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 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,[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.
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:
F=G
| m1m2 | |
| r2 |
where
m1
m2
G
r
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=-{GM\overr2}\hat{r
where
M
\hat{r
Then the attraction force
F
m
F=mg
Here
g
m
M
m
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 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 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 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 meters, the height of a skyscraper, is shown, along with the maximum speed reached. Air resistance is neglected.
| Body | data-sort-type="number" | Multiple of Earth gravity | data-sort-type="number" | m/s2 | data-sort-type="number" | ft/s2 | Notes | data-sort-type="number" colspan=2 | Time to fall 100 m and maximum speed reached |
|---|---|---|---|---|---|---|---|---|---|
| Sun | 27.90 | 274.1m (899.3feet) | 0.85 s | 843km/h | |||||
| Mercury | 0.3770 | 3.703m (12.149feet) | 7.4 s | 98km/h | |||||
| Venus | 0.9032 | 8.872m (29.108feet) | 4.8 s | 152km/h | |||||
| Earth | 1 | 9.8067m (32.1742feet) | 4.5 s | 159km/h | |||||
| Moon | 0.1655 | 1.625m (05.331feet) | 11.1 s | 65km/h | |||||
| Mars | 0.3895 | 3.728m (12.231feet) | 7.3 s | 98km/h | |||||
| Ceres | 0.029 | 0.28m (00.92feet) | 26.7 s | 27km/h | |||||
| Jupiter | 2.640 | 25.93m (85.07feet) | 2.8 s | 259km/h | |||||
| Io | 0.182 | 1.789m (05.869feet) | 10.6 s | 68km/h | |||||
| Europa | 0.134 | 1.314m (04.311feet) | 12.3 s | 58km/h | |||||
| Ganymede | 0.145 | 1.426m (04.678feet) | 11.8 s | 61km/h | |||||
| Callisto | 0.126 | 1.24m (04.07feet) | 12.7 s | 57km/h | |||||
| Saturn | 1.139 | 11.19m (36.71feet) | 4.2 s | 170km/h | |||||
| Titan | 0.138 | 1.3455m (04.4144feet) | 12.2 s | 59km/h | |||||
| Uranus | 0.917 | 9.01m (29.56feet) | 4.7 s | 153km/h | |||||
| Titania | 0.039 | 0.379m (01.243feet) | 23.0 s | 31km/h | |||||
| Oberon | 0.035 | 0.347m (01.138feet) | 24.0 s | 30km/h | |||||
| Neptune | 1.148 | 11.28m (37.01feet) | 4.2 s | 171km/h | |||||
| Triton | 0.079 | 0.779m (02.556feet) | 16.0 s | 45km/h | |||||
| Pluto | 0.0621 | 0.61m (02feet) | 18.1 s | 40km/h | |||||
| Eris | 0.0814 | 0.8m (02.6feet) | (approx.) | 15.8 s | 46km/h |
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.