In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies;[1] the measurement and analysis of these rates is known as gravimetry.
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation.[2][3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s2 (32.03 to 32.26 ft/s2),[4] depending on altitude, latitude, and longitude. A conventional standard value is defined exactly as 9.80665 m/s2 (32.1740 ft/s2). Locations of significant variation from this value are known as gravity anomalies. This does not take into account other effects, such as buoyancy or drag.
Newton's law of universal gravitation states that there is a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other. The formula is:
where and are any two masses, is the gravitational constant, and is the distance between the two point-like masses.
Using the integral form of Gauss's Law, this formula can be extended to any pair of objects of which one is far more massive than the other — like a planet relative to any man-scale artifact. The distances between planets and between the planets and the Sun are (by many orders of magnitude) larger than the sizes of the sun and the planets. In consequence both the sun and the planets can be considered as point masses and the same formula applied to planetary motions. (As planets and natural satellites form pairs of comparable mass, the distance 'r' is measured from the common centers of mass of each pair rather than the direct total distance between planet centers.)
If one mass is much larger than the other, it is convenient to take it as observational reference and define it as source of a gravitational field of magnitude and orientation given by:[5]
where is the mass of the field source (larger), and is a unit vector directed from the field source to the sample (smaller) mass. The negative sign indicates that the force is attractive (points backward, toward the source).
Then the attraction force vector onto a sample mass can be expressed as:
Here is the frictionless, free-fall acceleration sustained by the sampling mass under the attraction of the gravitational source. It is a vector oriented toward the field source, of magnitude measured in acceleration units. The gravitational acceleration vector depends only on how massive the field source is and on the distance 'r' to the sample mass . It does not depend on the magnitude of the small sample mass.
This model represents the "far-field" gravitational acceleration associated with a massive body. When the dimensions of a body are not trivial compared to the distances of interest, the principle of superposition can be used for differential masses for an assumed density distribution throughout the body in order to get a more detailed model of the "near-field" gravitational acceleration. For satellites in orbit, the far-field model is sufficient for rough calculations of altitude versus period, but not for precision estimation of future location after multiple orbits.
The more detailed models include (among other things) the bulging at the equator for the Earth, and irregular mass concentrations (due to meteor impacts) for the Moon. The Gravity Recovery and Climate Experiment (GRACE) mission launched in 2002 consists of two probes, nicknamed "Tom" and "Jerry", in polar orbit around the Earth measuring differences in the distance between the two probes in order to more precisely determine the gravitational field around the Earth, and to track changes that occur over time. Similarly, the Gravity Recovery and Interior Laboratory mission from 2011-2012 consisted of two probes ("Ebb" and "Flow") in polar orbit around the Moon to more precisely determine the gravitational field for future navigational purposes, and to infer information about the Moon's physical makeup.
Comparative gravities of the Earth, Sun, Moon, and planets
The table below shows comparative gravitational accelerations at the surface of the Sun, the Earth's moon, each of the planets in the Solar System and their major moons, Ceres, Pluto, and Eris. For gaseous bodies, the "surface" is taken to mean visible surface: the cloud tops of the gas giants (Jupiter, Saturn, Uranus and Neptune), and the Sun's photosphere. The values in the table have not been de-rated for the centrifugal force effect of planet rotation (and cloud-top wind speeds for the gas giants) and therefore, generally speaking, are similar to the actual gravity that would be experienced near the poles. For reference the time it would take an object to fall 100 meters, the height of a skyscraper, is shown, along with the maximum speed reached. Air resistance is neglected.
In Einstein's theory of general relativity, gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, masses distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. The gravitational force is a fictitious force. There is no gravitational acceleration, in that the proper acceleration and hence four-acceleration of objects in free fall are zero. Rather than undergoing an acceleration, objects in free fall travel along straight lines (geodesics) on the curved spacetime.
^This value excludes the adjustment for centrifugal force due to Earth's rotation and is therefore greater than the 9.80665 m/s2 value of standard gravity.
References
^ Gerald James Holton and Stephen G. Brush (2001). Physics, the human adventure: from Copernicus to Einstein and beyond (3rd ed.). Rutgers University Press. p. 113. ISBN978-0-8135-2908-0.
^Boynton, Richard (2001). "Precise Measurement of Mass" (PDF). Sawe Paper No. 3147. Arlington, Texas: S.A.W.E., Inc. Retrieved 2007-01-21.
