Orbit of the Moon

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https://en.wikipedia.org/wiki/Orbit_of_the_Moon

Orbit of the Moon

Diagram of the Moon's orbit with respect to the Earth. While angles and relative sizes are to scale, distances are not.
Semi-major axis	384,748 km (239,071 mi)
Mean distance	385,000 km (239,000 mi)
Inverse sine parallax	384,400 km (238,900 mi)
Perigee	363,228.9 km (225,700.0 mi), avg. (356400–370400 km)
Apogee	405,400 km (251,900 mi), avg. (404000–406700 km)
Mean eccentricity	0.0549006 (0.026–0.077)
Mean obliquity	6.687°
Mean inclination
of orbit to ecliptic	5.15° (4.99–5.30)
of lunar equator to ecliptic	1.543°
Period of
orbit around Earth (sidereal)	27.322 days
orbit around Earth (synodic)	29.530 days
precession of nodes	18.5996 years
precession of line of apsides	8.8504 years

The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days (a tropical month and sidereal month) and one revolution relative to the Sun in about 29.53 days (a synodic month). Earth and the Moon orbit about their barycentre (common centre of mass), which lies about 4,670 km (2,900 mi) from Earth's centre (about 73% of its radius), forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's centre, which corresponds to about 60 Earth radii or 1.282 light-seconds.

With a mean orbital velocity around the barycentre between the Earth and the Moon, of 1.022 km/s (0.635 miles/s, 2,286 miles/h), the Moon covers a distance approximately its diameter, or about half a degree on the celestial sphere, each hour. The Moon differs from most satellites of other planets in that its orbit is close to the ecliptic plane instead of to its primary's (in this case, Earth's) equatorial plane. The Moon's orbital plane is inclined by about 5.1° with respect to the ecliptic plane, whereas the Moon's equatorial plane is tilted by only 1.5°.

Properties

The properties of the orbit described in this section are approximations. The Moon's orbit around Earth has many variations (perturbations) due to the gravitational attraction of the Sun and planets, the study of which (lunar theory) has a long history.

Moon's orbit and sizes of Earth and Moon to scale.

 

Comparison of the Moon's apparent size at lunar perigee–apogee.

Elliptic shape

The orbit of the Moon is a nearly circular ellipse about the Earth (the semimajor and semiminor axes are 384,400 km and 383,800 km, respectively: a difference of only 0.16%). The equation of the ellipse yields an eccentricity of 0.0549 and perigee and apogee distances of 362,600 km (225,300 mi) and 405,400 km (251,900 mi) respectively (a difference of 12%).

Since nearer objects appear larger, the Moon's apparent size changes as it moves toward and away from an observer on Earth. An event referred to as a "supermoon" occurs when the full Moon is at its closest to Earth (perigee). The largest possible apparent diameter of the Moon is the same 12% larger (as perigee versus apogee distances) than the smallest; the apparent area is 25% more and so is the amount of light it reflects toward Earth.

The variance in the Moon's orbital distance corresponds with changes in its tangential and angular speeds, as stated in Kepler's second law. The mean angular movement relative to an imaginary observer at the Earth–Moon barycentre is 13.176° per day to the east (J2000.0 epoch).

Minimum, mean and maximum distances of the Moon from Earth with its angular diameter as seen from Earth's surface, to scale. Scroll to right to see moon.

Elongation

The Moon's elongation is its angular distance east of the Sun at any time. At new moon, it is zero and the Moon is said to be in conjunction. At full moon, the elongation is 180° and it is said to be in opposition. In both cases, the Moon is in syzygy, that is, the Sun, Moon and Earth are nearly aligned. When elongation is either 90° or 270°, the Moon is said to be in quadrature.

Precession

Main article: Lunar precession

Apsidal precession—The major axis of Moon's elliptical orbit rotates by one complete revolution once every 8.85 years in the same direction as the Moon's rotation itself. This image looks upwards depicting Earth's geographic south pole and the elliptical shape of the Moon's orbit (vastly exaggerated from its almost circular shape to make the precession evident) is rotating from white to greyer orbits.

Animation of Moon orbit around Earth
  Moon ·   Earth
Top: polar view; bottom: equatorial view

Earth's lunar orbit perturbations

The orientation of the orbit is not fixed in space but rotates over time. This orbital precession is called apsidal precession and is the rotation of the Moon's orbit within the orbital plane, i.e. the axes of the ellipse change direction. The lunar orbit's major axis – the longest diameter of the orbit, joining its nearest and farthest points, the perigee and apogee, respectively – makes one complete revolution every 8.85 Earth years, or 3,232.6054 days, as it rotates slowly in the same direction as the Moon itself (direct motion) – meaning precesses eastward by 360°. The Moon's apsidal precession is distinct from the nodal precession of its orbital plane and axial precession of the moon itself.

Inclination

Orbital inclination—the Moon's orbit is inclined by 5.14° to the ecliptic. This shows the specific configuration at major northern lunistice. At such times, the Earth's north pole is toward the Moon and the Moon is north of the ecliptic.

The mean inclination of the lunar orbit to the ecliptic plane is 5.145°. Theoretical considerations show that the present inclination relative to the ecliptic plane arose by tidal evolution from an earlier near-Earth orbit with a fairly constant inclination relative to Earth's equator. It would require an inclination of this earlier orbit of about 10° to the equator to produce a present inclination of 5° to the ecliptic. It is thought that originally the inclination to the equator was near zero, but it could have been increased to 10° through the influence of planetesimals passing near the Moon while falling to the Earth. If this had not happened, the Moon would now lie much closer to the ecliptic and eclipses would be much more frequent.

