Gravitational acceleration
[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.
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.
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
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.
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 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 the Moon's physical makeup.
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 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.
In Einstein's theory of general relativity, gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies.
Rather than undergoing an acceleration, objects in free fall travel along straight lines (geodesics) on the curved spacetime.
It has dimension of acceleration (L/T2) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s2).
Following Isaac Newton, Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid,[citation needed] 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.
