Is the Moon a planet? By some definitions it may become one in the distant future. The controversy over what makes a celestial body a planet has been going on for decades. In fact the planet Pluto became a casualty of that debate when it was demoted to a planetoid. So if Pluto can get the axe as a planet, then surely the Moon can be eventually promoted to being a planet. However we have to go by the currently accepted understanding of what a planet is.
According to the IAU a planet is any rocky body that has different layers, is geologically active, and most importantly orbits the Sun. We know that the Moon can easily fit these categories. First the moon is a rocky body composed of many of the same elements that the Earth is composed of. It also had volcanic activity in its past. Even now the Moon still experiences detectable quakes so it is still geologically active. The last is obvious in that it does orbit the Sun it just also orbits Earth while doing it.
A new wrinkle in the definition of a planet could be just the thing to put the Moon over the top in the future. According to the current definition of a moon can’t become a planet if it orbits another planet however it can be considered one if the center of gravity known as the barycenter lies outside of the larger planet. Right now the Moon is still solidly in the natural satellite category but each year it is drifting further and further away in its orbit from the Earth. This means that someday in the distant future scientist may consider reclassifying it as a planet. However, that is if the definition for what is a planet does not change in that time.
So in the end we know for certain that the Moon is not a planet. It is a natural satellite by even the most current definition issued by the IAU. However the question brings up the issue of how flexible the definition of what makes a planet a planet becomes. In either case it would be likely that tradition would remain too strong. The moon has been the moon for millennia so it would be very unlikely for astronomers to change its designation without very convincing evidence to back it up.
We’ve also recorded an entire episode of Astronomy Cast all about the Moon. Listen here, Episode 113: The Moon, Part 1.