As a response to premkudva’s comment, I wrote this stuff about the position of Moon and times of mooonrise and moonset. Just want to keep it here, so I can find it later…

Moon moves the same distance every day. Here is how the calculation works out… On new moon day, Moon is very close to the Sun and on full moon day, it is on the opposite side compared to the Sun. So, in 28 days it has to cover the whole sky which is 360 degrees. 360/28=12.8 degrees per day. Earth rotates 360 degrees in a day, i.e. 1440 minutes. so, 1440/360=4 minutes per degree. so, 12.8x4=51.2 minutes. That means it rises 51 minutes later everyday compared to the prior day and hence you see it at different location at the same time of the day.

The change in position of sunrise/moonrise and sunset/moonset has to do with the inclination of the axis of rotation of Earth. Sun, Moon and all the planets are approximately in a plane called “The ecliptic”. The axis of rotation for Earth is about 23.5 deg tilted with respect to the Ecliptic. That causes the heavenly bodies to rise and set at different location during the month for moon and through the year for others. On a new moon day, moon is towards the Sun and hence, close to new moon, it rises and sets around where the Sun is and on full moon day, it is at the opposite end of the range. For the days in between, you see it drift gradually every day.