If I wanted to figure that out, assuming this is a standard round home doorknob, I'd bind the knob with tape, and try hanging various weights off the end of it. Once it moves, you'd need to convert that weight into a measure of torque, then pick a motor with more torque than that. The motor needs to have a stop on it, so probably a stepper motor would be needed, and I'm assuming that since you want a motor for a doorknob, you're talking some form of remote access, meaning you need a microcontroller with either timing ability (pieze crystal), or with an Ethernet shield for network control.
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