Keep 3 IR receiver at some distance on the board to represent the East middle and West. Assuming that the sun rises in east when 1st IR receiver is illuminated using IR tx then the motor should rotate to some extent and stop. If middle IR receiver gets light the motor should rotate some more and should stop, when west IR gets IR tx signal the motor rotates and waits for some time. after some time assuming the sun has set, the motor should come back to orig position and again wait for the sun rise, or use an RTC and depending on the rtc value rotate the motor with proper delay
---------- Post added at 22:19 ---------- Previous post was at 22:17 ----------
Instead of IR you can use your LDR, if you use LDR then you need ADC.