quantity

gravitational acceleration

The rate at which an object accelerates due to gravity, a key target for testing antimatter behavior.
12 related articles · 5 formulas

Description

Gravitational acceleration is the rate at which an object's velocity changes due to gravity. On Earth, it is approximately 9.8 m/s² near the surface, but it varies slightly with altitude and latitude. This quantity is a fundamental test for theories of gravity, especially when applied to antimatter, which is expected to fall the same way as matter under general relativity but has never been directly measured until recently.

History

Galileo Galilei first demonstrated that gravitational acceleration is independent of mass in the early 17th century. Isaac Newton later formulated the law of universal gravitation in 1687. The first direct measurement of antimatter's gravitational acceleration was reported in 2023 by the ALPHA-g collaboration at CERN.

How it works

Gravity causes all objects to accelerate toward each other. For a body like Earth, the acceleration experienced by a test object depends on the mass of Earth and the distance from its center, following Newton's law of universal gravitation. In general relativity, this acceleration is a manifestation of spacetime curvature. Measuring gravitational acceleration on antimatter requires trapping antiparticles (like antihydrogen) and observing their free-fall motion, which is challenging because antimatter annihilates on contact with matter.

In practice

Gravitational acceleration is used in navigation (e.g., inertial guidance systems), geophysics to map underground structures, and in tests of fundamental physics, including the equivalence principle for antimatter.

Fun fact

The gravitational acceleration on the surface of a neutron star is about 10^12 m/s² — a billion times stronger than on Earth — which would flatten any object instantly.

Concept graph →

Formulas

$$f\frac{\partial u}{\partial z} = -\frac{g}{\Theta_0} \frac{\partial \Theta}{\partial y}$$
Relates vertical wind shear to horizontal temperature gradient.
What is in the formula
uvariablezonal wind component — velocity metre per second
zvariablevertical coordinate — length metre
Θvariablepotential temperature — temperature kelvin
yvariablemeridional coordinate — length metre
fconstantCoriolis parameter, twice the planetary rotation rate times sine of latitude — coriolis parameter = 1.458e-4 per second
gconstantstandard acceleration due to gravity at Earth's surface — gravitational acceleration = 9.80665 metre per second squared
Θ₀constantconstant reference potential temperature of the background state — reference potential temperature = 300 kelvin
∂/∂zoperatorvertical derivative — partial derivative
∂/∂yoperatormeridional derivative — partial derivative
$$\frac{\Delta f}{f} = \frac{g \Delta h}{c^2}$$
Clock frequency increases with height in a gravitational field.
What is in the formula
ΔfvariableChange in clock frequency — frequency change hertz
fvariableClock frequency at reference height — frequency hertz
gvariableLocal gravitational acceleration — gravitational acceleration metre per second squared
ΔhvariableHeight difference — height difference metre
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
$$\kappa = \frac{\Delta a / g}{\Delta (q/m)}$$
Relates acceleration difference to charge-to-mass ratio difference.
What is in the formula
κvariablesensitivity coefficient
Δavariabledifference in acceleration — acceleration metre per second squared
gvariablegravitational acceleration — gravitational acceleration metre per second squared
Δ(q/m)variabledifference in charge-to-mass ratio — charge to mass ratio coulomb per kilogram
$$h = \frac{kT}{mg}$$
Height where particle density decreases by factor e in gravitational field.
What is in the formula
hvariablescale height — length metre
Tvariabletemperature — temperature kelvin
mvariablemass of particle — mass kilogram
gvariablegravitational acceleration — gravitational acceleration metre per second squared
kconstantrelates energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin
$$v = \sqrt{\frac{2mg}{\rho A C_D}}$$
Speed where drag force equals gravitational force.
What is in the formula
vvariableterminal velocity — velocity metre per second
mvariablemass of the falling object — mass kilogram
gvariablegravitational acceleration — gravitational acceleration metre per square second
ρvariabledensity of the fluid — density kilogram per cubic metre
Avariablecross-sectional area — area square metre
C_Dvariabledrag coefficient — drag coefficient

Related articles · 12

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A Spinning Star Puts Gravity to the Test
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Quantum Physics2026-07-251 minarXiv:2607.23324express
How to Catch Acceleration by the Tail
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General Relativity2026-07-231 minarXiv:2607.20867express
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How to Hear the Warmth of the Void
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Gravity on a Cosmic Ruler
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A Tiny Shift That Spoils Precision
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Superfluid Helium Feels How the Earth Spins
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