The Moon is the only natural satellite of the Earth, and the 5th largest satellite in the Solar System. It is the largest natural satellite of a planet in the Solar System relative to the size of its primary, having 27% the diameter and 60% the density of Earth, resulting in 1/81 its mass. The Moon is the second densest satellite after Io, a satellite of Jupiter.
The Moon is in synchronous rotation with Earth, always showing the same face with its near side marked by dark volcanic maria that fill between the bright ancient crustal highlands and the prominent impact craters. It is the brightest object in the sky after the Sun, although its surface is actually very dark, with a reflectance similar to that of coal.
The Moon’s current orbital distance, about 30 times the diameter of the Earth, causes it to appear almost the same size in the sky as the Sun, allowing it to cover the Sun nearly precisely in total solar eclipses. This matching of apparent visual size is a coincidence.
Its prominence in the sky and its regular cycle of phases have, since ancient times, made the Moon an important cultural influence on language, calendars, art and mythology. The Moon’s gravitational influence produces the ocean tides and the minute lengthening of the day. The Moon’s linear distance from the Earth is currently increasing at a rate of 3.82±0.07cm per year, however this rate is not constant.
Origin of the Moon
The Moon is thought to have formed nearly 4.5 billion years ago, not long after the Earth. Although there have been several hypotheses for its origin in the past, the current most widely accepted explanation is that the Moon formed from the debris left over after a giant impact between Earth and a Mars-sized body.
Several mechanisms have been proposed for the Moon’s formation 4.527 ± 0.010 billion years ago, some 30–50 million years after the origin of the Solar System. These included:
- the fission of the Moon from the Earth’s crust through centrifugal force (which would require too great an initial spin of the Earth),
- the gravitational capture of a pre-formed Moon (which would require an unfeasibly extended atmosphere of the Earth to dissipate the energy of the passing Moon),
- and the co-formation of the Earth and the Moon together in the primordial accretion disk (which does not explain the depletion of metallic iron in the Moon).
These hypotheses also cannot account for the high angular momentum of the Earth–Moon system.
The Giant Impact Theory
The prevailing hypothesis today is that the Earth–Moon system formed as a result of a giant impact: a Mars-sized body hitting the newly formed proto-Earth, blasting material into orbit around it, which accreted to form the Moon.
Giant impacts are thought to have been common in the early Solar System. Computer simulations modelling a giant impact are consistent with measurements of the angular momentum of the Earth–Moon system and the small size of the lunar core. These simulations also show that most of the Moon came from the impactor, not from the proto-Earth. However more recent tests suggest more of the Moon coalesced from the Earth and not the impactor. Meteorites show that other inner Solar System bodies such as Mars and Vesta have very different oxygen and tungsten isotopic compositions to the Earth, while the Earth and Moon have near-identical isotopic compositions. Post-impact mixing of the vaporized material between the forming Earth and Moon could have equalized their isotopic compositions, although this is debated.
Despite its accuracy in explaining many lines of evidence, there are still some difficulties that are not fully explained by the giant impact hypothesis, most of them involving the Moon’s composition.
In 2001, a team at the Carnegie Institute of Washington reported the most precise measurement of the isotopic signatures of lunar rocks. To their surprise, the team found that the rocks from the Apollo program carried an isotopic signature that was identical with rocks from Earth, and were different from almost all other bodies in the Solar System. Since most of the material that went into orbit to form the Moon was thought to come from Theia, this observation was unexpected. In 2007, researchers from the California Institute of Technology announced that there was less than a 1% chance that Theia and Earth had identical isotopic signatures. Published in 2012, an analysis of titanium isotopes in Apollo lunar samples showed that the Moon has the same composition as the Earth, which conflicts with the moon forming far from Earth’s orbit or from Theia. Variations on GIH may explain this data.
Astronomical Units of Time
A “day” is a unit of time defined by Earth’s axial rotation: it is the period of time measured from local noon (sun at its highest point over horizon) to the following local noon (a solar day.)
This unit of time was used to define smaller units of time by dividing one day into 24 hours and further dividing each hour into 60 minutes and each minute into 60 seconds.
For many centuries astronomers counted the hours and days from noon, because it was the easiest solar event to measure accurately. In the modern 24-hour clock, counting the hours starts at midnight and hours are numbered from 0 to 23. Solar noon is always close to 12:00, again differing according to the equation of time. At the equinoxes sunrise is around 06:00 and sunset around 18:00. Even though today’s atomic clocks have a much more constant rate than the Earth, we use its star clock to determine mean solar time.