The rotational axis of the Moon is not perpendicular to its orbital plane, so the lunar equator is not in the plane of its orbit, but is inclined to it by a constant value of 6.688° (this is the obliquity). As was discovered by Jacques Cassini in 1722, the rotational axis of the Moon precesses with the same rate as its orbital plane, but is 180° out of phase (see Cassini's Laws). Therefore, the angle between the ecliptic and the lunar equator is always 1.543°, even though the rotational axis of the Moon is not fixed with respect to the stars. It also means that when the Moon is farthest north of the ecliptic, the centre of the part seen from Earth is about 6.7° south of the lunar equator and the south pole is visible, whereas when the Moon is farthest south of the ecliptic the centre of the visible part is 6.7° north of the equator and the north pole is visible. This is called libration in latitude.

Nodes

Main article: Lunar node

The nodes are points at which the Moon's orbit crosses the ecliptic. The Moon crosses the same node every 27.2122 days, an interval called the draconic month or draconitic month. The line of nodes, the intersection between the two respective planes, has a retrograde motion: for an observer on Earth, it rotates westward along the ecliptic with a period of 18.6 years or 19.3549° per year. When viewed from the celestial north, the nodes move clockwise around Earth, opposite to Earth's own spin and its revolution around the Sun. An Eclipse of the Moon or Sun can occur when the nodes align with the Sun, roughly every 173.3 days. Lunar orbit inclination also determines eclipses; shadows cross when nodes coincide with full and new moon when the Sun, Earth, and Moon align in three dimensions.

In effect, this means that the "tropical year" on the Moon is only 347 days long. This is called the draconic year or eclipse year. The "seasons" on the Moon fit into this period. For about half of this draconic year, the Sun is north of the lunar equator (but at most 1.543°), and for the other half, it is south of the lunar equator. Obviously, the effect of these seasons is minor compared to the difference between lunar night and lunar day. At the lunar poles, instead of usual lunar days and nights of about 15 Earth days, the Sun will be "up" for 173 days as it will be "down"; polar sunrise and sunset takes 18 days each year. "Up" here means that the centre of the Sun is above the horizon. Lunar polar sunrises and sunsets occur around the time of eclipses (solar or lunar). For example, at the Solar eclipse of March 9, 2016, the Moon was near its descending node, and the Sun was near the point in the sky where the equator of the Moon crosses the ecliptic. When the Sun reaches that point, the centre of the Sun sets at the lunar north pole and rises at the lunar south pole.

The solar eclipse of September 1 of the same year, the Moon was near its ascending node, and the Sun was near the point in the sky where the equator of the Moon crosses the ecliptic. When the Sun reaches that point, the centre of the Sun rises at the lunar north pole and sets at the lunar south pole.

Inclination to the equator and lunar standstill

Main article: Lunar standstill

Every 18.6 years, the angle between the Moon's orbit and Earth's equator reaches a maximum of 28°36′, the sum of Earth's equatorial tilt (23°27′) and the Moon's orbital inclination (5°09′) to the ecliptic. This is called major lunar standstill. Around this time, the Moon's declination will vary from −28°36′ to +28°36′. Conversely, 9.3 years later, the angle between the Moon's orbit and Earth's equator reaches its minimum of 18°20′. This is called a minor lunar standstill. The last lunar standstill was a minor standstill in October 2015. At that time the descending node was lined up with the equinox (the point in the sky having right ascension zero and declination zero). The nodes are moving west by about 19° per year. The Sun crosses a given node about 20 days earlier each year.

When the inclination of the Moon's orbit to the Earth's equator is at its minimum of 18°20′, the centre of the Moon's disk will be above the horizon every day from latitudes less than 70°43' (90° − 18°20' – 57' parallax) north or south. When the inclination is at its maximum of 28°36', the centre of the Moon's disk will be above the horizon every day only from latitudes less than 60°27' (90° − 28°36' – 57' parallax) north or south.

At higher latitudes, there will be a period of at least one day each month when the Moon does not rise, but there will also be a period of at least one day each month when the Moon does not set. This is similar to the seasonal behaviour of the Sun, but with a period of 27.2 days instead of 365 days. Note that a point on the Moon can actually be visible when it is about 34 arc minutes below the horizon, due to atmospheric refraction.

Because of the inclination of the Moon's orbit with respect to the Earth's equator, the Moon is above the horizon at the North and South Pole for almost two weeks every month, even though the Sun is below the horizon for six months at a time. The period from moonrise to moonrise at the poles is a tropical month, about 27.3 days, quite close to the sidereal period. When the Sun is the furthest below the horizon (winter solstice), the Moon will be full when it is at its highest point. When the Moon is in Gemini it will be above the horizon at the North Pole, and when it is in Sagittarius it will be up at the South Pole.

The Moon's light is used by zooplankton in the Arctic when the Sun is below the horizon for months and must have been helpful to the animals that lived in Arctic and Antarctic regions when the climate was warmer.

Scale model

Scale model of the Earth–Moon system: Sizes and distances are to scale. It represents the mean distance of the orbit and the mean radii of both bodies. Scroll to right to find Moon.

History of observations and measurements

The apparent trajectory of the Moon in the sky seen from Earth each night is like a wide ellipse, although the path depends on the time of the year and latitude.

