Newton's law of universal gravitation

Between any two bodies possessing mass there exists a mutual attraction. This is the intuition that Newton made quantitative: the force does not depend on the nature of the bodies, only on their masses and the distance separating them. The larger the masses, the stronger the attraction; the further apart the bodies, the weaker it becomes, decreasing with the square of the distance.

Newton's law of universal gravitation

Between two bodies of mass $m_1$ and $m_2$ at distance $d$ (measured between their centres) there exists an attractive force directed along the line joining their centres, of magnitude: $\ev{F = G\,\frac{m_1\,m_2}{d^2}}$ where $G = 6{,}67\cdot 10^{-11}\;\text{N\,m}^2/\text{kg}^2$ is the universal gravitational constant.

Note

$G$ was measured by Cavendish in 1798 using a torsion balance.

Two features distinguish this force. It is always attractive, unlike Coulomb’s law, where charges of the same sign repel each other: masses never repel. And it is universal, meaning it holds between any pair of objects possessing mass, from an apple to a galaxy. The two forces that the masses exchange are equal and opposite, in accordance with Newton’s third law.

The gravitational force between two masses is always attractive, directed along the line joining their centres. The two forces $\vec{F}_{12}$ and $\vec{F}_{21}$ are equal and opposite (Newton’s third law).

The tiny value of $G$ explains why we do not notice the attraction between everyday objects: two people standing close together attract each other with a wholly negligible force. Gravity only becomes dominant when at least one astronomical mass is involved, such as that of a planet or a star.

▶ What Everyone Gets Wrong About Gravity — Veritasium

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Topics: Gravitazione Concepts: Legge di gravitazione universale Skills: Impostazione simbolica

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