Let $G$ be a group acting on a set $X$. The orbit of some $x \in X$ is the set of elements of $X$ to which $x$ can be moved by the elements of $G$. It is denoted \(G\cdot x = \{g\cdot x \mid g \in G\}.\)
The set of orbits of points of $X$ creates a partition of $X$ with associated equivalence relation given by $x\sim y$ if and only if there exists $g \in G$ with $g\cdot x =y$, and the orbits are equivalence classes.
Equivalently, an orbit of $x$ is the subset of $X$ containing $x$ on which the action of $G$ is transitive transitive.
Wikidata ID: Q17859776