About 1000 BC, the Babylonians were the first human civilization known to have kept a consistent record of lunar observations. Clay tablets from that period, which have been found over the territory of present-day Iraq, are inscribed with cuneiform writing recording the times and dates of moonrises and moonsets, the stars that the Moon passed close by, and the time differences between rising and setting of both the Sun and the Moon around the time of the full moon. Babylonian astronomy discovered the three main periods of the Moon's motion and used data analysis to build lunar calendars that extended well into the future. This use of detailed, systematic observations to make predictions based on experimental data may be classified as the first scientific study in human history. However, the Babylonians seem to have lacked any geometrical or physical interpretation of their data, and they could not predict future lunar eclipses (although "warnings" were issued before likely eclipse times).

Ancient Greek astronomers were the first to introduce and analyze mathematical models of the motion of objects in the sky. Ptolemy described lunar motion by using a well-defined geometric model of epicycles and evection.

Sir Isaac Newton was the first to develop a complete theory of motion, mechanics. The observations of the lunar motion were the main test of his theory.

Lunar periods

See also: Lunar month and Month

 

Name	Value (days)	Definition
Sidereal month	27.321662	with respect to the distant stars (13.36874634 passes per solar orbit)
Synodic month	29.530589	with respect to the Sun (phases of the Moon, 12.36874634 passes per solar orbit)
Tropical month	27.321582	with respect to the vernal point (precesses in ~26,000 years)
Anomalistic month	27.554550	with respect to the perigee (precesses in 3232.6054 days = 8.850578 years)
Draconic month	27.212221	with respect to the ascending node (precesses in 6793.4765 days = 18.5996 years)

There are several different periods associated with the lunar orbit. The sidereal month is the time it takes to make one complete orbit around Earth with respect to the fixed stars. It is about 27.32 days. The synodic month is the time it takes the Moon to reach the same visual phase. This varies notably throughout the year, but averages around 29.53 days. The synodic period is longer than the sidereal period because the Earth–Moon system moves in its orbit around the Sun during each sidereal month, hence a longer period is required to achieve a similar alignment of Earth, the Sun, and the Moon. The anomalistic month is the time between perigees and is about 27.55 days. The Earth–Moon separation determines the strength of the lunar tide raising force.

The draconic month is the time from ascending node to ascending node. The time between two successive passes of the same ecliptic longitude is called the tropical month. The latter periods are slightly different from the sidereal month.

The average length of a calendar month (a twelfth of a year) is about 30.4 days. This is not a lunar period, though the calendar month is historically related to the visible lunar phase.

The Moon's distance from Earth and Moon phases in 2014.
Moon phases: 0 (1)—new moon, 0.25—first quarter, 0.5—full moon, 0.75—last quarter

Tidal evolution

See also: Tide, Tidal acceleration, and Axial tilt § Long term

The gravitational attraction that the Moon exerts on Earth is the cause of tides in both the ocean and the solid Earth; the Sun has a smaller tidal influence. The solid Earth responds quickly to any change in the tidal forcing, the distortion taking the form of an ellipsoid with the high points roughly beneath the Moon and on the opposite side of Earth. This is a result of the high speed of seismic waves within the solid Earth.

However the speed of seismic waves is not infinite and, together with the effect of energy loss within the Earth, this causes a slight delay between the passage of the maximum forcing due to the Moon across and the maximum Earth tide. As the Earth rotates faster than the Moon travels around its orbit, this small angle produces a gravitational torque which slows the Earth and accelerates the Moon in its orbit.

In the case of the ocean tides, the speed of tidal waves in the ocean is far slower than the speed of the Moon's tidal forcing. As a result, the ocean is never in near equilibrium with the tidal forcing. Instead, the forcing generates the long ocean waves which propagate around the ocean basins until eventually losing their energy through turbulence, either in the deep ocean or on shallow continental shelves.

Although the ocean's response is the more complex of the two, it is possible to split the ocean tides into a small ellipsoid term which affects the Moon plus a second term which has no effect. The ocean's ellipsoid term also slows the Earth and accelerates the Moon, but because the ocean dissipates so much tidal energy, the present ocean tides have an order of magnitude greater effect than the solid Earth tides.

Because of the tidal torque, caused by the ellipsoids, some of Earth's angular (or rotational) momentum is gradually being transferred to the rotation of the Earth–Moon pair around their mutual centre of mass, called the barycentre. See tidal acceleration for a more detailed description.

This slightly greater orbital angular momentum causes the Earth–Moon distance to increase at approximately 38 millimetres per year. Conservation of angular momentum means that Earth's axial rotation is gradually slowing, and because of this its day lengthens by approximately 24 microseconds every year (excluding glacial rebound). Both figures are valid only for the current configuration of the continents. Tidal rhythmites from 620 million years ago show that, over hundreds of millions of years, the Moon receded at an average rate of 22 mm (0.87 in) per year (2200 km or 0.56% or the Earth-moon distance per hundred million years) and the day lengthened at an average rate of 12 microseconds per year (or 20 minutes per hundred million years), both about half of their current values.

The present high rate may be due to near resonance between natural ocean frequencies and tidal frequencies. Another explanation is that in the past the Earth rotated much faster, a day possibly lasting only 9 hours on the early Earth. The resulting tidal waves in the ocean would have then been much shorter and it would have been more difficult for the long wavelength tidal forcing to excite the short wavelength tides.

