Gravitational acceleration
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In
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 (about 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.
Relation to the Universal Law
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
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
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
Body | Multiple of Earth gravity |
m/s2 | ft/s2 | Notes | Time to fall 100 m and maximum speed reached | |
---|---|---|---|---|---|---|
Sun | 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
In Einstein's theory of
Gravitational field
In
In its original concept,
In general relativity, rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived and measured as a "force".[citation needed] In such a model one states that matter moves in certain ways in response to the curvature of spacetime,[7] and that there is either no gravitational force,[8] or that gravity is a fictitious force.[9]
Gravity is distinguished from other forces by its obedience to the equivalence principle.See also
Notes
- ^ 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.). 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.
- 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.")
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: 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". .
- ^
ISBN 978-0-07-008836-8.
- ISBN 978-0-201-02115-8.
- ISBN 978-0-226-28864-2.
- ISBN 978-0-387-69199-2.
- ISBN 978-0-387-26078-5.