Physical Sciences

Classical Mechanics

Intermediate

Universal Gravitation

F = G\frac{m_1 m_2}{r^2}

Every mass attracts every other mass with a force proportional to their masses and inversely proportional to distance squared.

By Isaac Newton

Physical Sciences

1687 · Isaac Newton

Human Reviewed

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Story PortalWho discovered this?Discover how Isaac Newton and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — satellite orbits.Math PortalWhat does it derive from?Trace the mathematical lineage from newtons second law.Future PortalWhere is it going?Asteroid deflection

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Why it matters: Enabled celestial navigation, satellite orbits, and our understanding of the solar system.

Discoverers: Isaac Newton (1687)

What does it mean?

Every mass attracts every other mass with a force proportional to their masses and inversely proportional to distance squared.

Why should I care?

Enabled celestial navigation, satellite orbits, and our understanding of the solar system.

Equation Compass

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Isaac Newton

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$G$	Gravitational constant	—	6.674×10⁻¹¹ N·m²/kg²
$m_1, m_2$	Masses	kg	Gravitating bodies
$r$	Distance	m	Separation between centers

Worked Example

Earth-Moon attraction computed from their masses and mean distance.

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Isaac Newton

Pictures & video

Sources & further reading

Newton's law of universal gravitation — Wikipedia Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

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