Recession of the Moon

THE gravitational force, which is the weakest of the four fundamental forces in nature, is an action-reaction force. So, just as Moon's gravitational force on Earth results in tidal friction (action) that eventually slows down Earth's rotational and orbital speeds (TDS May 21, 2013), Earth's gravitational force also exerts a frictional force (reaction) on the Moon. However, the effect of tidal friction is more drastic on Moon because of its relatively smaller size and mass. The Moon being a solid body undergoes deformation of its surface only, a phenomenon known as solid tide. Its shape becomes slightly elongated along the line toward the Earth.

Earth as viewed from the Moon.

Tidal friction has slowed the rotational and orbital speeds of the Moon long ago to the extent that it takes the same time to spin once on its axis as it takes to go around the Earth, i.e. lunar month and day are equal – 29.53 days. This is known as synchronous rotation and is similar to the situation with communication satellites placed in Earth's orbit with 24-hour period. The Moon, therefore, keeps only one side, the "near side," facing the Earth. Does this mean that the "far side", also known as dark side, is perpetually dark? No. It is illuminated as often as the near side. When there's a full moon the far side is the dark side, but when it's a new moon the far side is the illuminated side.

The Earth, as viewed from the Moon by the Apollo astronauts, always remained in the exact same position in the sky. Eventually we will also be in same situation as the Moon, probably after billions of years from now. It happened to the Moon much earlier because Earth's tidal force is stronger. Most of the natural satellites in the solar system are in synchronous rotation because of the tidal effects of their parent planets.

As Earth slows down it loses rotational kinetic energy. Energy conservation requires that Moon gain energy. In other words, Earth transfers energy to Moon through the tidal bulge and gravity. This extra energy gained by the Moon causes it to speed up and move farther away from us. Current estimates show that the Moon is receding from us at a rate of 3.8 cm per year. This rate has been determined by a technique known as Lunar Laser Ranging, which uses "corner mirrors" installed on the Moon by the Apollo astronauts in the 1960s.

Planetary models indicate that the closest distance between Earth and the Moon was 18,400 km. It took only 1.37 billion years for the Moon to reach its present distance of 384,400 km. As the Moon grows more distant, its orbital period about the Earth increases adding about 0.014 seconds per century to the lunar month.

If the present rate of recession continues, sometime in the distant future Moon will be so far away that its shadow will no longer reach Earth and total solar eclipse will cease to exist. Different planetary models predict that when both solar day and lunar month will become equal to 47 of our present days, tidal friction will cease. The Earth and Moon will then be tidally locked to each other and Earth will rotate synchronously with Moon and no further recession will occur. Each will perpetually keep the same face turned toward each other and Moon will be visible from one side of Earth only. In other words, Moon as viewed from Earth will appear suspended in the sky. It is estimated that this will happen when Moon will be approximately 645,000 km away from Earth.

Within the solar system, Pluto and its Moon Charon are already in synchronous rotation. Outside the solar system, many binary stars (similar to the Earth-Moon system) are also in synchronous rotation.

The writer is a Professor in the Department of Physics & Engineering Physics, Fordham University, New York