
Self-gravity is
gravitational force exerted by a system, particularly a
celestial body
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists within the observable universe. In astronomy, the terms ''object'' and ''body'' are of ...
or system of bodies, onto itself. At a sufficient
mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
, this allows the system to hold itself together.
[Chamberlin, T. C. The Planetesimal Hypothesis. Journal of the Royal Astronomical Society of Canada, Vol. 10, p.473-497. November, 1916.]
The effects of self-gravity have significance in the fields of
astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
,
physics
Physics is the scientific study of matter, its Elementary particle, 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 whi ...
,
seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic ...
,
geology
Geology (). is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth ...
, and
oceanography
Oceanography (), also known as oceanology, sea science, ocean science, and marine science, is the scientific study of the ocean, including its physics, chemistry, biology, and geology.
It is an Earth science, which covers a wide range of to ...
.
[Wu, P. & van der Wal, W. Postglacial sealevels on a spherical, self-gravitating viscoelastic earth: effects of lateral viscosity variations in the upper mantle 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.]
The strength of self-gravity differs with regard to the size of an object, and the distribution of its mass. For example, unique gravitational effects are caused by the oceans on
Earth
Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
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 9 times that of Earth. It has an eighth the average density of Earth, but is over 95 tim ...
.
Donald Lynden-Bell, a British
theoretical astrophysicist, constructed the equation for calculating the conditions and effects of self gravitation. The equation's main purpose is to give exact descriptions of models for rotating flattened
globular clusters. It is also used in understanding how
galaxies and their
accretion discs interact with each other. Outside of astronomy, self-gravity is relevant to large-scale observations (on or near the scale of planets) in other scientific fields.
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 their
Roche limit. In this way, relatively small bodies can be torn apart, though typically the effects of self-gravitation keep the smaller body intact because the smaller body becomes elongated. This has been observed 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 9 times that of Earth. It has an eighth the average density of Earth, but is over 95 tim ...
because the rings are a function of inter-particle self-gravity.
Additionally, in most astronomical circumstances the transit through a Roche limit is temporary, so the force of self-gravitation can restore the body's composition after the fact.
Self-gravity is also necessary to understand
quasi-stellar object discs,
accretion disc formation, and stabilizing these discs around
quasi-stellar objects.
Self-gravitational forces are also significant in the formation of
planetesimals and indirectly the
formation of planets, which is critical to understanding how planets and
planetary systems 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 that can change the gravity within the Earth as the waves interact with large-scale subsurface structures. Some models depend on the use of the
spectral element method, 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, particularly for long
period waves. This kind of accuracy is critical in developing accurate
3D 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 mean, average surface level of one or more among Earth's coastal Body of water, bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical ...
and
ice caps for oceanographers and geologists, which is particularly important for anticipating the effects of
climate change
Present-day climate change includes both global warming—the ongoing increase in Global surface temperature, global average temperature—and its wider effects on Earth's climate system. Climate variability and change, Climate change in ...
.
[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 may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...
and the effects of self-gravity are taken into account. This is also used for the influence of
ocean tide loading to be taken into account when observing the Earth's deformation response to
harmonic surface loading.
The results of calculating
post-glacial 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 to try to understand how the deformation of the Earth and self-gravity within the ocean affect the
M2 tidal constituent (the tides dictated by the
Moon
The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...
).
See also
*
Gravitational energy
*
Gravitational field
In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as ...
*
Gravitational collapse
*
Kelvin-Helmholtz mechanism
*
Chamberlin–Moulton planetesimal hypothesis
*
Bound state
A bound state is a composite of two or more fundamental building blocks, such as particles, atoms, or bodies, that behaves as a single object and in which energy is required to split them.
In quantum physics, a bound state is a quantum state of a ...
References
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Gravity