Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (i. The tidal force is a secondary effect of the Force of Gravity and is responsible for the Tides It arises because the gravitational acceleration experienced A natural satellite or moon is a Celestial body that Orbits a Planet or smaller body which is called the primary. e. a moon), and the planet (called the primary) that it orbits. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is It causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. Direct motion is the motion of a Planetary body in a direction similar to that of other bodies within its system and is sometimes called prograde motion. The process eventually leads to tidal locking of first the smaller, and later the larger body. A separate article treats the phenomenon of Tidal resonance in Oceanography. The Earth-Moon system is the best studied case.
The similar process of tidal deceleration occurs for satellites that have an orbital period that is shorter than the primary's rotation period, or that orbit in a retrograde direction.
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Earth-Moon system
Effects of moon's gravity
Because the Moon's mass is a considerable fraction of that of the Earth (about 1:81), the two bodies can be regarded as a double planet system, rather than as a planet with a satellite. " Double planet " is an informal term used to describe a Planet with a moon that may be large enough to be considered a planet in its own right a common definition The plane of the Moon's orbit around the Earth lies close to the plane of the Earth's orbit around the Sun (the ecliptic), rather than in the plane perpendicular to the axis of rotation of the Earth (the equator) as is usually the case with planetary satellites. In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star The Sun (Sol is the Star at the center of the Solar System. The ecliptic is the apparent path that the Sun traces out in the sky during the year The equator (sometimes referred to colloquially as "the Line") is the intersection of the Earth 's surface with the plane perpendicular to the The mass of the Moon is sufficiently large and it is sufficiently close to raise tides in the Earth: the matter of the Earth, in particular the water of the oceans, bulges out along both ends of an axis passing through the centers of the Earth and Moon. Characteristics A tide is a repeated cycle of sea level changes in the following stages Over several hours the water rises or advances up a beach in the flood Water is a common Chemical substance that is essential for the survival of all known forms of Life. An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. The average tidal bulge closely follows the Moon in its orbit, and the Earth rotates under this tidal bulge in just over a day. A day (symbol d is a unit of Time equivalent to 24 Hours and the duration of a single Rotation of planet Earth with respect to the However, the rotation drags the position of the tidal bulge ahead of the position directly under the Moon. As a consequence, there exists a substantial amount of mass in the bulge that is offset from the line through the centers of the Earth and Moon. Because of this offset, a portion of the gravitational pull between Earth's tidal bulges and the Moon is perpendicular to the Earth-Moon line, i. e. there exists a torque between the Earth and the Moon. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about This accelerates the Moon in its orbit, and decelerates the rotation of the Earth.
So the result is that the mean solar day, which is nominally 86400 seconds long, is actually getting longer when measured in SI seconds with stable atomic clocks. A day (symbol d is a unit of Time equivalent to 24 Hours and the duration of a single Rotation of planet Earth with respect to the The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units An atomic clock is a type of Clock that uses an Atomic resonance Frequency standard as its timekeeping element The small difference accumulates every day, which leads to an increasing difference between our clock time (Universal Time) on the one hand, and Atomic Time and Ephemeris Time on the other hand: see ΔT. International Atomic Time ( TAI, from the French name Temps Atomique International) is a high-precision atomic Time standard that tracks Ephemeris Time ( ET) is a time scale used in Ephemerides of celestial bodies in particular the Sun (as observed from the Earth Moon planets and other members of This article is about the time difference for the temperature difference see Psychrometrics. This makes it necessary to insert a leap second at irregular intervals. A leap second is a one- Second adjustment that keeps broadcast standards for time of day close to mean solar time.
