Callisto, a nymph who was a servant of the hunter Artemis was made to bear a child by Zeus. Artemis then banished Callisto for her impurity. Callisto then gave birth to a son named Arcas, making Zeus’ wife, Hera jealous, seeking for revenge. She turned Callisto into a bear who ran away into the forest.
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Years later, Arcas grew up to become a hunter. One day while he was hunting, the bear Callisto heard Arcas' voice and rushed to greet her son. Arcas, not knowing that the bear was his mother was about to kill her when Zeus intervened and sent both mother and son into the sky as the Greater and Lesser Bears.
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Zeus had grabbed them by their tails and swung them around over his head and finally flung them into the sky, and that is why these two bears have long tails!