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The gravitational constant G is a key element in Newton's law of universal gravitation. The gravitational constant, denoted G, is a physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal gravitational constant, Newton's constant, and colloquially Big G. It should not be confused with "little g" (g), which is the local gravitational field (equivalent to the local acceleration due to gravity), especially that at the Earth's surface; see Earth's gravity and standard gravity. Isaac Newtons theory of universal gravitation (part of classical mechanics) states the following: Every single point mass attracts every other point mass by a force pointing along the line combining the two. ... A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. ... Gravity redirects here. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Isaac Newtons theory of universal gravitation (part of classical mechanics) states the following: Every single point mass attracts every other point mass by a force pointing along the line combining the two. ... “Einstein” redirects here. ... For a generally accessible and less technical introduction to the topic, see Introduction to general relativity. ... g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ... Earths gravity, denoted by g, refers to the attractive force that the Earth exerts on objects on or near its surface (or, more generally, objects anywhere in the Earths vicinity). ... g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ... According to the law of universal gravitation, the attractive force (F) between two bodies is proportional to the product of their masses (m1 and m2), and inversely proportional to the square of the distance (r) between them: For other uses, see Force (disambiguation). ... For other uses, see Mass (disambiguation). ... In physics, an inverse-square law is any physical law stating that some quantity is inversely proportional to the square of the distance from a point. ... The constant of proportionality, G, is the gravitational constant. This article is about proportionality, the mathematical relation. ... The gravitational constant is perhaps the most difficult physical constant to measure.[1] In SI units, the 2006 CODATA recommended value of the gravitational constant is:[2] Look up si, Si, SI in Wiktionary, the free dictionary. ... CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ... Another authoritative estimate is given by the International Astronomical Union (see Standish, 1995). IAU redirects here. ... Contents 1 Dimensions, units and magnitude 2 History of measurement 3 The GM product 4 See also 5 References 6 External links [edit] Dimensions, units and magnitude The dimensions assigned to the gravitational constant in the equation above — length cubed, divided by mass and by time squared (in SI units, metres cubed per kilogram per second squared) — are those needed to balance the units of measurements in gravitational equations. However, these dimensions have fundamental significance in terms of Planck units: when expressed in SI units, the gravitational constant is dimensionally and numerically equal to the cube of the Planck length divided by the Planck mass and by the square of Planck time. For other uses of this word, see Length (disambiguation). ... For other uses, see Mass (disambiguation). ... This article is about the concept of time. ... This article is about the unit of length. ... Kg redirects here. ... This article is about the unit of time. ... In physics, Planck units are one of several systems of natural units, units of measurement that normalize certain fundamental physical constants to 1. ... The Planck length, denoted by , is the unit of length approximately 1. ... The Planck mass is the natural unit of mass, denoted by mP. It is the mass for which the Schwarzschild radius is equal to the Compton length divided by Ï€. ≈ 1. ... In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. ... In natural units, of which Planck units are perhaps the best example, G and other physical constants such as c (the speed of light) may be set equal to 1. In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ... In physics, Planck units are one of several systems of natural units, units of measurement that normalize certain fundamental physical constants to 1. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... In cgs, G can be written as: This article or section is in need of attention from an expert on the subject. ... In many secondary school texts, the dimensions of G are derived from force in order to assist student comprehension: On galactic scales, where distances are measured in parsecs (pc), velocities in kilometers per second (km/s) and masses in solar units (), it is useful to express G as: A parsec is the distance from the Earth to an astronomical object which has a parallax angle of one arcsecond. ... In astronomy, the solar mass is a unit of mass used to express the mass of stars and larger objects such as galaxies. ... The gravitational force is extremely weak compared with other fundamental forces. For example, the gravitational force between an electron and proton 1 meter apart is approximately 10−67 newton, while the electromagnetic force between the same two particles still 1 meter apart is approximately 10−28 newton. Both these forces are weak when compared with the forces we are able to experience directly, but the electromagnetic force in this example is some 39 orders of magnitude (i.e. 1039) greater than the force of gravity — which is even greater than the ratio between the mass of a human and the mass of the Solar System. A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... For other uses, see Electron (disambiguation). ... For other uses, see Proton (disambiguation). ... For other uses, see Newton (disambiguation). ... In physics, the electromagnetic force is the force that the electromagnetic field exerts on electrically charged particles. ... [edit] History of measurement The gravitational constant appears in Newton's law of universal gravitation, but it was not measured until 1798 — 71 years after Newton's death — by Henry Cavendish (Philosophical Transactions 1798). Cavendish measured G implicitly, using a torsion balance invented by the geologist Rev. John Michell. He used a horizontal torsion beam with lead balls whose inertia (in relation to the torsion constant) he could tell by timing the beam's oscillation. Their faint attraction to other balls placed alongside the beam was detectable by the deflection it caused. However, it is worth mentioning that the aim of Cavendish was not to measure the gravitational constant but rather to measure the mass and density relative to water of the Earth through the precise knowledge of the gravitational interaction. Isaac Newtons theory of universal gravitation (part of classical mechanics) states the following: Every single point mass attracts every other point mass by a force pointing along the line combining the two. ... For other persons named Henry Cavendish, see Henry Cavendish (disambiguation). ... Year 1798 (MDCCXCVIII) was a common year starting on Monday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Friday of the 11-day slower Julian calendar). ... This article or section does not adequately cite its references or sources. ... John Michell (1724 – April 29, 1793) was an English natural philosopher and geologist, whose work was rediscovered in the 1970s. ... The accuracy of the measured value of G has increased only modestly since the original experiment of Cavendish. G is quite difficult to measure, as gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies. Furthermore, gravity has no established relation to other fundamental forces, so it does not appear possible to measure it indirectly. Further, published values of G have varied rather broadly, and some recent measurements of high precision are, in fact, mutually exclusive.