The Moon is gradually receding from Earth into a higher orbit, and calculations suggest that this would continue for about 50 billion years. By that time, Earth and the Moon would be in a mutual spin–orbit resonance or tidal locking, in which the Moon will orbit Earth in about 47 days (currently 27 days), and both the Moon and Earth would rotate around their axes in the same time, always facing each other with the same side. This has already happened to the Moon—the same side always faces Earth—and is also slowly happening to the Earth. However, the slowdown of Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects change the situation: approximately 2.3 billion years from now, the increase of the Sun's radiation will have caused Earth's oceans to evaporate, removing the bulk of the tidal friction and acceleration.

Libration

Main article: Libration

Animation of the Moon as it cycles through its phases. The apparent wobbling of the Moon is known as libration.

The Moon is in synchronous rotation, meaning that it keeps the same face toward Earth at all times. This synchronous rotation is only true on average because the Moon's orbit has a definite eccentricity. As a result, the angular velocity of the Moon varies as it orbits Earth and hence is not always equal to the Moon's rotational velocity which is more constant. When the Moon is at its perigee, its orbital motion is faster than its rotation. At that time the Moon is a bit ahead in its orbit with respect to its rotation about its axis, and this creates a perspective effect which allows us to see up to eight degrees of longitude of its eastern (right) far side. Conversely, when the Moon reaches its apogee, its orbital motion is slower than its rotation, revealing eight degrees of longitude of its western (left) far side. This is referred to as optical libration in longitude.

The Moon's axis of rotation is inclined by in total 6.7° relative to the normal to the plane of the ecliptic. This leads to a similar perspective effect in the north–south direction that is referred to as optical libration in latitude, which allows one to see almost 7° of latitude beyond the pole on the far side. Finally, because the Moon is only about 60 Earth radii away from Earth's centre of mass, an observer at the equator who observes the Moon throughout the night moves laterally by one Earth diameter. This gives rise to a diurnal libration, which allows one to view an additional one degree's worth of lunar longitude. For the same reason, observers at both of Earth's geographical poles would be able to see one additional degree's worth of libration in latitude.

Besides these "optical librations" caused by the change in perspective for an observer on Earth, there are also "physical librations" which are actual nutations of the direction of the pole of rotation of the Moon in space: but these are very small.

Path of Earth and Moon around Sun

Section of Earth's and Moon's trajectories around the Sun

When viewed from the north celestial pole (i.e., from the approximate direction of the star Polaris) the Moon orbits Earth anticlockwise and Earth orbits the Sun anticlockwise, and the Moon and Earth rotate on their own axes anticlockwise.

The right-hand rule can be used to indicate the direction of the angular velocity. If the thumb of the right hand points to the north celestial pole, its fingers curl in the direction that the Moon orbits Earth, Earth orbits the Sun, and the Moon and Earth rotate on their own axes.

In representations of the Solar System, it is common to draw the trajectory of Earth from the point of view of the Sun, and the trajectory of the Moon from the point of view of Earth. This could give the impression that the Moon orbits Earth in such a way that sometimes it goes backwards when viewed from the Sun's perspective. However, because the orbital velocity of the Moon around Earth (1 km/s) is small compared to the orbital velocity of Earth about the Sun (30 km/s), this never happens. There are no rearward loops in the Moon's solar orbit.

Considering the Earth–Moon system as a binary planet, its centre of gravity is within Earth, about 4,671 km (2,902 mi) or 73.3% of the Earth's radius from the centre of the Earth. This centre of gravity remains on the line between the centres of the Earth and Moon as the Earth completes its diurnal rotation. The path of the Earth–Moon system in its solar orbit is defined as the movement of this mutual centre of gravity around the Sun. Consequently, Earth's centre veers inside and outside the solar orbital path during each synodic month as the Moon moves in its orbit around the common centre of gravity.

The Sun's gravitational effect on the Moon is more than twice that of Earth's on the Moon; consequently, the Moon's trajectory is always convex (as seen when looking Sunward at the entire Sun–Earth–Moon system from a great distance outside Earth–Moon solar orbit), and is nowhere concave (from the same perspective) or looped. That is, the region enclosed by the Moon's orbit of the Sun is a convex set.

Lost minor planet

From Wikipedia, the free encyclopedia

More than 700,000 minor planets have been observed, many of which must be considered lost due to insufficient observational data.

A minor planet is "lost" when today's observers cannot find it, because its location is too uncertain to target observations. This happens if the orbital elements of a minor planet are not known accurately enough, typically because the observation arc for the object is too short, or too few observations were made before the object became unobservable (e.g. too faint due to increasing distance, or too close to the Sun to view at night).

By some definitions thousands, if not tens of thousands, of mostly small observed minor planets are lost. Some lost minor planets discovered in decades past cannot be found because the available observational data is insufficient for reliable orbit determination. With limited information astronomers cannot know where to look for the object at future dates.

Lost objects are sometimes recovered when serendipitously re-observed by a later astronomical survey. If the orbital elements of the newly found object are sufficiently close to those of the earlier lost object, the two may be equated. This can be established by calculating backwards the "new" object's orbit (once it is firmly known) and checking past positions against those previously recorded for the lost object. This usually greatly extends the object's arc length, thus fixing the orbit much more precisely. The back-orbit calculations are especially tricky for lost comets because their orbits can be affected by non-gravitational forces, such as emission of jets of gas from the comet nucleus. Many previously lost asteroids (a type of minor planet) were rediscovered in the 1980s and 1990s, but many minor planets are still lost.

