Good info, Harvey.

...The "no moon" line gives us a problem when TMP comes along, but that's the movie era for you. Continuity was not a priority.
I've always assumed that the giant sphere seen in the sky above Spock in TMP must be another planet in Vulcan's solar system as I've never forgotten his comments about Vulcan having no moon in The Man Trap!

JB
In our solar system even the closest planets to each other never get closer than tens of millions of kilometers or miles to each other, which means they always appear as dimensionless dots of light in the sky. And it was generally believed that must be the case in other star systems.
But there are examples of recently discovered exoplanets much closer to each other than those in our solar system.
Kepler-70c orbits Kepler-70 only 0.0016 AU or 240,000 kilometers farther out than Kepler-70b.
During closest approach, Kepler-70c would appear 5 times the size of the Moon in Kepler-70b's sky.
https://en.wikipedia.org/wiki/List_of_exoplanet_extremes
And there are unconfirmed reports of a planet orbiting between the orbits of Kepler-70b and Kepler-70c.
https://en.wikipedia.org/wiki/Kepler-70
Kepler-36b and Kepler-36c are separated by a larger absolute distance but smaller relative distance.
Kepler-36b and Kepler-36c have semi-major axes of 0.1153 AU and 0.1283 AU respectively, c is 11% further from star than b .
https://en.wikipedia.org/wiki/List_of_exoplanet_extremes
The planets in the TRAPPIST-1 system also orbit close to each other, and some of them are in the habitable zone of TRAPPIST-1.
The system is very flat and compact. All seven of TRAPPIST-1's planets orbit much closer than
Mercury orbits the Sun. Except for TRAPPIST-1b, they orbit farther than the
Galilean satellites do around Jupiter,
[42] but closer than most of the other
moons of Jupiter. The distance between the orbits of TRAPPIST-1b and TRAPPIST-1c is only 1.6 times the distance between the Earth and the Moon. The planets should appear prominently in each other's skies, in some cases appearing several times larger than the Moon appears from Earth.
[41] A year on the closest planet passes in only 1.5 Earth days, while the seventh planet's year passes in only 18.8 days.
[38][34]
https://en.wikipedia.org/wiki/TRAPPIST-1
Thus the idea that the large world in the sky is another planet which sometimes passes close to Vulcan is rather plausible.
Note that the scene in TMP has a smaller orb passing in front of the larger orb. This could be a moon of either Vulcan or the larger body. Since Spock said that Vulcan has no moon it would probably be a moon of the other body.
Since the smaller object is spherical it should probably be at least 200 miles in diameter. If the smaller object is not much more than that the larger object might be only about the size of Mars.
TAS "Yesteryear" was happy with showing a giant orb on the Vulcan sky (both day and night!), so the possible gap in continuity sits there...
...Although interpreting that heavenly phenomenon from TAS as a "moon" would really stretch the astronomical definition.
Timo Saloniemi
Of course it is common to photograph Earth's moon near the horizon with a telephoto lens and make it seem to have many times the apparent angular diameter that it actually does.
PS I have often interpreted the large object in Vulcan's sky as a large planet in the same orbit as Vulcan. Vulcan and the other astronomical body could be a double planet orbiting around their common center of gravity, or maybe that other astronomical body is many times as large as Vulcan and Vulcan is basically a moon of that other astronomical body. In either case that large astronomical body would not be a moon of Vulcan. Thus Spock would be accurate when he said "Vulcan has no moon".
I remember writing an imaginary dialog between Uhura and Spock where Uhura beams down to Vulcan and is shocked to see a large orb in the night sky and questions Spock about it, saying she could have come down with her current boyfriend to enjoy a moonlit night if Spock hadn't once lied to her about Vulcan having a moon. She soon regrets opening that can of worms.