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Is there a standard mapping of symbols to terms for celestial and orbital mechanics (and physics in general)?

For example here are some ambiguities

Angular Momentum: L, H, J, $\Gamma$,

Orbital period: T or P,

M: mean anomaly or mass of the Sun,

E: energy or eccentric anomaly,

p: linear momentum or length of semi-latus rectum,

a: acceleration or length of semi-major axis,

e: eccentricity or base of natural logarithms,

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There are a lot of instances (such as those you pointed out) in all of science and mathematics where a symbol can mean two different things. In mathematics, there's actually a good deal of this (and the article says that the list is incomplete!). Many are based on letters, although they may have deviated from the original shape in order to make a distinction regarding just what the heck the thing actually means.

Eventually, you run out of letters. You can opt to use symbols from another language, the first choice for many being Greek. That roughly doubles the amount of letter-based symbols available to you. But there are still a lot of duplicates, as you can see by browsing through the lists here and here.

To my knowledge, this is the most comprehensive list easily available. And yes, there are loads of duplicates. But the great thing is that you almost certainly won't have to use the same variable to mean multiple things in one equation, or set of equations. For example, I doubt you'll need to use $V$ for voltage, volume and shear force all in the same equation!

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  • $\begingroup$ Very helpful, thanks. Already found 2 more symbols for angular momentum! $\endgroup$
    – steveOw
    Oct 23, 2014 at 22:59
  • $\begingroup$ @steveOw I meant to clarify, not confuse! But seriously, a wider range of symbols means you can make equations a lot more clearer. $\endgroup$
    – HDE 226868 ♦
    Oct 23, 2014 at 23:02
  • $\begingroup$ I guess that is an upside but I wish in this digital age that we could just invent new symbols to avoid multiple use. I'm finding it hard sometimes to learn new concepts when referring to different articles using different notations. In one textbook the author even uses the same symbol for different things, without flagging which meaning he intends! $\endgroup$
    – steveOw
    Oct 23, 2014 at 23:12
  • $\begingroup$ I feel your pain. Nothing like poor usage of symbols to make a confusing idea even more confusing. Or a simple idea confusing. $\endgroup$
    – HDE 226868 ♦
    Oct 23, 2014 at 23:17
  • $\begingroup$ I give you the radial component of the electron wavefunction for the ground state of hydrogen (in units of $4\pi\epsilon_0=1$): $$\psi(r) = \frac{m^{3/2} e^3}{\pi^{1/2} \hbar^3}\,e^{-m e^2 r/\hbar^2}\text{.}$$ Notably, $e$ plays a dual role even in the same equation (Euler's constant or fundamental charge). If I were evil, I'd also play with $\pi$ used for the transcendental number and conjugate momentum at once. $\endgroup$
    – Stan Liou
    Oct 24, 2014 at 0:18
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There is no formal set of symbols for physical quantities that is recognised by all scientists. Units on the other hand are more formally recognised, e.g. International System of Units. Authors may select their own symbols to denote specific quantities (they should, however, always specify the meaning of a symbol). On the other hand, I imagine that it will be more difficult to get your paper published if you use different symbols then generally used ones.

This problem is a problem of disambiguation and is not limited to the physical sciences. In computer science, the W3C (Tim Berners Lee) has initiated the semantic web, where concepts on the web are tagged with unique identifiers (URIs). Ontologies (vocabularies of concepts) are used to link concepts to URIs, which can be reused for disambiguation. For instance a paper may use symbol $L$ for angular momentum and is linked to a URI for the concept angular momentum. A website may use the symbol $H$ for angular momentum and link to the same concept angular momentum using the same URI. As both symbols are linked to the same concept, they are both disambiguated.

I've been working together with Hajo Rijgersberg (see his PhD thesis) on the Ontology of Units of Measure, which is an ontology with a large number of quantities and units. This ontology can be used as a list of quantities and their symbols. But it is by no means complete.

One way we could use such an ontology is to insert the identifier (URI) into the text. At the SWAIE workshop, I outlined a method to do just that in LaTeX (paper). The physical symbols in the PDF output are then linked to the concept. Clicking on the symbol will cause a browser to open at the URL identifying the physical concept. At the moment I'm trying to implement this in MathJax, but I am finding some technical difficulties.

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  • $\begingroup$ @Dieudonne.Thanks. It certainly would be useful sometimes to be able to link from a symbol to a concept URI. It is surprising to me how many texts do not even include a list of symbols used. $\endgroup$
    – steveOw
    Oct 24, 2014 at 10:18

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