Thank you for the question on the ascension of Jesus, “The Gospel according to Saint Luke says the Ascension occurred in the vicinity of Bethany (Luke 24:50-51). Where do the Acts of the Apostles say it happened?”
The Gospel of Luke says that Jesus ascended in the vicinity of Bethany, not in Bethany. Bethany itself is approximately 1.72 miles from Jerusalem. Whether it was North, East, South or West is unclear, but Luke describes the place as being closer to Bethany than to Jerusalem.
Luke 24 says this, “When he had led them out to the vicinity of Bethany, he lifted up his hands and blessed them. 51 While he was blessing them, he left them and was taken up into heaven. 52 Then they worshiped him and returned to Jerusalem with great joy” (NIV).
Luke in writing Acts 1 does not state specifically the location since he knows that Theophilus had his previous writing. He says this in Acts 1, “After he said this, he was taken up before their very eyes, and a cloud hid him from their sight. 10 They were looking intently up into the sky as he was going, when suddenly two men dressed in white stood beside them. 11 “Men of Galilee,” they said, “why do you stand here looking into the sky? This same Jesus, who has been taken from you into heaven, will come back in the same way you have seen him go into heaven.” 12 Then the apostles returned to Jerusalem from the hill called the Mount of Olives, a Sabbath day’s walk[c] from the city” (NIV).
A Sabbath day’s walk is about 5/8 of a mile. It is important that the Luke states that the Apostles returned to Jerusalem from the hill called the Mount of Olives.
From reading geography, here are some additional information:
“’Mount of Olives’; in Arabic also الطور, At-Tur, ‘the Mountain’) is a mountain ridge east of and adjacent to Jerusalem’s Old City. … It is named for the olive groves that once covered its slopes. The southern part of the mount was the Silwan necropolis, attributed to the ancient Judean kingdom” from the Britannica.
“Mount of Olives, Arabic Jabal al-Ṭūr, Hebrew Har ha-Zetim, multi-summit limestone ridge just east of the Old City of Jerusalem and separated from it by the Kidron Valley” from Wikipedia.
Luke describes it as a hill being part of Mount of Olives. The nearest village is Bethany. Thus for general reference to location, one is describe a mountain range while the other is describing the nearest village.
For Theophilus, citing a city, gives him a better reference than citing a mountain range or hills, depending on how one wants to use the term. From Bethany to Jerusalem, he may be able to determine it is a relative short distance since it was a “Sabbath Day” walk.
SUMMARY: Luke is describing the nearest village to Jesus’ ascension which is Bethany while in Acts he is referring to the mountain range called the Mount of Olives. They are in the same general location.