Newton's Law of Universal Gravitation/Also presented as
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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