Geometric constraints on Planetary Gears

As long as the number of teeth of the sun plus ring gear divided by the number of planet gears is an integer, they will be equally spaced (120 deg for 3 planets). This is more about timing the points of highest and lowest tooth contact of the planet gears. When they're equally spaced the planet-sun meshes will all be hitting the highest tooth loads at the same time. These forces will balance out, minimizing vibration.

Think about 3 load vectors 120 degrees apart all pointing to the same point. The loading of gears is cyclical, so think about all 3 loads having the same sine function for intensity. If they're all in phase, they will always cancel out at the point of intersection. If they're out of phase, you'll always have one vector contributing more magnitude than the others, inducing vibration in your system. Excess vibration is bad.

AGMA 6123 is a helpful standard.