Standard gravity

Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely 9.80665 m/s2, or about 35.30394 (km/h)/s (~32.174 ft/s2 or ~21.937 mph/s). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration.[1][2][3] The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration; 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). The symbol g should not be confused with G, the gravitational constant, 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. 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 g0 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 metrological 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 (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 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 gn = 9.80665 N/kg. For each kilogram of mass, a nominal force of 9.80665 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 9.80665 N.

Calculating g0

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

g_0 = \frac{G \cdot m_{\mathrm{Earth}}}{ \left( \frac{1}{2} (r_{\mathrm{equator}} %2B r_{\mathrm{pole}}) \right)^2 } - \left(\frac{ 2 \pi }{ 86400\mathrm{s} }\right)^2 \cos( 45^\circ ) \cdot r_{\mathrm{equator}} \approx 9.807 \, \mathrm{m/s^2}

References

  1. ^ The international system of units (SI) – United States Department of Commerce, NIST Special Publication 330, 2001, p. 29
  2. ^ The International System of Units (SI) – Bureau international des poids et mesures, 8th edition, 2006, p. 142-143
  3. ^ The international system of units (SI) – United States Department of Commerce, NIST Special Publication 330, 2008, p. 57

See also