Overview

The orbits of kilometre class NEAs are generally well known, though a few have been lost. However, large numbers of smaller NEAs have highly uncertain orbits

This is a small selection of some early lost or notable asteroids with their discovery and rediscovery dates. (A more detailed description for some of these minor planets can be found in the following sections.) The true number of lost asteroids may be over 150,000. There are also about 30,000 unnumbered bodies with a condition code of U = 9, indicating the highest possible uncertainty of their orbit determination. Many of these bodies have been observed years if not decades ago and must be considered lost. There are also more than a thousand near-Earth objects (NEOs) with an observation arc of one or two days only.

Designation Year of discovery recovery 132 Aethra 1873 1922 1892 X (330 Adalberta) 1892 false positive 452 Hamiltonia 1899 1981 473 Nolli 1901 1987 (12126) 1999 RM11 (A904 RD) 1904 1999 719 Albert 1911 2000 724 Hapag 1911 1988 843 Nicolaia 1916 1981 878 Mildred 1916 1991 1009 Sirene 1923 1982 1026 Ingrid 1923 1986

Name Year of discovery recovery 3789 Zhongguo 1928 1986 1179 Mally 1931 1986 1862 Apollo 1932 1973 2101 Adonis 1936 1977 69230 Hermes 1937 2003 1537 Transylvania 1940 1981 1922 Zulu 1949 1974 (29075) 1950 DA 1950 2000 1916 Boreas 1953 1976 3494 Purple Mountain 1962 1980 7796 Járacimrman 1973 1996

Designation Year of Notes MPC discovery recovery 1927 LA  1927 false positive Observed 3 times between 1 June 1927 and 5 July 1927 MPC 1991 BA 1991 still lost Passed within a lunar distance of Earth MPC 1995 SN55 1995 2020 3:5 resonant TNO initially thought to be a large centaur MPC 2007 WD5 2007 still lost Passed close to Mars MPC 6344 P-L 1960 2007 Potentially hazardous object; probably a dormant comet MPC

20th-century recoveries

The number of asteroids that were only observed once and not re-observed grew throughout the 19th and 20th centuries, but improved telescopes, searches, and detection techniques led to resolution of most of these cases between 1970 and 2000. There are earlier examples also, such as 132 Aethra, which was lost between 1873 and 1922.

1970s

Recovered body	Description
1862 Apollo	Apollo is a Q-type asteroid, discovered by Karl Reinmuth in 1932, but lost and not recovered until 1973. Another Apollo asteroid is 2101 Adonis, discovered by Eugene Delporte in 1936 and lost until 1977 when it was rediscovered by Charles T. Kowal. It was also one of the first near-Earth asteroids to be discovered.
1916 Boreas	The Amor asteroid Boreas, provisionally designated 1953 RA, was discovered on 1 September 1953 by Sylvain Julien Victor Arend at the Royal Observatory of Belgium, and rediscovered in 1974 by Richard Eugene McCrosky, G. Schwartz and JH Bulger based on a predicted position by Brian G. Marsden.
1922 Zulu	The outer main-belt asteroid, provisionally designated 1949 HC, was discovered on 25 April 1949 by Ernest Leonard Johnson at Johannesburg (UO). It is one of very few asteroids located in the 2:1 mean-motion resonance with Jupiter. This asteroid was lost shortly after discovery and only rediscovered in 1974 by Richard Eugene McCrosky, Cheng-yuan Shao and JH Bulger based on a predicted position by C. M. Bardwell of the Cincinnati Observatory.

1980s and 1990s

Leif Kahl Kristensen at the University of Aarhus rediscovered 452 Hamiltonia and 1537 Transylvania, along with numerous other small objects, in 1981. At the time these results were published, only the nine numbered minor planets 330 Adalberta, 473 Nolli, 719 Albert, 724 Hapag, 843 Nicolaia, 878 Mildred, 1009 Sirene, 1026 Ingrid, and 1179 Mally (below) had remained unobserved since their discoveries:

Recovered body	Description
330 Adalberta	The object originally named Adalberta, provisionally designated 1892 X, turned out to be an erroneous observation. The designation was later reassigned to A910 CB.
843 Nicolaia	Nicolaia, provisionally designated 1916 AN, was rediscovered at the Heidelberg Astronomisches Rechen-Institut in 1981.
473 Nolli	Nolli, provisionally designated 1901 GC, was discovered by Max Wolf on 13 February 1901, but it remained lost for many decades until it was recovered finally in 1987, 86 years later.
724 Hapag	Hapag had first been found by Johann Palisa in 1911. It was given the provisional name 1911 NC, but was lost until it was rediscovered in 1988.
719 Albert	Near-Earth asteroid 719 Albert (1911 MT) had also been found by Johann Palisa in 1911. Due to inaccuracies in its computed orbit, Albert was also lost and not recovered until 2000, when Jeffrey A. Larsen located it using data from the Spacewatch asteroid survey project. At the time of its rediscovery, Albert was the last remaining "lost asteroid" among those assigned numbers (since 69230 Hermes was not numbered until 2003).
878 Mildred	Mildred, provisionally designated 1916 f, was originally discovered in 1916 using the 60-inch Hale telescope at the Californian Mount Wilson Observatory, but was subsequently lost until it was again observed on single nights in 1985 and 1991.
1009 Sirene	Sirene, provisionally designated 1923 PE, was recovered in 1982 by J. Gibson using exposures form the Samuel Oschin Telescope at Palomar Observatory, and he revised its ephemeris.
1026 Ingrid	Ingrid was discovered by Karl Reinmuth on 13 August 1923 and given the provisional designation 1923 NY. It was reidentified in 1986 by Syuichi Nakano.
1179 Mally	Mally was discovered by Max Wolf on 19 March 1931 and given the provisional designation 1931 FD. It was rediscovered in 1986 by Lutz Schmadel, Richard Martin West and Hans-Emil Schuster.

