Apollo

In Greek mythology, Apollo was one of the most important Olympian gods. The son of the god Zeus and Leto, Apollo was associated with prophecy, medicine, music and poetry, archery, and the care of flocks and herds. He was also frequently associated with the higher developments of civilization, such as law, philosophy, and the arts. Finally, in Greek mythology, Apollo driving his chariot through the sky was associated with the movement of the Sun. He was twin brother to Artemis, goddess of hunting, though Athena was also a sister of his as well.

The image of Apollo was preserved for thousands of years in artistic works. One of these artistic works, the design for the mission insignia of Apollo 17, included a profile of Apollo facing to his left. Additionally, the mission insignia for Apollo 13 depicted the steeds of Apollo riding over Luna. 

In 2267, the USS Enterprise (NCC-1701) encountered Apollo on Pollux IV. There, they learned that the Greek gods were in fact a band of explorers who had visited Earth five thousand years earlier, and established themselves as gods to the people of that era. From things Apollo said to Carolyn Palamas, it seems that they may actually have, in some sense, considered themselves to be gods, but it is clear they also knew they weren't gods in the same sense the ancient Greeks believed them to be.

Personality
Apollo came across as arrogant and accustomed to obedience from his 'children' (really, his slaves). While claiming to be in love with Carolyn Palamas, after she rejected him he showed signs that he wanted to control her like the slave-master her captain said he truly was (forbidding her to leave his presence and ordering her to stay there with him, for instance). When he seduced her, his words implied that he was offering her joint rule of Pollux IV, to sit by his side as his queen. However, once he achieved his ends by making her become the mother of the thousands of deities he desired, he would have had no more use for her and kill her. During Carolyn's rejection of him, Apollo stated to her that he has "chosen her", and earlier he noted her fearlessness, commenting that she is "fit indeed".

History
Apollo claimed he and his fellow travelers visited Earth, and there thrived on the worship and love of its people. But eventually, mankind turned away from the gods. Unable to survive as memories, the gods returned to Pollux IV, their home. They found it an empty place without worshipers, but they lacked the strength to leave. So they waited. Eventually, all of the gods save Apollo lost hope, and "spread themselves upon the wings of the wind... thinner, and thinner, until only the wind remained." Apollo claimed this was not death, at least, not as Humans understood it. But clearly, those who had departed in this fashion were beyond returning. Only Apollo was confident that mankind would one day leave Earth, and find the gods again. And when it happened, he planned to "restore the proper order" – to restore man to a worshipful species, provided for and loved by a new race of gods, fathered by him. (He needed a wife to accomplish this task, and so chose Carolyn to be his queen based on her beauty and intelligence.) This, unfortunately for Apollo, was a state of affairs unacceptable to men. James T. Kirk and his landing party schemed continuously; between them, and members of the crew still in orbit, they were eventually able to overcome Apollo, and destroy the source of his power. With his temple gone and his power broken, Apollo spread himself upon the wind, imploring his fellow gods to take him, and vanished.

Powers and abilities
Apollo, at various times, demonstrated command of an enormous reservoir of energy that he could evidently direct by acts of will. He was able to generate a powerful force field that caught and held the Enterprise, and resisted most attempts to break and disrupt it.

On approach to the planet, the ship encountered what appeared, visually, to be an enormous, translucent Human hand. In fact, it was a force field, conventional in composition but on unusual wavelengths, generated by Apollo. This field was powerful enough to stop the ship, and impulse engines could not break the ship free. Attempts to push it away with the tractor beam, and to reverse its polarity were equally unsuccessful in disrupting it. In addition to merely holding the ship, Apollo could exert pressure beyond the ship's tolerance, and in this fashion, threaten the ship. Spock was eventually able to pierce the field with powerful bursts of M-rays on carefully calculated wavelengths. Although this did not destroy the field, it enabled the Enterprise to fire her phasers. Presumably, the field vanished entirely when the Enterprise destroyed Apollo's power source.

Apollo could alter his physical form and the forms of material objects in his vicinity. He could hurl lightning-like energy bolts, interfere with Federation technology, transform Starfleet uniforms into ancient Greek clothing by simply waving his hand, transport himself and others from place to place, and alter the weather (at least locally). His senses extended great distances; while on the surface of his world, he was able to sense happenings on the bridge of the Enterprise and project his image and voice into her equipment for the purpose of conversation.

Apollo at one point claimed he could wipe out a man with a gesture, and bring him back again as easily. But he never demonstrated this particular ability.

A tricorder scan registered Apollo as a normal humanoid, but with an extra organ in his chest whose function was unknown to McCoy. It was presumed that this organ permitted him to tap a powerful field of energy generated within his temple. Even with this ability, Apollo occasionally overextended himself, requiring a brief period of rest during which his vitality was restored. Presumably, then, the organ tapped the energy field, stored some quantity of energy, and made that energy responsive to Apollo's wishes.

After the temple was destroyed, Apollo demonstrated that he still possessed some abilities when he expanded his corporeal form. However, from his reaction to the temple's destruction, it seems likely that when he expended the last of his stored energy, he would be powerless, or nearly so. 

Background
The depiction of Apollo in "Who Mourns for Adonais" was considerably changed during the episode's rewrite process. Writer and story editor D.C. Fontana offered, "He was [originally] something of an empty character and we needed to give him more character, more interaction with our regular leads." ("Writer's Notebook: D.C. Fontana", TOS Season 2 DVD & Blu-ray special features)

Apollo was played by actor Michael Forest. This portrayal varied from how Apollo has usually been depicted in mythological and artistic tradition, since the character is normally golden haired.

Apocrypha
Michael Forest reprises his role as Apollo in the first episode of the TOS fan series "Star Trek Continues".

In the comic book story "A Rude Awakening!", Apollo was mentioned as harassing space travelers.