How Do Planet Gears Work?

[IrisLab]

I have a question about how a planet gear system works. With a planet gear, suppose you have a DC motor connected to the planets. You are driving the planets with a constant torque Tp and angular velocity wp by applying a constant voltage v (or fixed width PWM).

Does the gear system split the torque between the sun and the ring such that Ts = Tp/N goes to the sun and Tr = Tp(1 - 1/N) goes to the ring? I'm using N to represent the gearing ratio between the sun and the planets and N>=1.

What about the angular velocity? Do these sum such that wp = ws + wr where ws is the angular velocity of the sun and wr is the angular velocity of the ring?

I guess my larger question is...what are the ratio relationships with gear turns for torque and angular velocity?