Other notable recoveries

• While studying in Chicago in 1928, Zhang Yuzhe discovered an asteroid that was given the provisional designation 1928 UF, and later the number 1125. He named it "China", or "中華" Zhōnghuá. However, this asteroid was not observed beyond its initial appearance and a precise orbit could not be calculated. In 1957, the Purple Mountain Observatory in China discovered a new asteroid, and with Zhang Yuzhe's agreement the new object 1957 UN₁ was reassigned the official designation 1125 China in place of the lost 1928 UF. However, in 1986, the newly discovered object 1986 QK₁ was confirmed to be a rediscovery of the original 1928 UF, and this object was named 3789 Zhongguo, which is also a name for China.
• The near-Earth asteroid (29075) 1950 DA was discovered on 23 February 1950 by Carl Wirtanen at Lick Observatory. It was observed for 17 days and then lost, since not enough observations were made to allow its orbit to be plotted. It was then rediscovered on 31 December 2000. The chance it will impact Earth on 16 March 2880 is about 1 in 4,000, or 0.025 percent.
• 7796 Járacimrman was discovered at the Czech Kleť Observatory on 16 January 1996 by Zdeněk Moravec and was designated 1996 BG. It was observed until April 1996 and then in June and July 1997. It was revealed, by precovery, to be a lost asteroid which had previously been observed twice: at the Brera-Merate Observatory in northern Italy on 12 December 1973 and at the Australian Mount Stromlo Observatory near Canberra, on 8 and 9 July 1990.

21st century

Recently lost minor planets

• 2007 WD5 is a 50 m (160 ft) Apollo-class NEO and a Mars-crosser discovered on 20 November 2007, by Andrea Boattini of the Catalina Sky Survey. Early observations of 2007 WD₅ caused excitement amongst the scientific community when it was estimated as having as high as a 1 in 25 chance of colliding with Mars on 30 January 2008. However, by 9 January 2008 additional observations allowed NASA's Near Earth Object Program (NEOP) to reduce the uncertainty region resulting in only a 1-in-10,000 chance of impact. 2007 WD₅ most likely passed Mars at a distance of 6.5 Mars radii. Due to this relatively small distance and the uncertainty level of the prior observations, the gravitational effects of Mars on its trajectory are unknown and, according to Steven Chesley of NASA's JPL-Near Earth Object program, 2007 WD₅ is currently considered "lost". The best fit trajectory had the asteroid passing within 21,000 km of Mars and only 16,000 km from its moon Deimos.
• 2010 AU118 is a kilometer-sized Amor-class NEO and Mars-crosser discovered on 27 May 2010, by the Wide-field Infrared Survey Explorer (WISE) spacecraft. The asteroid was only observed 19 times during 13–15 January 2010, and has not since been observed. Virtual clones of the asteroid that fit the uncertainty region in the known trajectory, showed a 1 in 770 million chance that the asteroid could have impacted the Earth on 2020 October 20. However, NEODyS lists the nominal 20 October 2020 Earth distance as 3 AU (450,000,000 km; 280,000,000 mi).
• In 2007, the object 2007 RR₉ was found to be the near-Earth asteroid 6344 P–L, lost since 1960. It is a potentially hazardous object and probably a dormant comet, although it was not visibly outgassing at that tim

Apophenia

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Apophenia

Apophenia (/æpoʊˈfiːniə/) is the tendency to perceive meaningful connections between unrelated things. The term (German: Apophänie from the Greek verb ἀποφαίνειν (apophaínein)) was coined by psychiatrist Klaus Conrad in his 1958 publication on the beginning stages of schizophrenia. He defined it as "unmotivated seeing of connections [accompanied by] a specific feeling of abnormal meaningfulness". He described the early stages of delusional thought as self-referential over-interpretations of actual sensory perceptions, as opposed to hallucinations. Apophenia has also come to describe a human propensity to unreasonably seek definite patterns in random information, such as can occur in gambling.

Introduction

Apophenia can be considered a commonplace effect of brain function. Taken to an extreme, however, it can be a symptom of psychiatric dysfunction, for example, as a symptom in paranoid schizophrenia, where a patient sees hostile patterns (for example, a conspiracy to persecute them) in ordinary actions.

Apophenia is also typical of conspiracy theories, where coincidences may be woven together into an apparent plot.

Examples

Pareidolia

Main article: Pareidolia

"The Organ Player": an example of pareidolia in Neptune's Grotto, Sardinia

Pareidolia is a type of apophenia involving the perception of images or sounds in random stimuli.

A common example is the perception of a face within an inanimate object—the headlights and grill of an automobile may appear to be "grinning". People around the world see the "Man in the Moon". People sometimes see the face of a religious figure in a piece of toast or in the grain of a piece of wood. There is strong evidence that psychedelic drugs tend to induce or enhance pareidolia.

Pareidolia usually occurs as a result of the fusiform face area—which is the part of the human brain responsible for seeing faces—mistakenly interpreting an object, shape or configuration with some kind of perceived "face-like" features as being a face.

Gambling

Gamblers may imagine that they see patterns in the numbers that appear in lotteries, card games, or roulette wheels, where no such patterns exist. A common example of this is the gambler's fallacy.

Statistics

In statistics, apophenia is an example of a type I error – the false identification of patterns in data. It may be compared to a so-called false positive in other test situations.

