Wrong
20mA is the value that can safely drawn form an output for an UNO.
You are the one who suggested timing. You need to apply power to the motor and time how long it takes. You need to time the number of turns.
For accuracy, a sensor wheel needs to be attached to the motor shaft and use an optical switch or physical switch (a limit switch would work) to detect one revolution.
Well if you want to open and close at a specific time of day it makes sense to use a controller. An RTC could be added and would tell the controller the time of day.