Standard gravity

Encyclopedia

**Standard gravity**, or

**standard acceleration due to free fall**, usually denoted by

*g*

_{0}or

*g*

_{n}, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about (~ or ~). This value was established by the 3rd CGPM

General Conference on Weights and Measures

The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...

(1901, CR 70) and used to define the

**standard weight**of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration

Centrifugal force

Centrifugal force can generally be any force directed outward relative to some origin. More particularly, in classical mechanics, the centrifugal force is an outward force which arises when describing the motion of objects in a rotating reference frame...

; the total (the apparent gravity) is about 0.5 percent greater at the poles than at the equator.

Although the symbol

*g*is sometimes incorrectly used for standard gravity,

*g*(without a suffix) strictly means the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth (see Earth's gravity

Earth's gravity

The gravity of Earth, denoted g, refers to the acceleration that the Earth imparts to objects on or near its surface. In SI units this acceleration is measured in metres per second per second or equivalently in newtons per kilogram...

). The symbol

*g*should not be confused with

*G*, the gravitational constant

Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

, or g, the abbreviation for gram. The

*g*(sometimes written "gee") is also used as a unit of acceleration, with the value defined as above; see g-force

G-force

The g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...

.

The acceleration due to gravity if a body after reaching the ground is always 0 due to the frictional force exerted by the Earth. However there is a misconception that acceleration due to gravity on Earth has a certain value other than zero.

The value of

*g*

_{0}defined above is a nominal midrange value on Earth, originally based on the acceleration of a body in free fall at sea level at a geodetic latitude of 45°. Although the actual acceleration of free fall on Earth varies according to location, the above standard figure is always used for meteorological purposes. (The actual average sea-level acceleration on Earth is slightly less.)

The SI unit of acceleration is meters per square second, which is exactly equal to the SI unit of specific force, the newton per kilogram

Kilogram

The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

(by the very definition of the newton). That N/kg unit can be used to express the acceleration of gravity in order to stress that it's also equal to the so-called

*gravitational field*which is the force (in newtons) exerted per unit of mass (kilogram). Just as an electric field

Electric field

In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

is an electrostatic force per unit of electric charge, a gravitational field is a gravitational force per unit of mass.

The standard gravitational field may thus also be expressed as

*g*

_{n}= . For each kilogram of mass, a nominal force of newtons is exerted by such a standard gravitational field.

On the surface of the Earth, the gravitational force exerted on an object is commonly called its

*weight*. Technically, the weight of an object is a force proportional to its mass and the coefficient of proportionality is the local gravitational field. In physics and engineering, units of force based on units of mass are no longer recommended because of the widespread confusion they induce. For example, the

*kilogram of force*is a unit of force (best abbreviated kgf, not kg) defined to be exactly equal to N.

## Calculating *g*_{0}

Using the mass, the polar and equatorial radii, and the angular velocity of the Earth:## See also

- Earth's gravityEarth's gravityThe gravity of Earth, denoted g, refers to the acceleration that the Earth imparts to objects on or near its surface. In SI units this acceleration is measured in metres per second per second or equivalently in newtons per kilogram...
- g-forceG-forceThe g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...

, a measure of acceleration -
*G*, the gravitational constant in Newton's law of gravityGravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...GravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped... - Gravitational accelerationGravitational accelerationIn physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....
- Metre per second squaredMetre per second squaredThe metre per second squared is the unit of acceleration in the International System of Units . As a derived unit it is composed from the SI base units of length, the metre, and the standard unit of time, the second...