Tidal acceleration

The Moon pulls on our oceans.

This makes the water bulge out. The bulge pulls on the Moon. This pull helps the Moon move away from Earth. It also makes our day longer.

Earth spins a little slower every year. This happens because of the pull between the two. Our days grow by a tiny bit every century. This is a very slow change. It takes a long time to notice. The Moon and Earth are always moving together.

The Moon and Earth are always pulling on each other.

This pull creates tides in our oceans. The Moon's gravity makes the water bulge out. Earth spins faster than the Moon orbits us. This spin carries the water bulge ahead of the Moon.

This offset bulge pulls on the Moon. This pull is called torque. It acts like a tiny push that moves the Moon away. The Moon moves to a higher orbit. Because it is farther away, it moves more slowly. This push also slows Earth's spin. We call this tidal braking. Our days get longer by about 2 milliseconds every 100 years. This is a very small change. If this kept going, Earth's spin would match the Moon's orbit. The Moon would stay over one spot on Earth. This is called tidal locking. This might happen in 50 billion years. However, the Sun will change before then. In about 1 billion years, the Sun will get hotter. This heat might turn our oceans into vapor. That would change how these tides work.

The Earth and the Moon are locked in a constant dance. They pull on each other using gravity. This pull creates tides in our oceans. The Moon's gravity makes the water bulge out.

Because Earth spins faster than the Moon orbits us, the spin carries that water bulge ahead of the Moon. This offset bulge pulls on the Moon with a force called torque. This torque acts like a tiny push. It moves the Moon into a higher orbit. This process is known as tidal acceleration. At the same time, this push slows down Earth's rotation. Scientists call this slowing effect tidal braking.

This process works in a very specific way. The Moon's gravity pulls on Earth's water and solid crust. This creates a tidal bulge. Because Earth rotates quickly, the bulge is carried forward. This bulge is not perfectly lined up with the Moon. The tilted bulge exerts torque on the Moon. This torque boosts the Moon to a higher orbit. As the Moon moves farther away, its orbital speed decreases.

The Moon also takes longer to complete one orbit. Meanwhile, the Earth loses energy. This energy loss comes from friction. The friction turns motion into heat. This heat comes from the flexing of Earth's crust. This crust flexing accounts for about 4% of the total effect. The rest comes from the oceans.

People have studied this movement for a long time. Edmond Halley first suggested the Moon's motion was changing in 1695. He used ancient records of eclipses to find this. He did not have all the data yet. In 1749, Richard Dunthorne confirmed this idea. He gave the first real estimate of the effect. He found a rate of about 10 arcseconds per century. Later, in 1786, Pierre-Simon Laplace wrote a theory about it. He thought the Moon's speed changed because of Earth's orbit around the Sun. However, in 1854, John Couch Adams found an error in that math. He showed that Laplace's idea only explained half the change. This started a big debate among astronomers.

We now know there are three main parts to this change. One part comes from the shape of Earth's orbit. The second part is a real slowing of the Moon's orbital motion. This happens because of the exchange of angular momentum. The third part is an apparent change in speed. This happens because Earth's rotation is slowing down. As Earth slows, our days get longer. The day grows by nearly 2 milliseconds every 100 years.

This tiny change adds up over a very long time. It even requires leap seconds to keep our clocks right.

This dance changes how the Earth-Moon system looks. If this continued, we would reach tidal locking. This means Earth's rotation would match the Moon's orbit. The Moon would always stay over one spot on Earth. This already happens in the Pluto-Charon system. Some think this could happen here in 50 billion years. But the Sun will change first. In about 1 to 1.5 billion years, the Sun will get hotter. This heat might turn our oceans into vapor. Without oceans, the tidal friction would change. The Sun might also become a red giant in 4.5 billion years. This could destroy both the Earth and the Moon before the dance ever ends.

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.