Moon

Earth's Moon: Facts & Figures (CC) Photo: Luc Viatour A Full Moon, as seen from Earth. Physical Characteristics Mean circumference 10,917.0 km Mean radius 1,737.5 km Mass 7.3477×1022 kg Volume 2.197×1010 km3 Density 3.344 g/cm3 Surface area 3.79367×107 km2 Surface gravity 1.624 m/s2 Escape velocity 2,376 m/s Surface temperature (night/day) -233/123 °C Rotational and Orbital Characteristics Distance from Earth: Average Apogee (farthest) Perigee (closest) 384,400 km 405,696 km 363,104 km Rotation velocity around own axis 4.6246 m/s Rotation period around own axis (length of "Moon day") (a) 655.73 hours 27.322 Earth days Orbit distance around the Earth 2.4134×106 km Orbit velocity around the Earth 1.0224 km/s Orbit period around the Earth (length of "Moon year") (a) 655.73 hours 27.322 Earth days Orbit period around the Sun 365 Earth days 13.359 Moon days (a) Defining a celestial body's year as the time it takes the celestial body to travel one orbit around a larger celestial body. Thus, the orbit period of the Moon around the Earth is a "Moon year". It is simply happenstance that the Moon also takes 27.322 Earth days to rotate around its own axis and so a "Moon day" equals a "Moon year".

The Moon is the second brightest object in the sky, after the Sun. It is the only natural satellite in orbit around the Earth, at a distance of 384,400 km. With a diameter of 3476 km and mass of 7.35×10^22 kg, the Moon is larger than any other satellite orbiting the other planets of the Solar System. The Romans called the Moon Luna and the adjective 'lunar' is still used to describe things related to the Moon.

The brightness of the Moon is from sunlight reflected off its surface. As the Moon orbits the Earth, different amounts of illumination of its surface are visible. This makes it appear as though it is changing shape throughout the month. When the Moon is almost directly between the Earth and the Sun, little or no illuminated lunar surface is visible. This is known as a New Moon. As it moves round, an arc of illuminated surface becomes visible, known as a Crescent Moon, a 'waxing' (growing) crescent. The width of the crescent gradually increases until, when the Moon is a quarter of the way round its orbit, a full semi-circle is visible, a Half Moon. This gradually gets rounder. This is known as a waxing gibbous. When the Sun and Moon are on opposite sides of the Earth, the Moon appears as a complete disc: this is called the Full Moon. It is at this time that its light reaching Earth is at its greatest. The Moon continues on its orbit, gradually narrowing through a waning gibbous, and again to half, then to a waning crescent before completing the cycle of phases, and becoming a New Moon again.

Humans have often dreamed of traveling to the Moon. During the twentieth century, that dream became a reality. The Soviet Union was the first nation to send a space craft to the Moon. Luna 2 impacted the Moon's surface in 1959. The first photographs of the far side of the Moon were taken by Luna 3, another Soviet craft, later that same year. The American Apollo program achieved a series of manned missions that landed on the Moon and subsequently returned to Earth. The first men, Neil Armstrong and 'Buzz' Aldrin, landed on the Moon on July 20, 1969 as part of Apollo 11. Several other manned Apollo missions followed with the last, Apollo 17, reaching the Moon on December 11, 1972. In total, 12 men have walked on the Moon.

The Moon's orbit around the Earth

Lunar declination

The Moon's orbit is elliptical and not circular. It passes closest to Earth at its perigee and furthest at its apogee. The Moon does not orbit around the Earth’s equator. The Moon's declination effect (change in angle with respect to the equator) means its orbit is offset from the Earth's equator, orbiting at 5 degrees above and below the plane of the ecliptic, an inclination from the Earth's equator ranging 18.3° and 28.6° over a period of 18.61 years during Earth's orbit around the Sun. The plane of the ecliptic in turn is itself about 23 degrees from the plane of the Earth's equator.

Orbital periods

The Moon’s orbit around the Earth has two different periods. The Moon’s sidereal period of about 27.3 days is its orbit around the Earth measured by comparison of the Moon’s motion to the fixed stars. The Moon’s synodic period, viewed from Earth as the phases of the Moon, is the Moon’s orbit around the Earth with respect to the Sun. The synodic, a period of approximately 29.5 days, is longer than the sidereal period because the Earth is moving while the Moon orbits around the Earth. In other words, a New Moon does not appear every 27.3 days, it appears every 29.5 days even though the Moon has already completed an orbit around the Earth more than two days earlier. In the period of one 365-day Earth sidereal year the Moon completes approximately 13.4 sidereal periods and 12.4 synodic periods. This is why it is possible to have more than one new Noon a month on the modern calendar.

Gravitational effects the Earth and Moon exert on each other

The Moon’s orbit is getting larger, increasing by about 3.8 centimetres per year. The Moon’s rotation has slowed to the point that it presents only one face toward the Earth. The Earth’s rotational period is slowing down by about 2 milliseconds every 100 years. These are all due to the mutual gravitational effects between the Earth and the Moon.