^Hofmann-Wellenhof, B.; Moritz, H. (2006). Physical Geodesy (2nd ed.). Springer. ISBN978-3-211-33544-4. § 2.1: "The total force acting on a body at rest on the earth’s surface is the resultant of gravitational force and the centrifugal force of the earth’s rotation and is called gravity."{{cite book}}: CS1 maint: postscript (link)
^ Hirt, C.; Claessens, S.; Fecher, T.; Kuhn, M.; Pail, R.; Rexer, M. (2013). "New ultrahigh-resolution picture of Earth's gravity field". Geophysical Research Letters. 40 (16): 4279–4283. Bibcode:2013GeoRL..40.4279H. doi:10.1002/grl.50838.
^ Fredrick J. Bueche (1975). Introduction to Physics for Scientists and Engineers, 2nd Ed. USA: Von Hoffmann Press. ISBN978-0-07-008836-8.
February 28, 2023
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For broader coverage of this topic see Classical mechanics This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Gravitational acceleration news newspapers books scholar JSTOR December 2010 Learn how and when to remove this template message In physics gravitational acceleration is the acceleration of an object in free fall within a vacuum and thus without experiencing drag This is the steady gain in speed caused exclusively by the force of gravitational attraction All bodies accelerate in vacuum at the same rate regardless of the masses or compositions of the bodies 1 the measurement and analysis of these rates is known as gravimetry At a fixed point on the surface the magnitude of Earth s gravity results from combined effect of gravitation and the centrifugal force from Earth s rotation 2 3 At different points on Earth s surface the free fall acceleration ranges from 9 764 to 9 834 m s2 32 03 to 32 26 ft s2 4 depending on altitude latitude and longitude A conventional standard value is defined exactly as 9 80665 m s2 32 1740 ft s2 Locations of significant variation from this value are known as gravity anomalies This does not take into account other effects such as buoyancy or drag Contents 1 Relation to the Universal Law 2 Comparative gravities of the Earth Sun Moon and planets 3 General relativity 4 See also 5 Notes 6 ReferencesRelation to the Universal Law EditNewton s law of universal gravitation states that there is a gravitational force between any two masses that is equal in magnitude for each mass and is aligned to draw the two masses toward each other The formula is F G m 1 m 2 r 2 displaystyle F G frac m 1 m 2 r 2 where m 1 displaystyle m 1 and m 2 displaystyle m 2 are any two masses G displaystyle G is the gravitational constant and r displaystyle r is the distance between the two point like masses Two bodies orbiting their center of mass red cross Using the integral form of Gauss s Law this formula can be extended to any pair of objects of which one is far more massive than the other like a planet relative to any man scale artifact The distances between planets and between the planets and the Sun are by many orders of magnitude larger than the sizes of the sun and the planets In consequence both the sun and the planets can be considered as point masses and the same formula applied to planetary motions As planets and natural satellites form pairs of comparable mass the distance r is measured from the common centers of mass of each pair rather than the direct total distance between planet centers If one mass is much larger than the other it is convenient to take it as observational reference and define it as source of a gravitational field of magnitude and orientation given by 5 g G M r 2 r displaystyle mathbf g GM over r 2 mathbf hat r where M displaystyle M is the mass of the field source larger and r displaystyle mathbf hat r is a unit vector directed from the field source to the sample smaller mass The negative sign indicates that the force is attractive points backward toward the source Then the attraction force F displaystyle mathbf F vector onto a sample mass m displaystyle m can be expressed as F m g displaystyle mathbf F m mathbf g Here g displaystyle mathbf g is the frictionless free fall acceleration sustained by the sampling mass m displaystyle m under the attraction of the gravitational source It is a vector oriented toward the field source of magnitude measured in acceleration units The gravitational acceleration vector depends only on how massive the field source M displaystyle M is and on the distance r to the sample mass m displaystyle m It does not depend on the magnitude of the small sample mass This model represents the far field gravitational acceleration associated with a massive body When the dimensions of a body are not trivial compared to the distances of interest the principle of superposition can be used for differential masses for an assumed density distribution throughout the body in order to get a more detailed model of the near field gravitational acceleration For satellites in orbit the far field model is sufficient