Sagittarius
Sagittarius as depicted in Urania's Mirror, a set of constellation cards published in London c.1825. The Terebellum is seen in the back of the centaur. Source.
The Constellation
The Babylonians identified Sagittarius as the god Nergal. Nergal was similar to Greek centaurs, and was depicted firing an arrow from his bow. He had wings, two heads: a panther and a human, and a scorpion's stinger raised above his horse tail. This figure is similar to modern depictions of Sagittarius.
The Greeks had many stories for this constellation. One story suggests the constellation is the satyr Crotus, son of Pan. He was thought by the Greeks to have invented archery. Crotus would hunt on horseback, and lived with the Muses. Once he died, the Muses asked Zeus to place him in the sky.
Many associate the constellation Sagittarius with the story of Chiron.
The Centaur Chiron
Peleus wrestling Thetis (who shapeshifts in fire and big cat), between Chiron and a Nereid. Side B of an Attic black-figure amphora, c. 510 BC. Source.
Long before the time of Zeus, in the Golden Age, the Titan Cronus ruled the lands. Cronus was a fair ruler, and gave humanity everything they desired or needed. The Golden Age prospered, and life on earth was peaceful.
Cronus often walked the earth, enjoying the beauty his mother Gaia created. Upon walking the beaches of Greece, Cronus noticed the Oceanid nymph, Philyra. The Titan approached the nymph, and made to take her then and there. Philyra did not reciprocate his advances, and she turned and ran away.
Cronus turned into a black stallion and made chase. It wasn't difficult for him to catch up to the nymph. He overtook her, and had her in his stallion form. The nymph, Philyra, fell pregnant.
As the months progressed, Philyra became incredibly large. Her pregnancy was not an easy one, and the nymph suffered immense pain throughout. As the birth neared, the nymph made her way up Mount Pelion to be closer to the heavens, hoping for a seamless birth. Alas, this was not to be.
The birth was long and agonizing. There was no end to the pain, and Philyra's screams could be heard throughout Greece. When at long last the baby was born, Philyra heard her midwives gasp. She worried for her child, expecting the worst.
Reluctantly, the midwives handed Philyra her baby. She couldn't help but love her child despite the suffering it inflicted, but when she received her baby she cried out in horror.
The child was a monster. He had the head and torso of a human baby, and the body of a black stallion. Her love turned to despair, and she knew she would not keep him. Philyra abandoned her son. In her anguish, she begged the gods to end her suffering. Zeus took pity on the nymph, and transformed her into a linden tree.
The baby was left alone atop Mount Pelion. For many days, the centaur cried in hunger and loneliness.
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The god Apollo was the protector of the young. He loved music, and took pride in overseeing the education of those less fortunate. As he sat playing his lyre, the sound of crying cut through his music. This intrigued him, and looking down from Mount Olympus, he saw the source of the noise.
A baby centaur sat alone on the mountain. The god was curious to know where his parents were. He went to the child, and looked around but found no other soul. The centaur was orphaned. Apollo decided to adopt the child, and took him to his sister Artemis.
It came to be that the twin gods raised the centaur, and taught him all they knew. Apollo trained the centaur in music, medicine, prophesy, astrology, and healing. Artemis trained him in archery and hunting. The centaur was so skilled with his hands that the gods named him "Chiron," meaning "skilled with hands."
Chiron grew into a kind and just being — thanks entirely to the upbringing of Artemis and Apollo. His intelligence and skills were unmatched, and Apollo encouraged the centaur to pass his intellect onto other students.
Chiron traveled back to his place of birth, Mount Pelion. He made it his home and place of teaching. He became the most sought after tutor for inspiring students, and his pupils became great heroes. Among them being Ajax, Jason, Achilles, Perseus, Heracles, and many other great heroes.
It came to be that Peleus, father of Achilles, entrusted the boy into the care of Chiron. Chiron taught the child Achilles everything about fighting, archery, and war.
One day, Heracles visited his old teacher, fresh from his fight with the Erymanthian boar. Heracles set his poisoned arrows on the table before him, and one slipped from the quiver and fell onto Chiron's hoof. The poison seeped through his body. Chiron, as a great healer, tried every herb and salve to save himself. Nothing worked, and he became sicker every day. As the child Achilles weeped over the weak centaur, he begged the gods to save him. The gods could not, but instead they placed his body among the stars as the constellation Sagittarius to honor the centaur's great deeds.
Author's Note: I liked writing this one — I think Chiron is such a good character, and I really liked when reading about him that he was constantly described as being one of the kindest beings to live. I think that's great considering his tragic birth, and his mother's rejection of him. It's a very sad story to begin with, but it morphs into something great. He's a very empathetic character! I also thought it was cool that Apollo and Artemis raised him — they're my two favorite Greek Gods. When researching this story, I found a few different sources stating that Sagittarius was different Greek figures. I went with Chiron as the myth, because it made more sense to me. The God Pan has a cool story, but he isn't a centaur so I didn't think it fit properly.