Why Moon rises 50 minutes later everyday?

Have you ever got curious to know why moon rises approximately 50 minutes later everyday as compared to the previous day?

For understanding this, first we need to understand how celestial bodies like earth, moon etc. rotate (around itself) and revolve (around some other planet or star). Its so wonderful to know how these celestial bodies move in tandem and that too for millions of years in perfect synchronisation. 

Its a well known fact that earth completes one rotation in 24 hours. And also moon completes one revolution around its parent earth in approximately one month. Now this approximate period of one month is calculated in two ways. 

First one is Sidereal Month which is equal to the time taken by moon to complete one revolution around the earth, but with respect to the background stars which we see from the earth. This period is equal to 27.32 days.

Second one is Synodic Month. Even though, moon completes one apparent revolution in one Sidereal Month, we won't be able to see the new moon just after one sidereal month is complete. This is because moon revolves around the earth and at the same time earth also revolves around the Sun. As a result, moon has to travel some extra distance so as to reach at the same place, with respect to the Sun and we get new moon again. So the total time taken, also called as a Lunar Month is equal to 29.53 days.

Visit http://www.sumanasinc.com/webcontent/animations/content/sidereal.html for nice animated presentation explaining Sidereal and Synodic Months.

Now lets understand why moon rises 50 minutes later everyday. 

Here for us, the relevant time taken by moon to complete one revolution around the earth is Sidereal Month, since we want the exact moonrise time i.e. the time when moon first appears on the horizon. Hence the position of the moon which is apparent from the earth with respect to the background is what matters for us rather than its position with respect to the Sun. 

Let is assume that in a figure beside, on Day 1, a person is standing at a point A on earth and he sees the moonrise exactly at 07:00 pm. 

Exactly 24 hours later, on Day 2, the man is standing at the same point A on earth at the same time i.e. at 07:00 pm expecting to see the moonrise again. But in those 24 hours, moon also has revolved around the earth. Now as we have seen, one sidereal month is 27.3 days. So moon completes 360 degrees revolution in 27.3 days. So in one day of 24 hours, it moves by 360/27.3= 13.18 degrees. So for a man standing at point A on the earth on day 2 at 07:00 pm expecting to see the moonrise, moon is still 13.18 degrees below the horizon. So he has to wait for the earth to rotate 13.18 degrees to see the moonrise again. So now the moon will rise for him when the point A on earth travels further to reach point B. As we know, earth rotates 360 degrees in 24 hours i.e in 1440 minutes. So it rotates 1 degree in 4 minutes. So to rotate 13.18 degrees, it takes 13.18 x 4 = 52.72 minutes. This is the delay in moonrise everyday.

This delay would have been same at all places on earth, if earth's plane of rotation around itself and moon's plane of revolution around the earth would have been co-planer with each other. Had the planes been like that, we would have seen solar eclipse on every dark moon day and lunar eclipse on every full moon day. But they are at a angle of almost 29 degrees with each other. So this delay calculated above is not the same at all places on earth and depends on the latitude of the place from where we see the moonrise but it averages out to be around 50 minutes per day.