparent increase in the Moon's angular rate when measured against mean solar time. This apparent acceleration happens because the Earth's rotation is slowing down, which changes the length of the day used as a reference.

The energy loss in this system comes from two main sources. The majority of the energy is dissipated through the movement of the oceans. A smaller portion, about 4% of the total effect, comes from the flexing of the Earth's solid crust. This flexing of the crust also generates heat. This process is different from most planetary motions because it is not a Hamiltonian system, meaning energy is not conserved within the motion itself but is lost to the environment as heat.

If this process continued indefinitely, the Earth-Moon system would eventually reach tidal locking. In this state, Earth's rotational period would match the Moon's orbital period. The Moon would appear to hang motionless over a single fixed location on Earth. This state is already seen in the Pluto-Charon system. However, Earth may never reach this state. In 1 to 1.5 billion years, increasing solar radiation may vaporize the oceans. Without oceans, the tidal friction would change significantly. Furthermore, the Sun may become a red giant in 4.5 billion years, potentially destroying both bodies before the process completes.