Newton's Law of Universal Gravitation/Also presented as

Newton's Law of Universal Gravitation: Also presented as

Newton's Law of Universal Gravitation can also be presented in the form:

$\mathbf F_{a b} \propto \dfrac {m_a m_b \hat {\mathbf r}_{b a} } {r^2}$

where $\hat {\mathbf r}_{a b}$ is the unit vector in the direction from $b$ to $a$.


Some presentations do not consider the vector aspects, merely expressing the relationship in terms of scalars:

$F = \dfrac {k m_a m_b} {r^2}$

where the constant is variously specified.


Sources

  • 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
  • 1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $4$: Gravitation: The Gravitational Constant
  • 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.21$: Newton's Law of Gravitation: $(11)$
  • 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): gravity
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.25$: Kepler's Laws and Newton's Law of Gravitation
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