The inputs are the current things you know about the planetary system.

Things you know:
1. Phase of the moon. (It would be trivial even for the ancients to keep track of the phases of the moon since the equinox.)
2. Where the planets currently are, if they are out.

You turn your little knob until everything matches what you currently see. Then you can turn it into the future and predict what will happen.

Even by your definition, this is a computer.

Why are you so vehement about this?

I'm not dead certain on the details but it went something like this...

They taxed narcotics. They set up a system where you could buy stamps that allowed you to posses them.

Then cleverly, they never sold the stamps. Therefore outlawing them all together.