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33-398: In its original concept, gravity was a force between point masses . Following Isaac Newton , Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid , and since the 19th century, explanations for gravity in classical mechanics have usually been taught in terms of a field model, rather than a point attraction. It results from the spatial gradient of

66-442: A vector pointing directly towards the particle. The magnitude of the field at every point is calculated by applying the universal law, and represents the force per unit mass on any object at that point in space. Because the force field is conservative, there is a scalar potential energy per unit mass, Φ , at each point in space associated with the force fields; this is called gravitational potential . The gravitational field equation

99-412: A gravitational field of magnitude and orientation given by: 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

132-461: A number of easily verifiable differences , one of the most well known being the deflection of light in such fields. Embedding diagrams are three dimensional graphs commonly used to educationally illustrate gravitational potential by drawing gravitational potential fields as a gravitational topography, depicting the potentials as so-called gravitational wells , sphere of influence . Gravity Too Many Requests If you report this error to

165-433: A test particle in the presence of a gravitational field, i.e. setting up and solving these equations allows the motion of a test mass to be determined and described. The field around multiple particles is simply the vector sum of the fields around each individual particle. A test particle in such a field will experience a force that equals the vector sum of the forces that it would experience in these individual fields. This

198-434: Is g = F m = d 2 R d t 2 = − G M R | R | 3 = − ∇ Φ , {\displaystyle \mathbf {g} ={\frac {\mathbf {F} }{m}}={\frac {d^{2}\mathbf {R} }{dt^{2}}}=-GM{\frac {\mathbf {R} }{\left|\mathbf {R} \right|^{3}}}=-\nabla \Phi ,} where F

231-675: Is g = ∑ i g i = 1 m ∑ i F i = − G ∑ i m i R − R i | R − R i | 3 = − ∑ i ∇ Φ i , {\displaystyle \mathbf {g} =\sum _{i}\mathbf {g} _{i}={\frac {1}{m}}\sum _{i}\mathbf {F} _{i}=-G\sum _{i}m_{i}{\frac {\mathbf {R} -\mathbf {R} _{i}}{\left|\mathbf {R} -\mathbf {R} _{i}\right|^{3}}}=-\sum _{i}\nabla \Phi _{i},} i.e.

264-535: Is equivalent to accelerating up the gradient of the field. By Newton's second law , this will cause an object to experience a fictitious force if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are

297-416: Is a fictitious force . Gravity is distinguished from other forces by its obedience to the equivalence principle . In classical mechanics, a gravitational field is a physical quantity. A gravitational field can be defined using Newton's law of universal gravitation . Determined in this way, the gravitational field g around a single particle of mass M is a vector field consisting at every point of

330-442: 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 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}

363-416: 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

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396-461: Is the Newtonian constant of gravitation and c is the speed of light . These equations are dependent on the distribution of matter, stress and momentum in a region of space, unlike Newtonian gravity, which is depends on only the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that being in a region of curved space

429-467: Is the gravitational force , m is the mass of the test particle , R is the radial vector of the test particle relative to the mass (or for Newton's second law of motion which is a time dependent function, a set of positions of test particles each occupying a particular point in space for the start of testing), t is time , G is the gravitational constant , and ∇ is the del operator . This includes Newton's law of universal gravitation, and

462-464: 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

495-467: Is the steady gain in speed caused exclusively by gravitational attraction . All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies; 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 . At different points on Earth's surface,

528-496: Is used to explain gravitational phenomena, such as the gravitational force field exerted on another massive body. It has dimension of acceleration (L/T ) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s ). In its original concept, gravity was a force between point masses . Following Isaac Newton , Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid , and since

561-401: The gravitational potential field . 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". In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that there is either no gravitational force , or that gravity

594-421: 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. In physics , a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field

627-399: 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,

660-413: The 19th century, explanations for gravity in classical mechanics have usually been taught in terms of a field model, rather than a point attraction. It results from the spatial gradient of the gravitational potential field . 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

693-573: 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 to 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

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726-467: The Moon's physical makeup. 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 giant planets (Jupiter, Saturn, Uranus, and Neptune), and the Sun's photosphere . The values in

759-510: The Wikimedia System Administrators, please include the details below. Request from 172.68.168.226 via cp1108 cp1108, Varnish XID 762159858 Upstream caches: cp1108 int Error: 429, Too Many Requests at Fri, 29 Nov 2024 05:49:40 GMT Gravitational acceleration In physics , gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag ). This

792-523: The attracting mass is: ∇ ⋅ g = − ∇ 2 Φ = − 4 π G ρ {\displaystyle \nabla \cdot \mathbf {g} =-\nabla ^{2}\Phi =-4\pi G\rho } which contains Gauss's law for gravity , and Poisson's equation for gravity . Newton's law implies Gauss's law, but not vice versa; see Relation between Gauss's and Newton's laws . These classical equations are differential equations of motion for

825-486: 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

858-457: The free fall acceleration ranges from 9.764 to 9.834 m/s (32.03 to 32.26 ft/s ), 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. Newton's law of universal gravitation states that there

891-458: The gravitational field on mass m j is the sum of all gravitational fields due to all other masses m i , except the mass m j itself. R i is the position vector of the gravitating particle i , and R is that of the test particle. In general relativity , the Christoffel symbols play the role of the gravitational force field and the metric tensor plays the role of

924-478: The gravitational potential. In general relativity, the gravitational field is determined by solving the Einstein field equations G = κ T , {\displaystyle \mathbf {G} =\kappa \mathbf {T} ,} where T is the stress–energy tensor , G is the Einstein tensor , and κ is the Einstein gravitational constant . The latter is defined as κ = 8 πG / c , where G

957-430: 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

990-475: The relation between gravitational potential and field acceleration. ⁠ d R / d t ⁠ and ⁠ F / m ⁠ are both equal to the gravitational acceleration g (equivalent to the inertial acceleration, so same mathematical form, but also defined as gravitational force per unit mass). The negative signs are inserted since the force acts antiparallel to the displacement. The equivalent field equation in terms of mass density ρ of

1023-409: The source). Then the attraction force F {\displaystyle \mathbf {F} } vector onto a sample mass m {\displaystyle m} can be expressed as: Here g {\displaystyle \mathbf {g} } is the frictionless , free-fall acceleration sustained by the sampling mass m {\displaystyle m} under the attraction of

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1056-445: 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

1089-418: The table have not been de-rated for the centrifugal force effect of planet rotation (and cloud-top wind speeds for the giant planets) 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 metres (330 ft), the height of a skyscraper, is shown, along with the maximum speed reached. Air resistance

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