standard gravity

(′stan·dərd ′grav·əd·ē)

(mechanics) A value of the acceleration of gravity equal to 9.80665 meters per second per second.

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acceleration of free fall, g, standard acceleration of gravity

acceleration Metric 1901 Established at the 3rd CGPM as 9.806 65 m·s^-2 (32.174 049~ ft·s^-2).
[Le Système International d'Unités (Sèvres, France: Bureau International de Poids et Mesures, 1985)] Originally conceived as the gravity at mean sea level at latitude 45°N, the term ‘standard gravity’ has become a label for a conventional value.

From 1907 the ‘accepted international base’ value for gravity measurements was 9.812 74 m·s^-2, as recorded at Potsdam, Germany,
[Clark J. S. Proc. Roy. Soc. London Ser. A Vol. 186, 192-5 (1946)] but this figure was acknowledged at the 9th CGPM in 1948 as ‘appreciably in error’.
[Nature Vol. 163, 427-8 (1949)] It was subsequently determined that 9.812 60 m·s^-2 (32.193 57~ ft s^-2) would be more appropriate. However, the 1901 value, being entrenched for units in the gravitational systems, continues to be acknowledged as the conventional standard gravity, defining the kilogram-force and slug, and in the standard atmosphere.

The Potsdam figure, with its associated period for the swing of a standard pendulum, provided the base via use of a like pendulum elsewhere, but was superseded by International Gravity Standardization Network (IGSN), now the International Absolute Gravity Base Station Network (IAGBN).¹⁶³

Until 1941 the standard atmosphere for aviation used values relating to the original concept, as favoured by the International Meteorological Committee, being 9.806 6 m·s^-2 initially for the US standard and then, from 1924, internationally 9.806 2 m·s^-2.

The effective gravitational pull at Earth's surface varies consistently by latitude and by altitude, and, because of local geology, erratically too. The downward pull experienced at Earth's surface represents the net effect of the static gravitational pull downwards and the contrary dynamic ‘centrifugal’ force caused by the rotation of Earth (modified minutely further by the gravitational influence of the Moon and the Sun, and technically other bodies). The former acts vertically downwards towards (but not precisely towards) the centre of Earth and, above the surface, is inversely proportional to the square of the distance from the centre (hence declining with altitude). The centrifugal force acts at right angles to Earth's axis of rotation and outwards from it, increasing proportionally to the distance from the axis. At Earth's surface, the strength of the latter is everywhere well below 1% of the former.

The oblateness of Earth makes the gravitational pull least at the Equator, greatest at the Poles. It is also slightly distorted by Earth's centroid not being exactly at the geographical centre. The offsetting centrifugal force is nil at the Poles (as well as being virtually horizontal in the proximity), and maximal at the Equator, so accentuating the static disparity. The net value of the downward acceleration at sea level varies from 9.780 4~ m·s^-2 (32.088~ ft s^-2) at the Equator to an average 9.832~ m·s^-2 (32.26~ ft s^-2) at the Poles (differing between the two).

The standard value is roughly the mean of these extremes and close to true for the developed inhabited world. Increasing altitude reduces the static factor while increasing the centrifugal factor (for a given speed). For an object travelling at Earth's angular rotational speed, the first 35 000 m (115 000 ft) above sea level reduces the above net figures by little more than 1%, but at 35 788 km (22 238 mi) the net figure is reduced to zero, hence the positioning (in the equatorial plane and orbiting directionally as Earth) at this height of the orbiting ‘geostationary’ satellites. Table 53 gives sample values for actual gravity, these being finely variable for specific locations.

	Latitude:	0°	15°	30°	45°	60°	75°	90°
at	sea level	9.780 5	9.784 0	9.793 4	9.806 3	9.819 2	9.828 7	9.832 2
at	1 000 m	9.777 4	9.780 9	9.790 3	9.803 2	9.816 1	9.825 7	9.829 1
at	10 000 m	9.749 6	9.753 1	9.762 6	9.775 4	9.788 4	9.797 9	9.801 3

For imprecise use, the values 9.81 m·s^-2 and 32.2 ft s^-2 are appropriate. The close proximity to 10 m·s^-2 led to the definition of the leo.

1901	3rd CGPM: in pursuit of clarity for mass vis-à-vis weight ‘The Conference declares:…
	3. The value adopted in the International Service of Weights and Measures for the standard acceleration due to gravity is 980.665 cm/s2, a value already stated in the laws of some countries.’see note below

[Le Système International d'Unités (Sèvres, France: Bureau International de Poids et Mesures, 1985)]