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| Discoidea, Ernst Haeckel, Kunstformen der Natur. Chromolithograph 32 x 40 cm, Verlag des Bibliographischen Instituts, Leipzig 1899-1904. Photograph by D Dunlop. |
Let some particle P be described by its mechanical energy $E$, and its angular momentum $\, 𝘑$. Definition: the orbital radius of P is the number
$\begin{align} R \equiv \frac{hc}{2 \pi } \frac{ \sqrt{ 𝘑 \vphantom{𝘑^2} \; \, } }{E} \end{align}$
where $h$, $c$ and $\pi$ are constants. Since $E$ and $𝘑$ have been defined from tallies of quarks, the orbital radius is thus established from quark counts too. But now we use it to make a rudimentary account of the expanse or extent of P.
Any non-rotating particle has an orbital radius of zero, like a point or a line.
For photons, the angular momentum $𝘑$ is always one. And the wavelength $\lambda$ is related to the energy by $\lambda = h c / E$. So the orbital radius of a photon can be written as
$\begin{align} R \left( \gamma \right) = \frac{ \lambda }{ 2 \pi } \end{align}$
Then a circular perimeter of $2 \pi R$ is the same as one wavelength.
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