The Earth rotates once in 24 hours from the point of view of the sun and once every 23 hours 56 minutes and 4 seconds (23.93447 h) from the point of view of the stars (this is the time of one complete rotation of Earth on its axis).
The Motion of the Moon
The Moon makes a complete orbit around the Earth with respect to the fixed stars about once every 27.3 days (its sidereal period). However, since the Earth is moving in its orbit about the Sun at the same time, it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days (its synodic period).
Drawing not to scale
Unlike most satellites of other planets, the Moon orbits nearer the ecliptic plane than to the planet’s equatorial plane. The Moon’s orbit is subtly perturbed by the Sun and Earth in many small, complex and interacting ways. For example, the plane of the Moon’s orbital motion gradually rotates, which affects other aspects of lunar motion.
Earth’s rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth’s rotation. Atomic clocks show that a modern day is longer by about 1.7 milliseconds than a century ago, slowly increasing the rate at which UTC is adjusted by leap seconds. The Moon is spiraling away from Earth at an average rate of 3.8 cm (1.5 in) per year, as detected by the Lunar Laser Ranging Experiment. The current recession rate is considered anomalously high. The tidal dissipation rate varied in the Earth geological history.
Over millions of years, the rotation of earth is noticeably slowed by gravitational interactions with the Moon; both rotational energy and angular momentum are being slowly transferred to the Moon (due to tidal acceleration.) The present rate of tidal dissipation in the Earth-Moon system is known to be anomalously high, in the sense that the implied age of the lunar orbit is only 1.5×109 years, though other evidence suggests an age closer to 4×109 years. [ http://isotope.colorado.edu/~geol5700/Bills_1999.pdf ]
The Moon’s orbit (its circular path around the Earth) is getting larger, at a rate of about 3.8 centimeters per year. (The Moon’s orbit has a radius of 384,000 km.)
The reason for the increase is that the Moon raises tides on the Earth. Because the side of the Earth that faces the Moon is closer, it feels a stronger pull of gravity than the center of the Earth. Similarly, the part of the Earth facing away from the Moon feels less gravity than the center of the Earth. This effect stretches the Earth a bit, making it a little bit oblong. We call the parts that stick out “tidal bulges.” The actual solid body of the Earth is distorted a few centimeters, but the most noticeable effect is the tides raised on the ocean.
Now, all mass exerts a gravitational force, and the tidal bulges on the Earth exert a gravitational pull on the Moon. Because the Earth rotates faster (once every 24 hours) than the Moon orbits (once every 27.3 days) the bulge tries to “speed up” the Moon, and pull it ahead in its orbit. The Moon is also pulling back on the tidal bulge of the Earth, slowing the Earth’s rotation. Tidal friction, caused by the movement of the tidal bulge around the Earth, takes energy out of the Earth and puts it into the Moon’s orbit, making the Moon’s orbit bigger (but, a bit paradoxically, the Moon actually moves slower!).
The Earth’s rotation is slowing down because of this. One hundred years from now, the day will be 2 milliseconds longer than it is now.
This same process took place billions of years ago – the Moon was slowed down by the tides raised on it by the Earth. That’s why the Moon always keeps the same face pointed toward the Earth. Because the Earth is so much larger than the Moon, this process, called tidal locking, took place very quickly, in a few tens of millions of years.
There are three ways for us to actually measure the effects of tidal friction.
* Measure the change in the length of the lunar month over time.
This can be accomplished by examining the thickness of tidal deposits preserved in rocks, called tidal rhythmites, which can be billions of years old, although measurements only exist for rhythmites that are 900 million years old. As far as I can find (I am not a geologist!) these measurements have only been done since the early 90’s.
* Measure the change in the distance between the Earth and the Moon.
This is accomplished in modern times by bouncing lasers off reflectors left on the surface of the Moon by the Apollo astronauts. Less accurate measurements were obtained in the early 70’s.
* Measure the change in the rotational period of the Earth over time.
Nowadays, the rotation of the Earth is measured using the Very Long Baseline Interferometry, a technique using many radio telescopes a great distance apart. With VLBI, the positions of quasars (tiny, distant, radio-bright objects) can be measured very accurately. Since the rotating Earth carries the antennas along, these measurements can tell us the rotation speed of the Earth very accurately.
