...but afterwards, when she was already with child, was seen bathing and so discovered. Upon this, the goddess was enraged and changed her into a beast. Thus she became a bear and gave birth to a son called Zuthra.
Either Artemis "slew Kallisto with a shot of her silver bow, perhaps urged by the wrath of Hera, or, later, Arcas, the eponym of Arcadia, nearly killed his bear-mother, when she had wandered into the forbidden precinct of Zeus. In every case, Zeus placed them both in the sky as the constellations Ursa Major, called Arktos, the "Bear", by Greeks, and Ursa Minor.
According to Ovid, it was Jove (the Roman Zeus) who took the form of Diana so that he might evade his wife Juno’s detection, forcing himself upon Callisto while she was separated from Diana and the other nymphs. Her pregnant condition was discovered some months later while bathing with Diana and her fellow nymphs. Upon this, Diana was enraged and expelled Callisto from the group, and subsequently she gave birth to Arcas. Juno then took the opportunity to avenge her wounded pride and transformed the nymph into a bear. Sixteen years later Callisto, still a bear, encountered her son Arcas hunting in the forest. Just before Arcas killed his own mother with his javelin, Jove averted the tragedy by placing mother and son amongst the stars as Ursa Major and Minor, respectively. Juno, enraged that her attempt at revenge had been frustrated, appealed to Ocean that the two might never meet his waters, thus providing a poetic explanation as their circumpolar positions.
The stars of Ursa Major were all circumpolar in Athens of 400 BCE, and all but the stars in the Great Bear's left foot were circumpolar in Ovid's Rome, in the first century CE. Now, however, due to the precession of the equinoxes, the feet of the Great Bear constellation do sink below the horizon from Rome and especially from Athens — so Ursa Major gets to cool her feet and legs in the sea, in spite of Ovid; however, Ursa Minor (Arcas) does remain completely above the horizon, even from latitudes as far south as Honolulu and Hong Kong.
Aeschylus' tragedy Callisto is lost.
The myth in Catasterismi may be derived from the fact that a set of constellations appear close together in the sky, in and near the Zodiac sign of Libra, namely Ursa Minor, Ursa Major, Boötes, and Virgo.
The constellation Boötes, was explicitly identified in the Hesiodic Astronomia as Arcas, the "Bear-warden" (Arktophylax):
he is Arkas the son of Kallisto and Zeus, and he lived in the country about Lykaion. After Zeus had seduced Kallisto, Lykaon, pretending not to know of the matter, entertained Zeus, as Hesiod says, and set before him on the table the babe [Arkas] which he had cut up.