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Self-gravity is the
gravitational force In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
exerted on a body, or group of bodies, by the body/bodies that allows it/them to be held together.Chamberlin, T. C. The Planetesimal Hypothesis. Journal of the Royal Astronomical Society of Canada, Vol. 10, p.473-497. November, 1916. Self-gravity (self-gravitation) has effects in the fields of
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
,
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
,
seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
,
geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology ...
, and
oceanography Oceanography (), also known as oceanology and ocean science, is the scientific study of the oceans. It is an Earth science, which covers a wide range of topics, including ecosystem dynamics; ocean currents, waves, and geophysical fluid dynami ...
.Wu, P. & van der Wal, W. Postglacial sealevels on a spherical, self-gravitating viscoelastic earth: effects of lateral viscosity variations in the
upper mantle The upper mantle of Earth is a very thick layer of rock inside the planet, which begins just beneath the crust (at about under the oceans and about under the continents) and ends at the top of the lower mantle at . Temperatures range from appr ...
on the inference of viscosity contrasts in the lower mantle. Earth and Planetary Science Letters, Volume 211, Issues 1–2, June 15, 2003, Pages 57–68.
Colwell, J. E., Esposito, L. W. & M. Sremcevic. Self-gravity wakes in Saturn’s A ring measured by stellar occultations from Cassini. Geophysical Research Letters, volume 33, April 1, 2006. L07201 p. 1-4.Mitrovica, J., Tamisiea, M., Davis, J. & Milne, G. Recent mass balance of polar ice sheets inferred from patterns of global sea-level change. Nature 409, p. 1026-1029. February 22, 2001. Self-gravity differs with regards to the physical behavior on large scale (planet size or larger) objects, such as the oceans on
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
or the rings of
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
. Lynden-Bell, a British theoretical astrophysicist, constructed the equation for calculating the effects of self gravitation. The equation's main purpose is giving exact descriptions of models for rotating flattened globular clusters. It is also used in understanding how clusters of
stars A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ma ...
interact with each other. Self-gravity deals with large-scale observations in fields outside of astronomy as well. Self-gravity does not typically appear as the central focus of scientific research, but understanding it and being able to include its effects mathematically increases the accuracy of models and understanding large-scale systems.


Astronomy

Self-gravity must be taken into account by astronomers because the bodies being dealt with are large enough to have gravitational effects on each other and within themselves. Self-gravity affects bodies passing each other in space within the sphere defined by the Roche limit, because relatively small bodies could be torn apart by differential attraction. Though, typically the effects of self-gravitation keep the smaller body intact because the smaller body becomes elongated and the gravity of the body is able to overcome the momentum from this interaction. This has been demonstrated on
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
because the rings are a function of inter-particle self-gravity. Self-gravity is also necessary to understand
quasi-stellar object A quasar is an extremely luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a mass ranging ...
discs,
accretion disc An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other ...
formation, and stabilizing these discs around quasi-stellar objects. Self-gravitational forces are significant in the formation of
planetesimal Planetesimals are solid objects thought to exist in protoplanetary disks and debris disks. Per the Chamberlin–Moulton planetesimal hypothesis, they are believed to form out of cosmic dust grains. Believed to have formed in the Solar System ...
s, and indirectly the formation of planets, which is critical to understanding how planets and
planetary system A planetary system is a set of gravitationally bound non- stellar objects in or out of orbit around a star or star system. Generally speaking, systems with one or more planets constitute a planetary system, although such systems may also consi ...
s form and develop over time. Self-gravity applies to a range of scales, from the formation of rings around individual planets to the formation of planetary systems.


Seismology

Self-gravity has implications in the field of seismology, because the Earth is large enough that it can have
elastic waves Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum me ...
that can change the gravity within the Earth as the waves interact with large scale subsurface structures. There are models that depend on the use of the
spectral element method In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high degree piecewise polynomials as basis functions. The spectral ...
, which take into account the effects of self-gravitation because it can have a large influence on results for certain receiver-source configurations and creates complications in the
wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and ...
, particularly for long
period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...
waves. This kind of accuracy is critical in developing accurate 3-D crustal models in a spherical body (Earth) in the field of seismology, which allows for more accurate and higher quality interpretations to be drawn from data. The influence of self-gravity (and gravity) alters the importance of Primary (P) and Secondary (S) waves in seismology because when gravity is taken into account, the effects of the S wave become less significant than they would without.


Oceanography

Self-gravity is influential in understanding the
sea level Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardis ...
and
ice cap In glaciology, an ice cap is a mass of ice that covers less than of land area (usually covering a highland area). Larger ice masses covering more than are termed ice sheets. Description Ice caps are not constrained by topographical feat ...
s for oceanographers and geologists, which is particularly important for anticipating the effects of
climate change In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to ...
.Hendershott, M. The Effects of Solid Earth Deformation on Global Ocean Tides. Geophysical Journal International (published on behalf of the Royal Astronomical Society) (1972) 29, 389-402.Pagiatakis, S. Ocean tide loading on a self-gravitating, compressible, layered, anisotropic, viscoelastic and rotating Earth with solid inner core and fluid outer core. Geodesy and Geomatics Engineering. July 1988. p. 1-146. The deformation of the Earth from the forces on the oceans can be calculated if the Earth is treated as
fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
and the effects of self-gravity are taken into account. This has also allowed for the influence of ocean tide loading to be taken into account when observing the Earth's deformation response to
harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', t ...
surface loading. The results of calculating
post-glacial The Holocene ( ) is the current geological epoch. It began approximately 11,650 cal years Before Present (), after the Last Glacial Period, which concluded with the Holocene glacial retreat. The Holocene and the preceding Pleistocene togethe ...
sea levels near the ice caps are significantly different when using a flat Earth model that does not take self-gravity into account, as opposed to a spherical Earth where self-gravity is taken into account because of the sensitivity of the data in these regions, which shows how results can drastically change when self-gravity is ignored.Wang, H. & Wu, P. Effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced relative sea levels and long wavelength gravity field in a spherical, self-gravitating Maxwell Earth. Earth and Planetary Science Letters 249 (2006) 368–383. There has also been research done to better understand
Laplace's Tidal Equations The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans (especially Earth's oceans) under the gravitational loading of anot ...
to try to understand how deformation of the Earth and self-gravity within the ocean affect the
M2 tidal constituent Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can ...
(the tides dictated by the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
). There have been suggestions that if the Greenland ice complex melts, the sea level will actually fall around
Greenland Greenland ( kl, Kalaallit Nunaat, ; da, Grønland, ) is an island country in North America that is part of the Kingdom of Denmark. It is located between the Arctic and Atlantic oceans, east of the Canadian Arctic Archipelago. Greenland ...
and rise in areas further away because the effects of self-gravity .


See also

*
Chamberlin–Moulton planetesimal hypothesis The Chamberlin–Moulton planetesimal hypothesis was proposed in 1905 by geologist Thomas Chrowder Chamberlin and astronomer Forest Ray Moulton to describe the formation of the Solar System. It was proposed as a replacement for the Laplacian versio ...


References

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