for rough calculations of altitude versus period but not for precision estimation of future location after multiple orbits The more detailed models include among other things the bulging at the equator for the Earth and irregular mass concentrations due to meteor impacts for the Moon The Gravity Recovery and Climate Experiment GRACE mission launched in 2002 consists of two probes nicknamed Tom and Jerry in polar orbit around the Earth measuring differences in the distance between the two probes in order to more precisely determine the gravitational field around the Earth and to track changes that occur over time Similarly the Gravity Recovery and Interior Laboratory mission from 2011 2012 consisted of two probes Ebb and Flow in polar orbit around the Moon to more precisely determine the gravitational field for future navigational purposes and to infer information about the Moon s physical makeup Comparative gravities of the Earth Sun Moon and planets EditThe table below shows comparative gravitational accelerations at the surface of the Sun the Earth s moon each of the planets in the Solar System and their major moons Ceres Pluto and Eris For gaseous bodies the surface is taken to mean visible surface the cloud tops of the gas giants Jupiter Saturn Uranus and Neptune and the Sun s photosphere The values in the table have not been de rated for the centrifugal force effect of planet rotation and cloud top wind speeds for the gas giants and therefore generally speaking are similar to the actual gravity that would be experienced near the poles For reference the time it would take an object to fall 100 meters the height of a skyscraper is shown along with the maximum speed reached Air resistance is neglected Body Multiple ofEarth gravity m s2 ft s2 Notes Time to fall 100 m andmaximum speed reachedSun 27 90 274 1 899 0 85 s 843 km h 524 mph Mercury 0 3770 3 703 12 15 7 4 s 98 km h 61 mph Venus 0 9032 8 872 29 11 4 8 s 152 km h 94 mph Earth 1 9 8067 32 174 a 4 5 s 159 km h 99 mph Moon 0 1655 1 625 5 33 11 1 s 65 km h 40 mph Mars 0 3895 3 728 12 23 7 3 s 98 km h 61 mph Ceres 0 029 0 28 0 92 26 7 s 27 km h 17 mph Jupiter 2 640 25 93 85 1 2 8 s 259 km h 161 mph Io 0 182 1 789 5 87 10 6 s 68 km h 42 mph Europa 0 134 1 314 4 31 12 3 s 58 km h 36 mph Ganymede 0 145 1 426 4 68 11 8 s 61 km h 38 mph Callisto 0 126 1 24 4 1 12 7 s 57 km h 35 mph Saturn 1 139 11 19 36 7 4 2 s 170 km h 110 mph Titan 0 138 1 3455 4 414 12 2 s 59 km h 37 mph Uranus 0 917 9 01 29 6 4 7 s 153 km h 95 mph Titania 0 039 0 379 1 24 23 0 s 31 km h 19 mph Oberon 0 035 0 347 1 14 24 0 s 30 km h 19 mph Neptune 1 148 11 28 37 0 4 2 s 171 km h 106 mph Triton 0 079 0 779 2 56 16 0 s 45 km h 28 mph Pluto 0 0621 0 610 2 00 18 1 s 40 km h 25 mph Eris 0 0814 0 8 2 6 approx 15 8 s 46 km h 29 mph General relativity EditSee also Gravitational field General relativity and Gravitational potential General relativity In Einstein s theory of general relativity gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies In Einstein s theory masses distort spacetime in their vicinity and other particles move in trajectories determined by the geometry of spacetime The gravitational force is a fictitious force There is no gravitational acceleration in that the proper acceleration and hence four acceleration of objects in free fall are zero Rather than undergoing an acceleration objects in free fall travel along straight lines geodesics on the curved spacetime See also EditAir track Gravimetry Gravity of Earth Gravitation of the Moon Gravity of Mars Newton s law of universal gravitation Standard gravityNotes Edit This value excludes the adjustment for centrifugal force due to Earth s rotation and is therefore greater than the 9 80665 m s2 value of standard gravity References Edit Gerald James Holton and Stephen G Brush 2001 Physics the human adventure from Copernicus to Einstein and beyond 3rd ed Rutgers University Press p 113 ISBN 978 0 8135 2908 0 Boynton Richard 2001 Precise Measurement of Mass PDF Sawe Paper No 3147 Arlington Texas S A W E Inc Retrieved 2007 01 21 Hofmann Wellenhof B Moritz H 2006 Physical Geodesy 2nd ed Springer ISBN 978 3 211 33544 4 2 1 The total force acting on a body at rest on the earth s surface is the resultant of gravitational force and the centrifugal force of the earth s rotation and is called gravity a href Template Cite book html title Template Cite book cite book a CS1 maint postscript link Hirt C Claessens S Fecher T Kuhn M Pail R Rexer M 2013 New ultrahigh resolution picture of Earth s gravity field Geophysical Research Letters 40 16 4279 4283 Bibcode 2013GeoRL 40 4279H doi 10 1002 grl 50838 Fredrick J Bueche 1975 Introduction to Physics for Scientists and Engineers 2nd Ed USA Von Hoffmann Press ISBN 978 0 07 008836 8 Retrieved from https en wikipedia org w index php title Gravitational acceleration amp oldid 1140599103, wikipedia, wiki, book, books, library,
