Moon

A moon (also known as a natural satellite) was an astronomical object found in orbit around a planet.

You may be looking for Earth's moon or Doctor Moon.

Some moons, like Voga, were planetoids brought into orbit around a planet by the planet's gravity, while others were the result of a collision between objects during the formation of a solar system. (TV: Revenge of the Cybermen)

Mutter's Spiral

Sol

By the year 200,000, Earth was orbited by five moons. (TV: The Long Game) Earth's first Moon was in fact an alien egg and hatched in 2049, being replaced immediately by another egg the hatchling laid. (TV: Kill the Moon) By the time of the Fourth Great and Bountiful Human Empire, the Earth had four additional moons. (TV: The Long Game, Bad Wolf)

The Third Doctor sang of Martian moons, (TV: Inferno) of which there were two: Deimos and Phobos. (AUDIO: Deimos, Phobos)

Kasterborous

Across its history, Gallifrey had at least three moons. An unnamed satellite, the heavily industrialised Pazithi Gallifreya (COMIC: Agent Provocateur) and the lost moon, Botoya. Built into the latter was a device that could rewrite history on a grand scale, which was why the Doctor suspected the Ancients of Gallifrey had hidden the moon. Botoya subsequently became a legend in Gallifreyan culture, one not widely believed in. (AUDIO: The End of the Beginning)

By some accounts of the Doctor and Susan's escape from Gallifrey, the First Doctor had stolen one of Gallifrey's moons, (TV: The Magician's Apprentice, PROSE: A Brief History of Time Lords) though the Twelfth Doctor defended to Clara Oswald that he'd only lost the moon. (TV: Hell Bent)

Other moons

The Eleventh Doctor once offered to take Amy Pond and Rory Williams to a moon that was actually made of honey for their honeymoon. He later corrected himself, saying it wasn't made of actual honey, and it wasn't actually a moon. It was in fact technically alive "and a bit carnivorous, but there are some lovely views." (TV: A Christmas Carol)

The Shadow Proclamation tended to the matter of "suicide moons". (TV: The Magician's Apprentice)

Kepzyr, a moon of Zorbos, was well populated with trees before it was heavily deforested in the 39th century. (PROSE: Frank Reade, Jr.'s Electric Time Canoe)

Poosh was either a famously lost moon or a planet that had famously lost one of its moons. (TV: Midnight) Part of the New Dalek Empire's stolen planets, (TV: The Stolen Earth) the celestial body was returned to its rightful place in the cosmos by Donna Noble. (TV: Journey's End)

Skaro had at least three moons Omega Mysterium, Flidor and Falkus, (AUDIO: Davros, Innocence, Purity) the latter of which hosted a Dalek facility where they imprisoned an alternate version of Davros during the Last Great Time War. (AUDIO: Restoration of the Daleks)

During the Time War, the Eternity Circle harvested three moons in the Tantalus Spiral as the foundation for their construction of a large scale version of the Temporal Cannon. (PROSE: Engines of War)

Villengard was orbited by a partially-destroyed moon. (TV: Twice Upon a Time)

Other references

"Moons of madness" was a curse sworn by the Captain. (TV: The Pirate Planet)

"By the moons" was an oath sworn by the Ice Warriors and those who did them honour, such as Clara Oswald and the Twelfth Doctor. (TV: Cold War, Empress of Mars)