Why does the sun rise and set at the same time and moon rises and sets a different times each day?
The Sun does rise and set at a different time each day, but the daily difference is small. Since the December solstice, the days have been getting longer in the northern hemisphere and shorter in the southern hemisphere. After the June solstice, this will reverse. The moon moves from West to East across the sky. It makes one journey every 27.3 months. The moon must travel 360 degrees in 27.3 days which means 13.18 degrees in a day towards the east. Thus, The next night moon is located 13.18 degrees to the East from last night’s location. So Earth has to turn an extra 13.18 degrees such that tonight’s moon is in the same sky position as the last night’s moon. If last night moon was at the eastern horizon, it would be 13.18 degrees below the eastern horizon tonight at the same time. This causes the Moon to rise about 50 minutes later each night.