Central Force/Examples/Gravitation

Example of Central Force

Gravitation is an example of a central force.


Let $a$ and $b$ be particles with mass $m_a$ and $m_b$ respectively.


Then $a$ and $b$ exert a force upon each other whose magnitude and direction are given by Newton's Law of Universal Gravitation:

$\mathbf F_{a b} \propto \dfrac {m_a m_b {\mathbf r_{b a} } } {r^3}$

where:

$\mathbf F_{a b}$ is the force exerted on $b$ by the gravitational force on $a$
$\mathbf r_{b a}$ is the displacement vector from $b$ to $a$
$r$ is the distance between $a$ and $b$.


Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): central force
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): central force
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