Finance

The problem of apophenia in finance has been addressed in academic articles. More specifically, within the world of finance itself, the examples most prone to apophenia are trading, structuring, sales and compensation.

Related terms

In contrast to an epiphany, an apophany (i.e., an instance of apophenia) does not provide insight into the nature of reality nor its interconnectedness, but is a "process of repetitively and monotonously experiencing abnormal meanings in the entire surrounding experiential field". Such meanings are entirely self-referential, solipsistic, and paranoid—"being observed, spoken about, the object of eavesdropping, followed by strangers". Thus the English term "apophenia" has a somewhat different meaning than that which Conrad defined when he coined the term "Apophänie".

Synchronicity

Main article: Synchronicity

Synchronicity can be considered synonymous with correlation, without any statement about the veracity of various causal inferences.

Patternicity

In 2008, Michael Shermer coined the word patternicity, defining it as "the tendency to find meaningful patterns in meaningless noise".

Agenticity

In The Believing Brain (2011), Shermer wrote that humans have "the tendency to infuse patterns with meaning, intention, and agency", which he called agenticity.

Clustering illusion

A clustering illusion is a type of cognitive bias in which a person sees a pattern in a random sequence of numbers or events. Many theories have been disproved as a result of this bias being highlighted.

One case, during the early 2000s, involved the occurrence of breast cancer among employees of ABC Studios in Queensland. A study found that the incidence of breast cancer at the studios was six times higher than the rate in the rest of Queensland. However, an examination found no correlation between the heightened incidence and any factors related to the site, or any genetic or lifestyle factors of the employees.

Causes

Although there is no confirmed reason as to why apophenia occurs, there are some respected theories.

Models of pattern recognition

Pattern recognition is a cognitive process that involves retrieving information either from long-term, short-term or working memory and matching it with information from stimuli. There are three different ways in which this may happen and go wrong, resulting in apophenia.

Template matching

The stimulus is compared to templates, which are abstracted or partial representations of previously seen stimuli. These templates are stored in long-term memory as a result of past learning or educational experiences. For example, D, d, D and d are all recognized as the same letter.

Template-matching detection processes, when applied to more complex data sets (such as, for example, a painting or clusters of data) can result in the wrong template being matched. A false positive detection will result in apophenia.

Prototype matching

This is similar to template matching, except for the fact that prototypes are complete representations of a stimulus. The prototype need not be something that has been previously seen -- for example it might be an average or amalgam of previous stimuli. Crucially, an exact match is not needed.

An example of prototype matching would be to look at an animal such as a tiger and instead of recognizing that it has features that match the definition of a tiger (template matching), recognizing that it's similar to a particular mental image one has of a tiger (prototype matching).

This type of pattern recognition can result in apophenia based on the fact that since the brain is not looking for exact matches, it can pick up some characteristics of a match and assume it fits. This is more common with pareidolia than data collection.

Feature analysis

The stimulus is first broken down into its features and then processed. This model of pattern recognition says that the processing goes through four stages: detection, pattern dissection, feature comparison in memory, and recognition.

Evolution

One of the explanations put forth by evolutionary psychologists for apophenia is that it is not a flaw in the cognition of human brains but rather something that has come about through years of need. The study of this topic is referred to as error management theory.

One of the most accredited studies in this field is Skinner's box. This experiment involved taking a hungry pigeon, placing it in a box and releasing food pellets at random times. The pigeon received a food pellet while performing some action; and so, rather than attributing the arrival of the pellet to randomness, the pigeon repeats that action, and continues to do so until another pellet falls. As the pigeon increases the number of times it performs the action, it gains the impression that it also increased the times it was "rewarded" with a pellet, although the release in fact remained entirely random.

In art

Literature

• William Gibson's Pattern Recognition
• Jorge Luis Borges's Library of Babel
• Umberto Eco's Foucault's Pendulum
• Stanislaw Lem's His Master's Voice
• Peter Watts's Blindsight
• Vladimir Nabokov's "Signs and Symbols"
• Samuel R. Delany's "Dhalgren"
• John Gardner's Grendel

Films

• The Number 23 (2007)
• 23 (1998)
• A Beautiful Mind (2001)
• Pi (1998)

Music

• Dark Side of the Rainbow

Floating man

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Floating_man

 

The floating man, flying man, or man suspended in air argument is a thought experiment by the Persian philosopher Ibn Sina (Avicenna) which argues for the existence of the soul. This thought experiment is used to argue in favor of knowledge by presence.

Background

It has been said that Ibn Sina wrote the argument while imprisoned in the castle of Fardajan in the Iranian province of Hamadan. He concluded that the soul is immaterial and substantial. He also claimed that no human could deny their own consciousness or awareness. According to Ibn Sina, the floating man could attain the concept of being without any sense experience.

Using his knowledge, Ibn Sina saved one of the Iranian rulers, Shams al-Dawla, from death, which caused the envy of many of the courtiers. As a result, after the death of Shams al-Dawla, Ibn Sina was arrested and imprisoned in a castle between the Iranian provinces of Hamadan and Isfahan. The name of that castle is recorded in the old books as "Fardjan," "Mazdjan," or "Mazdavan." It has been said that Ibn Sina wrote the floating man argument while imprisoned in this castle.

Concept

The floating man argument considers a man who falls or floats freely in the air, unable to touch or perceive anything (as in a modern sensory deprivation chamber). This subject lacks any sensory perception data about the material world, yet is still self-aware, and is able to think to himself.

