What is the device called that automatically points the antenna toward a satellite as it passes across the sky?

[VE3EAR]

You might find something with a Google search for "satellite tracking rotor control" or something else to that effect. Good luck!

73, Bruce, VE3EAR

[snn47]

What dish size and what tracking range do you need, what type of satellite do you want to track in orbit or geostationary?

For small dishes used in airplanes and ships they are called Automatic Tracking Satellite Dish.

If you look for sate TV you can find two motor driven actuator mounts for steering the dish between 0° to 180° and elevation up to 90° available. If you combine seperate azimuth and elevation actuators cou can have 0° to 360°, however your caox cable will limit movement.

Dual Axis Satellite Actuators
Inclined Orbit Satellite Tracking Actuators
Dual Axis Horizon to Horizon Chain Drive Mount
EAR-1000
Elevation-over-Azimuth Positioner

You can some of these products here https://www.satellitedish.com/page95.htm

However this is jaust the mechanical part, you would still need some tracking programs to steer this dish mount.

You might also search HAM Radio documentation for dish steering for EME or satellite use.