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The surface gravity, ''g'', of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in order not to disturb the system, has negligible mass. Surface gravity is measured in units of acceleration, which, in the SI system, are meters per second squared. It may also be expressed as a multiple of the Earth's standard surface gravity, ''g'' = 9.80665 m/s2.〔p. 29, (The International System of Units (SI) ), ed. Barry N. Taylor, NIST Special Publication 330, 2001.〕 In astrophysics, the surface gravity may be expressed as log ''g'', which is obtained by first expressing the gravity in cgs units, where the unit of acceleration is centimeters per second squared, and then taking the base 10 logarithm. Therefore, as gravity affects all things equally, regardless of their mass in grams or kilograms, and because 1 m/s2 = 100 cm/s2, the surface gravity of Earth could be expressed in cgs units as 980.665 cm/s2 and at base 10 logarithm (log ''g'') as 2.992. The surface gravity of a white dwarf is very high, and of a neutron star even more. The neutron star's compactness gives it a surface gravity of up to 7 m/s2 with typical values of a few m/s2 (that is more than 1011 times that of Earth). One measure of such immense gravity is the fact that neutron stars have an escape velocity of around 100,000 km/s, about a third of the speed of light. ==Mass, radius and surface gravity== In the Newtonian theory of gravity, the gravitational force exerted by an object is proportional to its mass: an object with twice the mass-produces twice as much force. Newtonian gravity also follows an inverse square law, so that moving an object twice as far away divides its gravitational force by four, and moving it ten times as far away divides it by 100. This is similar to the intensity of light, which also follows an inverse square law: with relation to distance, light becomes less visible. Generally speaking, this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space. A large object, such as a planet or star, will usually be approximately round, approaching hydrostatic equilibrium (where all points on the surface have the same amount of gravitational potential energy). On a small scale, higher parts of the terrain are eroded, with eroded material deposited in lower parts of the terrain. On a large scale, the planet or star itself deforms until equilibrium is reached.〔(Why is the Earth round? ), at Ask A Scientist, accessed online May 27, 2007.〕 For most celestial objects, the result is that the planet or star in question can be treated as a near-perfect sphere when the rotation rate is low. However, for young, massive stars, the equatorial azimuthal velocity can be quite high—up to 200 km/s or more—causing a significant amount of equatorial bulge. Examples of such rapidly rotating stars include Achernar, Altair, Regulus A and Vega. The fact that many large celestial objects are approximately spheres makes it easier to calculate their surface gravity. The gravitational force outside a spherically symmetric body is the same as if its entire mass were concentrated in the center, as was established by Sir Isaac Newton.〔Book I, §XII, pp. 218–226, ''Newton's Principia: The Mathematical Principles of Natural Philosophy'', Sir Isaac Newton, tr. Andrew Motte, ed. N. W. Chittenden. New York: Daniel Adee, 1848. First American edition.〕 Therefore, the surface gravity of a planet or star with a given mass will be approximately inversely proportional to the square of its radius, and the surface gravity of a planet or star with a given average density will be approximately proportional to its radius. For example, the recently discovered planet, Gliese 581 c, has at least 5 times the mass of Earth, but is unlikely to have 5 times its surface gravity. If its mass is no more than 5 times that of the Earth, as is expected,〔(Astronomers Find First Earth-like Planet in Habitable Zone ), ESO 22/07, press release from the European Southern Observatory, April 25, 2007〕 and if it is a rocky planet with a large iron core, it should have a radius approximately 50% larger than that of Earth.〔(The HARPS search for southern extra-solar planets XI. Super-Earths (5 & 8 M_Earth) in a 3-planet system ), S. Udry, X. Bonfils), X. Delfosse, T. Forveille, M. Mayor, C. Perrier, F. Bouchy, C. Lovis, F. Pepe, D. Queloz, and J.-L. Bertaux. arXiv:astro-ph/0704.3841.〕〔(Detailed Models of super-Earths: How well can we infer bulk properties? ), Diana Valencia, Dimitar D. Sasselov, and Richard J. O'Connell, arXiv:astro-ph/0704.3454.〕 Gravity on such a planet's surface would be approximately 2.2 times as strong as on Earth. If it is an icy or watery planet, its radius might be as large as twice the Earth's, in which case its surface gravity might be no more than 1.25 times as strong as the Earth's.〔 These proportionalities may be expressed by the formula: : where ''g'' is the surface gravity of an object, expressed as a multiple of the Earth's, ''m'' is its mass, expressed as a multiple of the Earth's mass (5.976·1024 kg) and ''r'' its radius, expressed as a multiple of the Earth's (mean) radius (6,371 km).〔(2.7.4 Physical properties of the Earth ), web page, accessed on line May 27, 2007.〕 For instance, Mars has a mass of 6.4185·1023 kg = 0.107 Earth masses and a mean radius of 3,390 km = 0.532 Earth radii.〔(Mars Fact Sheet ), web page at NASA NSSDC, accessed May 27, 2007.〕 The surface gravity of Mars is therefore approximately : times that of Earth. Without using the Earth as a reference body, the surface gravity may also be calculated directly from Newton's law of universal gravitation, which gives the formula : where ''M'' is the mass of the object, ''r'' is its radius, and ''G'' is the gravitational constant. If we let ρ = ''m''/''V'' denote the mean density of the object, we can also write this as : so that, for fixed mean density, the surface gravity ''g'' is proportional to the radius ''r''. Since gravity is inversely proportional to the square of the distance, a space station 100 miles above the Earth feels almost the same gravitational force as we do on the Earth's surface. The reason a space station does not plummet to the ground is not that it is not subject to gravity, but that it is in a free-fall orbit. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「surface gravity」の詳細全文を読む スポンサード リンク
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