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When we study actions in group theory, we consider sets of the form $$\text{Orb}_G(x)=\{gx\mid g\in G\} $$ that are called orbits. Although, the only reason I find convincing for that name is that in some sense the action of group over a set can be viewed as a dynamical system and thus the name orbit has the usual physical "interpretation" and justification. Is this explanation correct or only a funny coincidence? In the second case, which is the origin of the term?

D. N.
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Josué Tonelli-Cueto
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    http://math.stackexchange.com/questions/76255/show-every-subgroup-of-d4-can-be-regarded-as-an-isotropy-group-for-a-suitable-ac/76423#76423 my picture might help you to see why we use the term "orbits". What better word could we use when dealing with groups of symmetries? :) – Bill Cook Oct 06 '13 at 02:55
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    The dynamical system interpretation is also the most convincing motivation I can think of, but I don't know anything about the history of the term. – anon Oct 06 '13 at 03:13

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You can think of the group action allowing you to move from one point to the next. In a "physical" sense, we are looking at where we can go in the set so we are looking at what elements we pass through on our way through.

Matt B
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