Why Don't Mercury Or Venus Have Any Moons?

"For mercury it's pretty clear that there isn't much room for a moon in the stable region"

- Charles F. Gammie

Planets have a region around them where orbiting objects can be gravitationally bound. In planetary science this is called the ‘Hill sphere’, named after 19th-century American astronomer George Hill, who worked on the Moon’s orbit. The size of the Hill sphere depends on how massive a planet is in comparison to the Sun, and how close it is to the Sun.

Any bound object must orbit inside the Hill sphere. But for its orbit to be ‘stable’ it needs to orbit at less than about one-third of the radius of the Hill sphere. Therefore we expect that all moons must orbit at less than about a third of a Hill sphere radius.