Neither the sun overtakes the moon nor the moon overtakes the sun. How great the force of gravity is! The sun is situated millions of miles away yet it has a pull over the earth and other planets while the moon is subdued by the earth. A balance between the spheres and their orbits has been created. Why is it so?

The crescent moon seen on the first day of the month is like a curved thread. Its size doubles the next night. Then by the thirteenth and fourteenth night a whole round moon is sighted. Then from the sixteenth it goes on thinning until in the last night, called moonless night, it disappears completely; so the counting of days of the month may be known. The Quran explains this in a clear way:
 
"He it is Who made the sun a shining brightness and the moon a light, and ordained for it mansions that you might know the computation of years and the reckoning. Allah did not create it but with truth; He makes the signs manifest for a people who know. (10:5)"
 
As for the words:
 
"…as an old dry palm branch."
 
They compare the appearance of the moon to an old withered branch of date palm curved like an arch, yellow and weak. If you look at the moon in the last nights of the month you will find that it is exactly so.
It is also like the last phase of my and your age. Repentance has much value now and not when one sees the angel of death.
 
"We have ordained for it stages…"
 
There are 27 stages for the moon. Look at it night by night, to follow its course. Zamakhshari has written inRabiul Abrar, quoting Sharhe Sahifa that it was the night of fourteenth of the month when Imam Sajjad (‘a) woke up before dawn for Tahajjud prayers.

He put his hands in the can of water for making ablution. When he raised his head towards the sky he observed the moon. He remained in that position until the Muezzin (caller from the minaret of the mosque) cried: “God is the Greatest (Allahu Akbar).”
 
"Most surely in the creation of the heavens and the earth and the alternation of the night and the day there are signs for men who understand. "(3:190)
 
Observe the greatness of God in the sky; planets in the limitless space, especially according to modern scientific research all these things are indeed amazing.