If other effects were ignored, tidal acceleration would continue until the rotational period of the Earth matched the orbital period of the Moon. At that time, the Moon would always be overhead of a single fixed place on Earth. Such a situation already exists in the Pluto-Charon system. Charon (ˈʃærən; also, as in Χάρων) discovered in 1978 is either the largest Moon of Pluto or the smaller member of a double However, the slowdown of the Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects make this irrelevant: About 2. 1 billion years from now, the continual increase of the Sun's radiation will cause the Earth's oceans to boil away, removing the bulk of the tidal friction and acceleration. Radiation, as in Physics, is Energy in the form of waves or moving Subatomic particles emitted by an atom or other body as it changes from a higher energy Even without this, the slowdown to a month-long day would still not have been completed by 4. 5 billion years from now when the Sun will evolve into a red giant and possibly destroy both the Earth and Moon. A red giant is a luminous Giant star of low or intermediate mass (roughly 0 (Tidal acceleration is also moving the Earth outward from the Sun, but it is unknown whether it will be enough to save it from destruction. )
Tidal acceleration is one of the few examples in the dynamics of the solar system of a so-called secular perturbation of an orbit, i. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. e. a perturbation that continuously increases with time and is not periodic. Up to a high order of approximation, mutual gravitational perturbations between major or minor planets only cause periodic variations in their orbits, that is, parameters oscillate between maximum and minimum values. Gravitation is a natural Phenomenon by which objects with Mass attract one another A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star The tidal effect gives rise to a quadratic term in the equations, which leads to unbounded growth. In the mathematical theories of the planetary orbits that form the basis of ephemerides, quadratic and higher order secular terms do occur, but these are mostly Taylor expansions of very long time periodic terms. An ephemeris (plural ephemerides; from the Greek word ἐφήμερος ephemeros "daily" is a table of values that gives the positions of In Mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its Derivatives The reason that tidal effects are different is that unlike distant gravitational perturbations, friction is an essential part of tidal acceleration, and leads to permanent loss of energy from the dynamical system in the form of heat. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature
Angular momentum and energy
The gravitational torque between the Moon and the tidal bulge of the Earth causes the Moon to be accelerated in its orbit, and the Earth to be decelerated in its rotation. As in any physical process, total energy and angular momentum are conserved. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position Effectively, energy and angular momentum are transferred from the rotation of the Earth to the orbital motion of the Moon. The Moon moves farther away from the Earth, so its potential energy (in the Earth's gravity well) increases. Potential energy can be thought of as Energy stored within a physical system In Physics, a gravity well is the Gravitational potential field around a massive body (a particular kind of Potential well) It stays in orbit, and from Kepler's 3rd law it follows that its velocity actually decreases, so the tidal acceleration of the Moon causes an apparent deceleration of its motion across the celestial sphere. In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. In Physics, velocity is defined as the rate of change of Position. In Astronomy and Navigation, the celestial sphere is an imaginary rotating Sphere of "gigantic Radius " Although its kinetic energy decreases, its potential energy increases by a larger amount. The kinetic energy of an object is the extra Energy which it possesses due to its motion The Moon's orbital angular momentum also increases. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position
The rotational angular momentum of the Earth decreases and consequently the length of the day increases. The net tide raised on Earth by the Moon is dragged ahead of the Moon by Earth's much faster rotation. Tidal friction is required to drag and maintain the bulge ahead of the Moon, and it dissipates the excess energy of the exchange of rotational and orbital energy between the Earth and Moon as heat. If the friction and heat dissipation were not present, the Moon's gravitational force on the tidal bulge would rapidly (within two days) bring the tide back into synchronization with the Moon, and the Moon would no longer recede. Most of the dissipation occurs in a turbulent bottom boundary layer in shallow seas such as the European shelf around the British Isles, the Patagonian shelf off Argentina, and the Bering Sea. The British Isles (Irish variously Na hOileáin Bhriotanacha, Oileáin Iarthair Eorpa, Éire agus an Bhreatain Mhór; Ellanyn Goaldagh Eileanan Llao LLaojpg|thumb|250px| Lake Nahuel Huapi, near Bariloche, Argentina For a topic outline on this subject see List of basic Argentina topics. The Bering (or Imarpik) Sea is a body of water in the Pacific Ocean that comprises a deep water basin (the Aleutian Basin) which rises through [1]
A tidal bulge (called an equilibrium tide) does not really exist on Earth because the continents break up the tide when they pass under the Moon. Oceanic tides actually rotate around each ocean basin as vast gyres around several amphidromic points where no tide exists. A gyre is any manner of swirling Vortex. It is often used to describe large-scale Wind or Ocean currents. An amphidromic point is a point within a tidal system where the Tidal range is almost zero The Moon pulls on each individual undulation as Earth rotates—some undulations are ahead of the Moon, others are behind it, while still others are on either side. The equilibrium tide in the shape of a prolate spheroid that actually does exist for the Moon to pull on is the net result of integrating the actual undulations over all the world's oceans. A prolate spheroid is a Spheroid in which the polar Diameter is longer than the Equatorial diameter Earth's net equilibrium tide has an amplitude of only 3. 23 cm, which is totally swamped by oceanic tides that can exceed one metre.