The Floating Man argument that is known today is the product of three distinct yet related versions. In the early days of its creation, Ibn Sina attempts to prove the dissociability of a consciousness and its physical body. In doing so, this initial version focuses on the principle of existential separability, the self and its ability to conceptualize its existence. In an attempt to solidify his argument, Sina expands his argument into what is known as the second version. In this updated version, Sina creates a new ideology, namely conceptual separability, which details that because the body and self are perceptible, one is able to conceptualize the self without the associated bodily parts. In the final edition of his argument, Sina brings into question self-awareness and the continuity of consciousness.

Ibn Sina states that that the eyes are the only thing preventing them from seeing anything externally, and he further describes that the floating man is created in the air, like a vacuum. Thus, this is to make sure that nothing was to overlap, allowing him the form to continue connecting with no issues. Additionally, he suggests that his extremities are separate and not interlocked. Therefore, since they are separate, Ibn Sina believes that he has no consciousness of his limbs, innards, heart or anything external to him that is truly there. Although He won't know his exact length, breadth, or depth, he will be aware of the existence of his essence. Even if he were to be conscious of his extremities, for instance, he still would perceive them as an essence of a condition of his essence. Therefore, he is warned and instructed to pay attention to the existence of his soul as something separate from his body and immaterial.

Existential separability

This form of separability concentrates on the unavoidable truth that exists within the self. The concept deals with the affirmation of the self, independent of anything - a certainty that exists naturally. Sina uses the word ānniyya to describe individual existence or quiddity, and declares its independence from the physical realm. Sina asserts the intrinsic essence of the ānniyya, regardless of its quantitative and qualitative characteristics.

Conceptual separability

This version of separability expands on the ability to conceptualize the body and to conceive the self as a separate entity accordingly. When defining the ānniyya as a separate entity from the body, Sina believes it is essential to distinguish the external limbs and parts from the internal organs, specifically the brain. This is primarily due to the impossibility of determining whether the self would even be conceivable without the brain as a vessel. Sina argues that there must be a relationship between the intellect and the brain. However, none between the self and sensory stimuli or the external body.

The immediateness and constancy of self-awareness

Sina argues that the self is immediate and is determined by no preceding action or activity. He states that no measure or operation could produce self-awareness. Similarly, Sina proclaims the continuity of self-awareness and that there is never a point at which the mind unaware of itself. He insists that a circumstance whereupon the absolute state of self-awareness would be interrupted, is impossible.

Premises of the argument

According to Ibn Sina, we cannot deny the consciousness of the self. His argument is as follows:

One of us must suppose that he was just created at a stroke, fully developed and perfectly formed but with his vision shrouded from perceiving all external objects – created floating in the air or in the space, not buffeted by any perceptible current of the air that supports him, his limbs separated and kept out of contact with one another, so that they do not feel each other. Then let the subject consider whether he would affirm the existence of his self. There is no doubt that he would affirm his own existence, although not affirming the reality of any of his limbs or inner organs, his bowels, or heart or brain or any external thing. Indeed he would affirm the existence of this self of his while not affirming that it had any length, breadth or depth. And if it were possible for him in such a state to imagine a hand or any other organ, he would not imagine it to be a part of himself or a condition of his existence.

— Ibn Sina, quoted in Goodman (2013, pp. 155–156) 

We can deconstruct Ibn Sīnā’s Floating Man argument into the following points:

1. The Floating Man is conscious of the existence of his soul without being conscious of the existence of his body.

2. The Floating Man validates the existence of his soul without validating the existence of his body.

3. When the Floating Man is taken out of his body; all that is left is his soul, which is validated in itself.

Therefore, one may determine that:

4. Rejecting the existence of his soul is unimaginable, since it is necessary for his existence.

5. Rejecting the existence of his body is plausible, since it is not necessary condition to validate his existence.

6. Following the points 4 and 5: validating the existence of the soul without validating the existence of the body is plausible.

This argument relies on an introspective thought experiment. We have to suppose a man who comes into existence fully developed and formed, but he does not have any relation with sensory experience of the world or of his own body. There is no physical contact with the external world at all. According to Ibn Sina, this subject is, nonetheless, necessarily conscious of himself. In other words, such a being possesses the awareness of his own existence. He thereby believes that the soul has an unmediated and reflexive knowledge of its own existence. Thus appealing to self-consciousness, Ibn Sina tries to prove the existence of soul, or Nafs. Some scholars like Wisnovsky believe that the flying man argument proved the substantiality of the soul. Ibn Sina believes that innate awareness is completely independent of sensory experience.

Dualist perspective

The Floating Man argument is a dualist argument, supporting the idea that the mental realm is separate from the physical world (such as the physical body). In the argument of the floating man, Ibn Sina affirms the existence of a mental self, even without any physical perception. Many dualist philosophers have used this thought experiment to confirm the essence of the soul and other arguments of dualist origin.

Descartes' famous phrase "Cogito ergo sum" ("I think, therefore I am") bears some resemblance to the Floating Man argument, in that both argue for knowledge by presence. Whether these similarities are deep or trivial is a matter of scholarly disagreement.

Criticism

Adamson claims that even if the man floating in air were aware of himself, the argument fails to prove that the soul (the seat of that awareness) is something separate from the body: one could argue that self-awareness is seated in the brain. In being self-aware, the floating man is aware only through a property of his nervous system, whether or not he is aware of his nervous system.

This argument is not supported by the concept of substance in metaphysics. This experiential field shows that the self is not consequently a substance and thereby there is no subjectivity.