In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), it permutes the elements of X. Any particular element X moves around in a fixed path which is called its orbit. In the notation of set theory, the group orbit of a group element x can be defined as G(x) = {g x element X:g element G}, where g runs over all elements of the group G. For example, for the permutation group G_1 = {(1234), (2134), (1243), (2143)}, the orbits of 1 and 2 are {1, 2} and the orbits of 3 and 4 are {3, 4}.
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