concept

gravity

Gravity is the fundamental force of attraction between masses, governing the motion of celestial bodies and the structure of spacetime.
11 related articles · 4 formulas · 6 who worked here

Description

Gravity is the weakest of the fundamental interactions, but it shapes the large-scale structure of the Universe. Classical physics describes it with Newton's law of universal gravitation, where the force is inversely proportional to the square of the distance. General Relativity replaces force with geometry: mass and energy tell spacetime how to curve, and curved spacetime tells matter how to move.

History

Kepler's laws (early 17th century) described planetary motions, but the universal law of gravitation was formulated by Newton. In 1915, Einstein created General Relativity, where gravity propagates at the speed of light, not instantaneously. The ideas of Henri Poincaré and Hendrik Lorentz paved the way for relativity. Direct proof of GR came with the detection of gravitational waves from black hole mergers by LIGO in 2015.

How it works

According to GR, mass and energy curve spacetime, and free particles move along geodesics—the shortest paths in this curvature. Einstein's equations: R_{μν} - ½ R g_{μν} = (8πG/c⁴) T_{μν} define this connection. In the weak-field limit, Newton's law F = G·m₁·m₂/r² is obtained. Gravitational waves are perturbations of the metric propagating at the speed of light. Quantum gravity attempts to describe gravitational interaction at Planck scales.

In practice

Without accounting for gravity, satellite launches and accurate GPS operation would be impossible: clocks on satellites run slightly faster due to lower gravity, and without corrections, a navigator would be off by kilometers.

Fun fact

Clocks on the top floor of a skyscraper run slightly faster than on the ground floor: over 100 years, the difference would be about 10 microseconds—a manifestation of gravitational time dilation.

Concept graph →

Formulas

$$F = P \cdot A$$
Force equals pressure times area.
What is in the formula
Fvariableforce exerted on the sphere — force newton
Pvariablepressure applied to the surface — pressure pascal
Avariablearea over which pressure acts — area square metre
f=4πr^2p(r) · 2607.23661v1
$$F = -\gamma v$$
Friction force is proportional and opposite to velocity.
What is in the formula
FvariableFriction force — force newton
γvariableDamping coefficient (friction coefficient) — damping coefficient kilogram per second
vvariableVelocity of the object — velocity metre per second
\bar{f}(v)=-\bar{γ}(v)v · 2606.31555
$$v = \sqrt{\frac{2mg}{\rho A C_D}}$$
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
v_{{slip}}=(\frac{2m_\star|\nabla\phi_{{eff}}|}{c_dπr_\star^2ρ_{{env}}})^{1/2} · 2607.20617v1
$$\mathbf{F} = G \frac{m_1 m_2}{r^2} \hat{\mathbf{r}}$$
Force between two masses is proportional to product and inversely to square of distance.
What is in the formula
\mathbf{F}variablegravitational force vector — force newton
m_1variablemass of first object — mass kilogram
m_2variablemass of second object — mass kilogram
rvariabledistance between the centers of mass — distance metre
\hat{\mathbf{r}}variableunit vector pointing from one mass to the other — unit vector
GconstantNewtonian gravitational constant, fundamental constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\ddot{{r}}_i=\sum_{j\neqi}\frac{gm_j({r}_j-{r}_i)}{|{r}_j-{r}_i|^3} · 2607.03724
\ddot{{r}}_i=\sum_{j\neqi}\frac{gm_j({r}_j-{r}_i)}{|{r}_j-{r}_i|^3} · 2607.03724v1

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