Each night for the next several nights, the Moon sets much later than it did the previous night. This happens for two reasons.
First, this week the plane of the Moon’s orbit is nearly perpendicular to our horizon, so much of the Moon’s orbital motion eastward relative to the background stars (if we could see them) during the day takes it directly away from the western horizon, thus slowing as much as possible its inexorable march towards the west caused by the Earth’s rotation.
Second, this week the Moon is moving north in declination, and this, too, increases the amount of time the Moon stays above the horizon. The closer to the north celestial pole an object is, the longer it stays above our horizon, the further north along the western horizon it sets, and the later it sets. The Moon’s motion during the day northward relative to the celestial equator causes the Moon to set further north than it would have otherwise. The combination of these two factors makes moonset much later each night, as shown in the table below.
But, why doesn’t moonrise also occur much later each morning? As you can see by inspecting the table above, the Moon rises only a little later each day, in marked contrast to the leaps and bounds moonset is later each night. The factors are the same, but the effect is different. Because the Moon is moving north and is thus rising further north every morning, it rises earlier than it would have otherwise. Although the Moon is rising later each day due to its eastward orbital motion, moonrise is only a little later due to the countereffect of an earlier rise time stemming from the Moon’s more northerly declination.
It is no wonder humans have always been fascinated by the Moon’s complex motion. Throughout history, a number of mathematicians have taken up the challenge of trying to understand and predict the Moon’s motion, leading to several important advancements in mathematics.