St. Maximus the Confessor ca. 580-662
Why did the Spirit descend ten days after the Ascension of the Lord?
Some who have been taught the divine things say that since the angelic powers are [composed of] nine orders, according to Dionysius the Areopagite, when the Lord ascended in His humanity (for His divinity fills all things Eph. 1:23) He assigned to each order one day from His last day [His Ascension] until the final one [Pentecost]. For they were also in need of a visit from the Lord. For “in Him,” according to the Apostle, “are summed up” not only “the things on earth,” but also “the things in heaven.” (Eph. 1:10) And after this He appeared “to God the Father,” (1 Cor. 11:31) and thereafter, the Spirit descends. (Questions and Doubts, Question 142)
St. Nikolai Velimirovich 1880-1956
Certain divine mystics were able to comprehend what occurred in the heavens between the Ascension of our Lord and Savior Jesus Christ and the Day of the Holy Spirit.
It was granted unto them from God to see that which was unapproachable to others. Therefore, they say that during those days from the Ascension of the Lord to the Descent of the Holy Spirit on the Apostles the angelic ranks prostrated themselves before the Lord by rank, who with His pure blood washed mankind from sin and with His death He brought death to death, and with His descent into Hades He pillaged Satan, and with His Resurrection He witnessed to the resurrection of all of His faithful and with His Ascension He opened and showed the path to the Heavenly Kingdom. Therefore, the nine angelic ranks, by rank, from day to day and in their myriads to their myriad prostrated themselves before Christ the Victor, that is:
the first day of Ascension – the Holy Thrones
the second day of Ascension – the Holy Principalities
the third day of Ascension – the Holy Powers
the fourth day of Ascension – the Holy Dominions
the fifth day of Ascension – the Holy Authorities
the sixth day of Ascension – the Holy Seraphims
the seventh day of Ascension – the Cherubim
the eight day of Ascension – the Holy Archangels
the ninth day of Ascension – the Holy Angels
Therefore, nine days – the nine ranks of Angels and on the tenth day, the Descent of the Holy Spirit.
source: http://frmilovan.wordpress.com/2010/05/19/the-ten-days-of-ascension/