Historical evidence
This mechanism has been working for 4. 5 billion years, since oceans first formed on the Earth. There is geological and paleontological evidence that the Earth rotated faster and that the Moon was closer to the Earth in the remote past. Tidal rhythmites are alternating layers of sand and silt laid down offshore from estuaries having great tidal flows. An estuary is a semi-enclosed Coastal body of Water with one or more Rivers or Streams flowing into it and with a free connection to the open Daily, monthly and seasonal cycles can be found in the deposits. This geological record is consistent with these conditions 620 million years ago: the day was 21. 9±0. 4 hours, and there were 13. 1±0. 1 synodic months/year and 400±7 solar days/year. The length of the year has remained virtually unchanged during this period because no evidence exists that the constant of gravitation has changed. The average recession rate of the Moon between then and now has been 2. 17±0. 31 cm/year, which is about half the present rate. [2]
Quantitative description of the Earth-Moon case
The motion of the Moon can be followed with an accuracy of a few centimeters by lunar laser ranging (LLR). The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Laser pulses are bounced off mirrors on the surface of the moon, emplaced during the Apollo missions of 1969 to 1972 and by Lunokhod 2 in 1973. Year 1969 ( MCMLXIX) was a Common year starting on Wednesday (link will display full calendar of the Gregorian calendar. Year 1972 ( MCMLXXII) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar. Lunokhod ( Russian Луноход "Moonwalker") 1 and 2 were a pair of by the Soviet robotic lunar rovers landed on the [3] Measuring the return time of the pulse yields a very accurate measure of the distance. These measurements are fitted to the equations of motion. This yields numerical values for the parameters, among others the secular acceleration. From the period 1969–2001, the result is:
- (cy is centuries; the first is a quadratic term. )
This is consistent with results from satellite laser ranging (SLR), a similar technique applied to artificial satellites orbiting the Earth, which yields a model for the gravitational field of the Earth, including that of the tides. In satellite laser ranging ( SLR) a global network of observation stations measure the round trip time of flight of ultrashort pulses of Light to Satellites The model accurately predicts the changes in the motion of the Moon.
Finally, ancient observations of solar eclipses give fairly accurate positions for the Moon at those moments. An eclipse is an astronomical event that occurs when one Celestial object moves into the shadow of another Studies of these observations give results consistent with the value quoted above. [6]
The other consequence of the tidal acceleration is the deceleration of the rotation of the Earth. The rotation of the Earth is somewhat erratic on all time scales (from hours to centuries) due to various causes. [7] The small tidal effect cannot be observed in a short period, but the cumulative effect on the Earth's rotation as measured with a stable clock (ephemeris time, atomic time) of a shortfall of even a few milliseconds every day becomes readily noticeable in a few centuries. Ephemeris Time ( ET) is a time scale used in Ephemerides of celestial bodies in particular the Sun (as observed from the Earth Moon planets and other members of International Atomic Time ( TAI, from the French name Temps Atomique International) is a high-precision atomic Time standard that tracks Since some event in the remote past, more days and hours have passed (as measured in full rotations of the Earth) (Universal Time) than as measured with stable clocks calibrated to the present, longer length of the day (ephemeris time). Ephemeris Time ( ET) is a time scale used in Ephemerides of celestial bodies in particular the Sun (as observed from the Earth Moon planets and other members of This is known as ΔT. This article is about the time difference for the temperature difference see Psychrometrics. Recent values can be obtained from the International Earth Rotation and Reference Systems Service (IERS). "IERS" redirects here for other uses see IERS (disambiguation The International Earth Rotation and Reference Systems Service is [8] A table of the actual length of the day in the past few centuries is also available. [9]
From the observed acceleration of the Moon, the corresponding change in the length of the day can be computed:
- +2. 3 ms/cy
- (cy in centuries).
