The Willis equation
Every planetary gearset obeys one rule linking the speeds of sun, ring and carrier: (sun speed minus carrier speed) / (ring speed minus carrier speed) = minus ring teeth / sun teeth. Set any one speed to zero and the ratio between the other two falls out.
Ring held: sun to carrier ratio is 1 + Zr / Zs. Carrier held: sun to ring ratio is Zr / Zs, reversed. Sun held with the carrier as input: carrier to ring ratio is 1 / (1 + Zs / Zr), an overdrive below 1:1.
Try it: with the ring held, drop the sun to 12 teeth and raise the ring to 96. The ratio jumps to 9:1 from a single gear stage, something two plain gears could only do with a very large wheel.
Why the teeth must add up
Planets fill the gap between the sun and the ring, so planet teeth must equal (ring teeth minus sun teeth) / 2. The drawing keeps one set of gear sizes for clarity; the numbers and speeds follow your tooth counts.