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Acceleration due to gravity

The acceleration that a mass acquires because of a gravitational field, commonly denoted g on Earth. A vector quantity with a standard value 9.80665 m/s² that varies with location and conditions.

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Overview

Acceleration due to gravity describes the rate at which the velocity of an object changes when it is influenced only by gravity. In everyday contexts on Earth this acceleration is represented by the symbol g. It is a vector quantity, meaning it has both magnitude and direction: the magnitude measures how quickly speed changes, and the direction points toward the source of the gravitational attraction. For a concise definition see acceleration.

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Characteristics and basic formula

In Newtonian physics the gravitational acceleration produced by a spherical mass can be approximated by the formula g = GM/r², where G is the universal gravitational constant, M is the mass of the attracting body, and r is the distance from its centre. The SI unit is metres per second squared (m/s²). As a vector it is discussed also as a gravitational field; see vector quantity, and note the distinction between magnitude and direction at magnitude and direction.

Standard value and variability

Internationally, a conventional standard gravity value is defined as 9.80665 m/s² (32.1740 ft/s²) and is used for calibration and unit definitions. The actual free-fall acceleration on Earth's surface, commonly called local g, differs from this standard because of the Earth's rotation, its equatorial bulge, altitude, subsurface density variations and tidal effects from the Moon and Sun. Typical values at Earth's surface lie roughly between about 9.78 and 9.83 m/s², but local surveys report smaller or larger deviations in some regions; for the Earth-specific context see Earth's surface.

History and development

Concepts of gravitational acceleration were developed over centuries. Observations by early scientists such as Galileo established that falling objects accelerated at a consistent rate (neglecting air resistance). Newton's formulation of universal gravitation provided the theoretical relation g = GM/r². Later laboratory and field measurements refined the value of G, the distribution of Earth's mass, and methods to measure g with increasing precision.

Measurement techniques and applications

Modern measurements use suspended mass devices, free-fall absolute gravimeters, superconducting gravimeters, and gravimeters based on atom interferometry. Common practical applications include engineering (structural loads and dynamics), ballistics, calibration of instruments, geodesy and hydrology (detecting mass changes underground), and spacecraft navigation.

Factors affecting g and notable distinctions

  • Factors that change local g: latitude (centrifugal reduction near equator), altitude (distance from Earth's centre), nearby topography and subsurface density anomalies.
  • Apparent gravity differs from gravitational acceleration because it includes centrifugal acceleration due to rotation; this affects weight measurements and pendulum periods.
  • In precise contexts, relativistic corrections are applied; gravitational acceleration is closely related to the concept of a gravitational field in general relativity.

For accessible introductions and further technical detail, readers can consult overview resources and educational materials at direction and field guides or technical references on measurement methods at measurement techniques and vector field theory. For authoritative tables and standards the conventional reference remains the defined standard gravity of 9.80665 m/s².

A plumb line shows the direction of the gravitational field
A plumb line shows the direction of the gravitational field

Measurement

→ Main article: Gravimetry

In addition to directly measuring the acceleration of a freely falling body, one can calculate the amount of gravitational acceleration from the period of oscillation of a pendulum. A modern gravimeter is a special spring balance and achieves a precision of one microgal, approx. 10-9 g. One could use it to register a change in altitude on Earth of less than a centimeter. Fluctuations in atmospheric pressure cause changes of the same order of magnitude, mountains or different rock densities in the Earth's crust affect g even by up to 100 milligal, somewhat weaker also tidal forces due to the inhomogeneity of external gravitational fields, especially from the Moon and the Sun.

Sum of gravitational and centrifugal acceleration

The gravitational acceleration is the vector sum of a gravitational and a centrifugal component:

{\vec {g}}={\vec {g}}_{\mathrm {Gravitation} }+{\vec {a}}_{\mathrm {Zentrifugal} }

  • The gravitational acceleration is caused by the gravitational field. Provided that the celestial body can be considered spherically symmetrical, the gravitational acceleration is calculated according to the law of gravity:

{\vec {g}}_{\mathrm {Gravitation} }=-{\frac {GM}{r^{2}}}\,{\vec {e}}_{r}

Here G is the gravitational constant, M is the mass of the celestial body, r is the distance between the center of gravity of the celestial body and the sample, and {\vec {e}}_{r} is a unit vector directed from the center of gravity of the celestial body to the sample. If the mass distribution of the celestial body is not isotropic, as is usually the case, this results in gravity anomalies.

  • The centrifugal acceleration {\vec {a}}_{\mathrm {Zentrifugal} } affects because one is on the surface of the celestial body in a co-rotating reference frame.
  • Tidal forces arise from the influence of other celestial bodies (e.g. the moon or the sun). Whether these forces are considered part of the gravitational field is a matter of definition. In this article they are not counted as part of the gravitational field.

For the gravitational field at a planetary surface it follows: The gravitational acceleration depends on the altitude, because according to the law of gravity {\displaystyle {\vec {g}}_{\mathrm {Gravitation} }\sim {\tfrac {1}{r^{2}}}} . It also follows from this relationship that due to the oblateness of the planet, the distance to the center of the planet is smallest at the poles, and therefore the gravitational effect is greatest. In addition, at the poles of the celestial body the centrifugal acceleration disappears because the distance from the axis of rotation is zero. The gravitational field is thus weakest at the equator: there the centrifugal acceleration is at a maximum and counter to the gravitational effect, and the distance from the centre of the planet is at its greatest.

The direction of the gravitational acceleration is called the perpendicular direction. This perpendicular direction points approximately towards the gravitational centre of the celestial body. Deviations occur (apart from gravity anomalies) because the centrifugal acceleration at mid-latitudes is at an oblique angle to the gravitational acceleration. Lines that follow the perpendicular direction are called perpendiculars. They are the field lines of the gravitational field. If a body moves in the gravitational field, the direction of the effective acceleration deviates from the perpendicular direction with increasing velocity. This can be interpreted as the effect of the Coriolis force.

Questions and answers

Q: What is acceleration due to gravity?

A: Acceleration due to gravity is the acceleration gained by an object because of gravitational force.

Q: What is the SI unit of acceleration due to gravity?

A: The SI unit of acceleration due to gravity is m/s2.

Q: Is acceleration due to gravity a scalar or a vector?

A: Acceleration due to gravity is a vector because it has both a magnitude and a direction.

Q: What is the symbol used to represent the acceleration due to gravity at the surface of Earth?

A: The symbol used to represent the acceleration due to gravity at the surface of Earth is g.

Q: What is the standard value of the acceleration due to gravity at the surface of Earth?

A: The standard value of acceleration due to gravity at the surface of Earth is 9.80665 m/s2 (32.1740 ft/s2).

Q: Does the actual acceleration of a body in free fall vary with location?

A: Yes, the actual acceleration of a body in free fall varies with location.

Q: What is the definition of acceleration due to gravity?

A: Acceleration due to gravity is the acceleration gained by an object due to gravitational force and is represented by the letter g with a standard value of 9.80665 m/s2 at the surface of Earth, while the actual acceleration may vary with location.

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