However, from historical records over the past 2700 years the following average value is found:
The corresponding cumulative value is a parabola having a coefficient of T² (time in centuries squared) of:
- ΔT = +31 s/cy²
Opposing the tidal deceleration of the Earth is a mechanism that is in fact accelerating the rotation. The Earth is not a sphere, but rather an ellipsoid that is flattened at the poles. SLR has shown that this flattening is decreasing. The explanation is, that during the ice age large masses of ice collected at the poles, and depressed the underlying rocks. An ice age is a period of long-term reduction in the Temperature of the Earth 's surface and atmosphere resulting in an expansion of continental Ice sheets The ice mass started disappearing over 10000 years ago, but the Earth's crust is still not in hydrostatic equilibrium and is still rebounding (the relaxation time is estimated to be about 4000 years). As a consequence, the polar diameter of the Earth increases, and since the mass and density remain the same, the volume remains the same; therefore the equatorial diameter is decreasing. As a consequence, mass moves closer to the rotation axis of the Earth. This means that its moment of inertia is decreasing. Because its total angular momentum remains the same during this process, the rotation rate increases. This is the well-known phenomenon of a spinning figure skater who spins ever faster as she retracts her arms. From the observed change in the moment of inertia the acceleration of rotation can be computed: the average value over the historical period must have been about −0. 6 ms/cy. This largely explains the historical observations.
Other cases of tidal acceleration
Most natural satellites of the planets undergo tidal acceleration to some degree (usually small), except for the two classes of tidally decelerated bodies. In most cases, however, the effect is small enough that even after billions of years most satellites will not actually be lost. The effect is probably most pronounced for Mars' second moon Deimos, which may become an Earth-crossing asteroid after it leaks out of Mars' grip. TemplateInfobox Planet.--> Deimos (ˈdaɪməs; also /ˈdiːməs/ The effect also arises between different components in a binary star. A binary star is a Star system consisting of two Stars orbiting around their Center of mass. [11]
Tidal deceleration
This comes in two varieties:
- Fast satellites: Some inner moons of the gas giant planets and Phobos orbit within the synchronous orbit radius so that their orbital period is shorter than their planet's rotation. A gas giant (sometimes also known as a Jovian planet after the planet Jupiter, or giant planet) is a large Planet that is not primarily A synchronous orbit is an Orbit in which an orbiting body (usually a Satellite) has a period equal to the average rotational period of the body being orbited (usually In this case the tidal bulges raised by the moon on their planet lag behind the moon, and act to decelerate it in its orbit. The net effect is a decay of that moon's orbit as it gradually spirals towards the planet. The planet's rotation also speeds up slightly in the process. In the distant future these moons will impact the planet or cross within their Roche limit and be tidally disrupted into fragments. Determining the Roche limit The Roche limit depends on the rigidity of the satellite However, all such moons in the solar system are very small bodies and the tidal bulges raised by them on the planet are also small, so the effect is usually weak and the orbit decays slowly. The moons affected are:
- Around Mars: Phobos
- Around Jupiter: Metis and Adrastea
- Around Saturn: none (like Jupiter, Saturn is a very rapid rotator but has no satellites close enough)
- Around Uranus: Cordelia, Ophelia, Bianca, Cressida, Desdemona, Juliet, Portia, Rosalind, Cupid, Belinda, and Perdita
- Around Neptune: Naiad, Thalassa, Despina, Galatea and Larissa;
- Retrograde satellites: All retrograde satellites experience tidal deceleration to some degree because the moon's orbital motion and the planet's rotation are in opposite directions, causing restoring forces from their tidal bulges. TemplateInfobox Planet.--> Metis (, or as in Greek Μήτις Adrastea (, or as in Greek Αδράστεια also known as Jupiter XV, is the second by distance and the smallest of the four inner moons of Jupiter TemplateInfobox Planet.--> Cordelia (kor-dee'-lee-ə There is also an Asteroid called 171 Ophelia. There is also an Asteroid called 218 Bianca. There is also an Asteroid called 548 Kressida. There is also a Minor planet called 666 Desdemona. There is also an Asteroid called 1285 Julietta. Portia (por'-shə ˈpɔrʃə is an Inner satellite of Uranus. There is also an Asteroid called 900 Rosalinde. TemplateInfobox Planet.--> Belinda (bə-lin'-də bɨˈlɪndə Perdita (pər'-di-tə ˈpɝdɨtə is an Inner satellite of Uranus. Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. See also Discovery It was first discovered by Harold J Reitsema, William B A difference to the previous "fast satellite" case here is that the planet's rotation is also slowed down rather than sped up (angular momentum is still conserved because in such a case the values for the planet's rotation and the moon's revolution have opposite signs). The only satellite in the Solar System for which this effect is non-negligible is Neptune's moon Triton. TemplateInfobox Planet.--> Triton (ˈtraɪtən, or as in Greek All the other retrograde satellites are on distant orbits and tidal forces between them and the planet are negligible.