However, the change in the Earth’s rotational period was first measured using eclipses, of all things. Astronomers who studied the timing of eclipses over many centuries found that the Moon seemed to be accelerating in its orbit, but what was actually happening was the the Earth’s rotation was slowing down. The effect was first noticed by Edmund Halley in 1695, and first measured by Richard Dunthorne in 1748–though neither one really understood what they were seeing. I think this is the earliest discovery of the effect.
Moon Related Questions
The Moon slows the Earth’s rotation, but how fast was it spinning billions of years ago?
When was the Moon formed and how fast was the Earth spinning then?
In a previous answer you said: “The Earth’s rotation is slowing down because of the Moon pulling back on its tidal bulge. One hundred years from now, the day will be 2 milliseconds longer than it is now.”
I’ve seen numbers for the Moon’s formation from 4 to 4.6 billion years ago. At the rate you gave above, the Earth would have been making a rotation every couple hours in the first case, or actually spinning BACKWARDS in the latter. I understand that the rate is definitely not constant, but wouldn’t the Moon pull harder, and thus lengthen the day faster, when it was closer, making the problem even worse?
Everything you’ve said is quite right! The missing piece of the puzzle is in the details how the Moon interacts with the Earth via tides.
The Moon does cause a small distortion in the Earth’s shape, but as everyone knows, the major effect is tides on the ocean. The Moon’s gravity is actually dragging most strongly on the tidal bulge raised on the oceans.
And as it happens, it takes about 12 hours for a big wave to slosh across the Pacific Ocean and back–just in time for its height to be reinforced by the next high tide. So because of the size of the Pacific Basin, the Moon is very effective at slowing the Earth’s rotation right now. However, the size of the ocean changes due to continental drift, so in the past, even though the Moon was closer, tidal friction was a much weaker effect. Unfortunately, it’s very difficult to measure or calculate exactly how the positions of the continents have changed over time to the degree of precision that is necessary to work out the effect on tides, and we have just a few ways to measure the rotation of the Earth at different times in its history, so we do not have a complete history of how the Earth and Moon have interacted, and we are not sure exactly how far from the Earth the Moon was when it first formed, or how fast the Earth was rotating at that time.
How close was the Moon to the Earth when it formed?
Given the fact that the Moon is moving away from the Earth, could you please tell me how close the moon was when it was at it’s closest to Earth, presumably when it formed? I am curious to know how big the moon would have looked at that time. Also, do you know if the rate of departure has ALWAYS been constant?
The Moon is thought to have formed when an object roughly the size of Mars hit the Earth. The impact was so violent that it threw large amounts of the Earth’s mantle into orbit. This material eventually coalesced and formed the Moon.
It is not easy to estimate how far away from the Earth the Moon was when it formed, but simulations suggest is was about 3-5 times the radius of the Earth, or about 19-30 thousand km. (The Moon is currently about 384,000 km away from Earth).
The Moon probably couldn’t have formed closer than 3 Earth radii because tidal forces from the Earth would just pull it apart again, and it is unlikely that the impact could have ejected material further than 5 Earth radii. It’s not a totally easy questions to answer though as it depends a lot on the (unknown) details of the impact and how the hot material behaved in space.
The exact rate of the Moon’s movement away from Earth has varied a lot over time. It depends both on the distance between the Earth and the Moon, and the exact shape of the Earth. The details of continents and oceans moving around on Earth actually change the rate, which make it a very hard thing to estimate. The rate is currently slowing down slightly, and it is estimated that in about 15 billion years the Moon’s orbit will stop increasing in size.
The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred to as the barycenter.
The barycenter is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting around a point that lies away from the center of the primary (larger) body.
For example, the Moon does not orbit the exact center of the Earth, but a point on a line between the center of the Earth and the Moon, approximately 1,710 km (1062 miles) below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun. If the masses are more similar, e.g., Pluto and Charon, the barycenter will fall outside both bodies.
Perhaps the motion of the barycenter of the Solar System as the whole is responsible for subtle (and periodic) changes in the solar activity which in turn could cause major changes on our planet (e.g. ice ages, level of radiation, etc)?
Motion of the Solar System barycenter relative to the Sun. Source: Wikipedia, Carl Smith
The Conservation of Angular Momentum
In orbits, the angular momentum is distributed between the spin of the planet itself and the angular momentum of its orbit:
If a planet is found to rotate slower than expected, then astronomers suspect that the planet is accompanied by a satellite, because the total angular momentum is shared between the planet and its satellite in order to be conserved.
The conservation of angular momentum is used extensively in analyzing what is called central force motion. If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant. Constant angular momentum is extremely useful when dealing with the orbits of planets and satellites, and also when analyzing the Bohr model of the atom.