The Moon’s gravitational effect raises tides on Earth displacing the Earth’s water outward by meters (about 1 meter in the open ocean and as high as 18 meters in coastal waters as takes place in the Bay of Fundy) and its solid surface by about 30 centimetres. This is called a tidal bulge:

In addition to this lunar tidal effect, the Earth’s rotation on its axis has a greater effect on this bulging configuration and the diameter of the Earth at the Equator, equatorial bulging, is about 23 kilometers, (about 0.4% of the Earth's radius) higher than it would be if the Earth did not rotate.

Since the centre of gravity for the Moon’s orbit around Earth, the barycenter, is not the centre of gravity for the Earth, as the Earth bulges outward, this barycenter or shared centre of gravity around which the Moon orbits actually extends further from the Earth’s centre of gravity.

The Earth’s rotation (approximately once every 24 hours) has the effect of exerting a force on the Moon’s orbital period around the Earth (once every 27.3 days). Because of the Earth’s rotation, tidal bulge actually precedes the Moon by about 3 degrees, which exerts gravitational forces to pull the Moon forward in its orbit. This increases the Moon’s energy to resist Earth’s gravitational pull and allows the Moon to move away from the Earth and increase its orbit, a phenomenon referred to as lunar recession. As the Moon’s orbit increases its orbital period decreases and slows it down.

The Moon is also pulling back on the Earth through the phenomenon of tidal breaking caused by tidal friction on the Earth’s surface and slowing the Earth’s rotation at the rate of about 2 milliseconds every 100 years. This has a significant accumulative effect however and it is estimated that the terrestrial day about 900 million years ago was approximately 18 hours.

This lunar tide dissipation is not a steady rate of change however. The amount of water being pulled in the tidal bulge, the depth of the water, the size and presence of ice shelves, the position and size of the ancient continents which may have altered the path of the tidal bulge would all have varying effects on the amount of energy loss taking place and the eventual changes in the Moon's orbit and the Earth's rotation.

The Moon is generating vast amounts of energy on the Earth's surface as it generates the tidal bulge. The lunar tides dissipate about 3.3 to 4 tW of energy (3.3 to 4 × 10¹² watts) in the Earth's oceans.

Tidal locking

So the resultant ‘tidal friction’ of this mutual gravitational effect of the Moon and the Earth takes energy out of the Earth pulling it into the Moon’s orbit, and increases the Moon’s orbital diameter while slowing the moon’s orbit around the Earth. The slowing effect of the tidal friction would have taken place in the space of billions of years with the result that the Moon eventually slowed so much that it now keeps the same side toward the Earth today, a phenomenon called “tidal locking”.

Tidal locking will also happen on Earth. If the tidal friction continues unabated, the length of a day on Earth and the Moon’s orbital period will equalize at about 55 days. Then the Earth will always face the Moon on the same side just as we now only see one side of the Moon. The tidal bulge leading the Moon today will point directly at the Moon and the Moon will no longer move away from the Earth.

Tidal locking is a common occurrence between other bodies in the solar system. Pluto and Charon are already tidally locked.

Tidal friction

Tidal friction is measured in several ways.

The length of the lunar month can be measured by measuring the thickness of tidal deposits, “tidal rhythmites”, preserved in the Earth’s rock layers over billions of years although the measurements currently cover only about 900 million years. The resultant studies have shown the tidal layers correspond to increases in the lunar month, hence a slowing of the lunar orbit. This rate of change has remained nearly unchanged.

The Earth’s rotational period has also been measured by bouncing laser beams off reflectors placed on the Moon’s surface by Apollo astronauts. These studies show increases in the Moon’s orbit.

Another way to study the phenomenon of tidal friction is to measure the change in the rotational period of the Earth. Very Long Baseline Interferometry studies utilising many radio telescopes on the Earth’s surface to study the positions of the quasars have shown that over time very accurate measures of the rotational period of the Earth show that the Earth’s rotation is in fact slowing down.

The ultimate result

Disappearance of total solar eclipses

Sometime within the next 500 million to 1 billion years the Moon will be so far away that total solar eclipses will no longer be possible. The Moon will have moved about 5% further away of the distance it is today and the lunar disc will be too small to hide the Sun resulting only in partial solar eclipses.

A distant orb or an explosive collision

There are two alternative scenarios. Eventfully the Moon’s orbit would stabilise at about 1.6 times the distance it is today. This would take about 15 billion years.

On the other hand, as tidal locking is obtained, the Moon would lose momentum. Its orbit would then degrade and eventually it would collide with the Earth.

Climate change

There is increasing evidence that also implicates the lunar tides in climate change. The energy of the lunar tides was long thought to dissipate in the surface water of the oceans. However, since the late 90s, studies using Topex/Poseidon satellite altimeter data to measure changes worldwide have shown that the lowest depths of the ocean are stirred by lunar tides, mixing the cold water of the oceans depths with the warmer waters of the surface and affecting ocean currents and global temperatures. Massive currents that sweep across the surface of the Earth's oceans and those that sweep through the abyssal plains together comprise the thermohaline circulation or oceanic conveyor belt system, changing ocean temperature, and salinity worldwide.