Self-gravity is gravity exerted by a system, particularly a celestial body or system of bodies, onto itself. At a sufficient mass, 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, physics, seismology, geology, and oceanography.[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[Lynden-Bell, D. Stellar dynamics: Exact solution of the self-gravitation equation. Monthly Notices of the Royal Astronomical Society, Vol. 123, p.447. November, 1962.] 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 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 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.
[Goodman, J. Self-gravity and quasi-stellar object discs. Monthly Notices of the Royal Astronomical Society, Volume 339, Issue 4, pages 937–948, March 2003.]
Self-gravitational forces are also significant in the formation of
and indirectly the
Planet formation, which is critical to understanding how planets and
form and develop over time.
[Johansen, A., Oishi, J., Low, M., Klahr, H., Henning, T. & Youdin, A. Rapid planetesimal formation in turbulent circumstellar disks. Nature 448, 1022-1025, (August 30, 2007).] 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,
[Komatitsch, D. & Tromp, J. Spectral-element simulations of global seismic wave propagation—II. Three-dimensional models, oceans, rotation and self-gravitation. Geophysical Journal International, (2002) 150. p. 303–318.] 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.
[Freeman, G. Gravitationally Perturbed Elastic Waves. Bulletin of the Seismological Society of America. Vol. 57, No. 4, pp. 783-794. August, 1967.]
Oceanography
Self-gravity is influential in understanding the
sea level and
for oceanographers and geologists, which is particularly important for anticipating the effects of
climate change.
[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 and the effects of self-gravity are taken into account. This is also used for the influence of
Ocean tides 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).
See also
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Gravitational energy
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Gravitational field
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Gravitational collapse
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Kelvin-Helmholtz mechanism
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Chamberlin–Moulton planetesimal hypothesis
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Bound state