The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation. By bringing part of mass of her body closer to the axis she decreases her body’s moment of inertia. Because angular momentum is constant in the absence of external torques, the angular velocity (rotational speed) of the skater has to increase.
The same phenomenon results in extremely fast spin of compact stars (like white dwarfs, neutron stars and black holes) when they are formed out of much larger and slower rotating stars (indeed, decreasing the size of object 104 times results in increase of its angular velocity by the factor 108).
The conservation of angular momentum in Earth–Moon system results in the transfer of angular momentum from Earth to Moon (due to tidal torque the Moon exerts on the Earth). This in turn results in the slowing down of the rotation rate of Earth (at about 42 ns/day), and in gradual increase of the radius of Moon’s orbit (at ~4.5 cm/year rate). [ Source: Wikipedia ]
- – -
The described above theories suggest that over long period of time the earth has tendency to slow down its axial rotation while the moon moves further away from our planet (taking longer to complete its full orbit around the earth).
As the result, in the very distant future, the earth will take less than 365.25 days to complete a full orbit around the sun. Once the orbital period of the earth goes down to 360 days, and further and slower moon takes 30 days to circle the earth, we would be able (perhaps again?) to use a “perfect calendar” with 12 lunar month (30 days each) and 360 days year.
Extrapolation into a distant past of the current tendency of earth to slow down its rotation, might suggest that millions of years ago our planet was rotating faster than today (the orbital period was more than 365.25 days). However it is also possible that long time ago the orbital speed of the earth WAS exactly 360 days, until a major asteroid impact accelerated this rotation and increased number of days in a year to 365.25 (and possibly tilted the axis of rotation).
This will be explored in the next post.
PS1 Asteroid Impact
Craters are the evidence of intensive “bombardment” of the planets and moons of the solar system
Virtually all planetary surfaces are cratered from the impact of interplanetary bodies. It is now clear from planetary bodies that have retained portions of their earliest surfaces that impact was a dominant geologic process throughout the early solar system. For example, the oldest lunar surfaces are literally saturated with impact craters, produced by an intense bombardment which lasted from 4.6 to approximately 3.9 billion years ago, at least a 100 times higher than the present impact flux.
Can asteroid impact change axial rotation of a planet?
Yes, collision with a large asteroid could have measurable impact on axial rotation and tilt.
- – -
In the context of the above theories, it is worth consideration that major asteroid impact could have disrupted “perfect” cycles of the Earth and Moon system (360 days year with 12 lunar month to a year) and caused Earth rotation to be slightly faster … so after the asteroid impact the Earth would take 365.25 days to complete its full 360 deg orbit around the sun.
Follow up this article:
PS2 Mars and Venus
Mars has approximately half the diameter of Earth. It is less dense than Earth, having about 15% of Earth’s volume and 11% of the mass.
Did you know that Mars has an axial tilt and a rotation period similar to those of Earth?
The average length of a Martian sidereal day is 24h 37m 22.663s (based on SI units), and the length of its solar day (often called a sol) is 88,775.24409 seconds or 24h 39m 35.24409s.
The corresponding values for Earth are 23h 56m 04.2s and 24h 00m 00.002s, respectively. This yields a conversion factor of 1.027491 days/sol.
Thus Mars’s solar day is only about 2.7% longer than Earth’s.
Its year, however, is almost twice as long as Earth’s:
Mars orbital period:
686.971 days = 1.8808 Julian years = 668.5991 sols
Synodic period = 779.96 days = 2.135 Julian years
The diameter of Venus is 12,092 km (only 650 km less than the Earth’s) and its mass is 81.5% of the Earth’s.
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days.
Venus Orbital period = 224.698 day = 0.615 190 yr = 1.92 Venus solar day
Synodic period 583.92 days
All the planets of the Solar System orbit the Sun in a counter-clockwise direction as viewed from above the Sun’s north pole. Most planets also rotate on their axis in a counter-clockwise direction, but Venus rotates clockwise (called “retrograde” rotation) once every 243 Earth days—the slowest rotation period of any planet. To an observer on the surface of Venus, the Sun would rise in the west and set in the east.
A Venusian sidereal day thus lasts longer than a Venusian year (243 versus 224.7 Earth days). Because of the retrograde rotation, the length of a solar day on Venus is significantly shorter than the sidereal day, at 116.75 Earth days (making the Venusian solar day shorter than Mercury’s 176 Earth days); one Venusian year is about 1.92 Venusian (solar) days long.