[1][3] In the January 5, 2007 issue of Science (page 74), the report "Atom Interferometer Measurement of the Newtonian Constant of Gravity" (J. B. Fixler, G. T. Foster, J. M. McGuirk, and M. A. Kasevich) describes a new measurement of the gravitational constant. According to the abstract: "Here, we report a value of G = 6.693 × 10−11 cubic meters per kilogram second squared, with a standard error of the mean of ±0.027 × 10−11 and a systematic error of ±0.021 × 10−11 cubic meters per kilogram second squared.".[4] Science is the academic journal of the American Association for the Advancement of Science and is considered one of the worlds most prestigious scientific journals. ... [edit] The GM product Main article: Standard gravitational parameter The quantity GM — the product of the gravitational constant and the mass of a given astronomical body such as the Sun or the Earth — is known as the standard gravitational parameter and is denoted μ. Depending on the body concerned, it may also be called the geocentric or heliocentric gravitational constant, among other names. In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s-2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting... This quantity gives a convenient simplification of various gravity-related formulas. Also, for the Earth and the Sun, the value of the product is known more accurately than each factor. (As a result, the accuracy to which the masses of the Earth and the Sun are known correspond to the accuracy to which G is known.) In calculations of gravitational force in the solar system, it is the products which appear, so computations are more accurate using the standard gravitational parameters directly (or, equivalently, using values for the masses and the gravitational constant which correspond, i.e., result in an accurate product, though not very accurate individually). In other words, because GM appear together, there really is no need to substitute values for each; rather use the more accurate measurement of their product, μ, in place of GM. For Earth, Calculations in celestial mechanics can also be carried out using the unit of solar mass rather than the standard SI unit kilogram. In this case we use the Gaussian gravitational constant which is k2, where Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ... In astronomy, the solar mass is a unit of mass used to express the mass of stars and larger objects such as galaxies. ... Carl Friedrich Gauss expressed the gravitational constant in units of the solar system rather than SI units. ... and A is the astronomical unit D is the mean solar day S is the solar mass. If instead of mean solar day we use the sidereal year as our time unit, the value is very close to 2π. The astronomical unit (AU or au or a. ... Solar time is based on the idea that, when the sun reaches its highest point in the sky, it is noon. ... In astronomy, the solar mass is a unit of mass used to express the mass of stars and larger objects such as galaxies. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... [edit] See also Cavendish experiment Standard gravity Planck units Dirac large numbers hypothesis Accelerating Universe Gravity expressed in terms of orbital periodhttp://en.wikipedia.org/wiki/Orbital_period#Small_body_orbiting_a_central_body Lunar Laser Ranging Experiment Cosmological constant In physics, the Cavendish experiment was the first experiment to accurately measure the gravitational constant by measuring the force of gravity between two masses in the laboratory. ... g (also gee, g-force or g-load) is a non-SI unit of acceleration defined as exactly 9. ... In physics, Planck units are one of several systems of natural units, units of measurement that normalize certain fundamental physical constants to 1. ... The Dirac large numbers hypothesis refers to an observation made by Paul Dirac in 1937 relating ratios of size scales in the universe to that of force scales. ... The accelerating universe is the observation that the universe appears to be expanding at an accelerated rate. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... The Lunar Laser Ranging Experiment from the Apollo 11 mission The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. ... In physical cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ... [edit] References E. Myles Standish. "Report of the IAU WGAS Sub-group on Numerical Standards". In Highlights of Astronomy, I. Appenzeller, ed. Dordrecht: Kluwer Academic Publishers, 1995. (Complete report available online: PostScript. Tables from the report also available: Astrodynamic Constants and Parameters) Jens H. Gundlach & Stephen M. Merkowitz (2000), "Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback", Physical Review Letters 85 (14): 2869-2872  ^ a b George T. Gillies (1997), "The Newtonian gravitational constant: recent measurements and related studies", Reports on Progress in Physics 60: 151-225, doi:10.1088/0034-4885/60/2/001, <http://www.iop.org/EJ/abstract/0034-4885/60/2/001> . A lengthy, detailed review. See Figure 1 and Table 2 in particular. ^ CODATA Value: Newtonian constant of gravitation ^ Peter J. Mohr & Barry N. Taylor (January 2005), "CODATA recommended values of the fundamental physical constants: 2002", Reviews of Modern Physics 77 (1): 1–107, <http://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/other%20rmp%20articles/CODATA2005.pdf>. Retrieved on 1 July 2006 . Section Q (pp. 42–47) describes the mutually inconsistent measurement experiments from which the CODATA value for G was derived. ^ J. B. Fixler; G. T. Foster; J. M. McGuirk & M. A. Kasevich (2007-01-05), Atom Interferometer Measurement of the Newtonian Constant of Gravity, vol. 315, pp. 74–77, doi:10.1126/science.1135459, <http://www.sciencemag.org/cgi/content/abstract/315/5808/74>  A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... [edit] External links CODATA Internationally recommended values of the Fundamental Physical Constants (at The NIST References on Constants, Units, and Uncertainty) The Controversy over Newton's Gravitational Constant — additional commentary on measurement problems The Gravitational Constant Categories: Celestial mechanics | Gravitation | Fundamental constants

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	Gravitational constant - Wikipedia, the free encyclopedia (820 words) According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. The gravitational constant is a physical constant which appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. However, these dimensions have fundamental significance in terms of Planck units: when expressed in SI units, the gravitational constant is dimensionally and numerically equal to the cube of the Planck length divided by the Planck mass and by the square of Planck time.
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