Tidal heating
Tidal heating occurs through the tidal friction processes explained above: orbital and rotational energy are dissipated as heat in the crust of the moons and planets involved. Io, a moon of Jupiter, is the most volcanically active body in the solar system, with no impact craters surviving on its surface. TemplateInfobox Planet.--> Io (ˈaɪoʊ, or as Greek The Solar System consists of the Sun and those celestial objects bound to it by Gravity. This is because the tidal force of Jupiter deforms Io; the eccentricity of Io's orbit (a consequence of its participation in a Laplace resonance) causes the height of Io's tidal bulge to vary significantly (by up to 100 m) over the course of an orbit; the friction from this tidal flexing then heats up its interior. In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape In Celestial mechanics, an orbital resonance occurs when two Orbiting bodies exert a regular periodic gravitational influence on each other usually due to their A similar but weaker process is theorised to have melted the lower layers of the ice surrounding the rocky mantle of Jupiter's next large moon, Europa. TemplateInfobox Planet.--> Europa (jʊˈroʊpə; or as Saturn's moon Enceladus is similarly thought to have a liquid water ocean beneath its icy crust. TemplateInfobox Planet.--> This article is about the moon of The liquid water geysers which eject material from Enceladus are thought to be powered by tidal friction of this moon's shifting ice crust.
See also
References
- ^ Walter Munk. A separate article treats the phenomenon of Tidal resonance in Oceanography. The tidal force is a secondary effect of the Force of Gravity and is responsible for the Tides It arises because the gravitational acceleration experienced Characteristics A tide is a repeated cycle of sea level changes in the following stages Over several hours the water rises or advances up a beach in the flood "Once again: once again—tidal friction". Progress in Oceanography 40 (1997) 7-35.
- ^ George E. Williams. "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit". Reviews of Geophysics 38 (2000), 37-60.
- ^ Another reflector emplaced by Lunokhod 1 in 1970 is no longer functioning. [1]
- ^ J. Chapront, M. Chapront-Touzé, G. Francou: "A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR". Astron. Astrophys. 387, 700. . 709 (2002).
- ^ a b Jean O. Dickey et al. (1994): "Lunar Laser Ranging: a Continuing Legacy of the Apollo Program". Science 265, 482. . 490.
- ^ F. R. Stephenson, L. V. Morrison (1995): Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990". Phil. Trans. Royal Soc. London Ser. A, pp. 165. . 202.
- ^ Jean O. Dickey (1995): "Earth Rotation Variations from Hours to Centuries". In: I. Appenzeller (ed. ): Highlights of Astronomy. Vol. 10 pp. 17. . 44.
- ^ Observed values of UT1-TAI, 1962-1999
- ^ LOD
- ^ F. R. Stephenson (1997): Historical Eclipses and Earth's Rotation. Cambridge Univ. Press.
- ^ Zahn, J. -P. (1977). "Tidal Friction in Close Binary Stars". Astron. Astrophys. 57: 383-394.
External links
- The Recession of the Moon and the Age of the Earth-Moon System
- Tidal Heating as Described by University of Washington Professor Toby Smith
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