The planet has (ring − sun) ÷ 2 teeth, so an odd difference asks for half a tooth and cannot be built. Separately, sun + ring must divide by the number of planets or they will not space equally.
The planet has to bridge the gap between sun and ring exactly, which fixes its size — it is not a free choice. And equal spacing needs each planet to land on a tooth space, which is an integer condition on the total. Both are pure assembly constraints: the ratio comes out looking perfectly reasonable either way, so nothing warns you until the parts are in your hands.
Unequal planet spacing is legal if you deliberately design for it — some sets use it to balance loads or fit an odd envelope — but then you lose the cancellation of radial forces that equal spacing buys, and the sun ends up pushed sideways against its bearing.
Estimate with the rule, then check it against the calculator that models it properly.
Open Gear Train Calculator →The planet has (ring − sun) ÷ 2 teeth, so an odd difference asks for half a tooth and cannot be built. Separately, sun + ring must divide by the number of planets or they will not space equally. The planet has to bridge the gap between sun and ring exactly, which fixes its size — it is not a free choice.