AP: This cannot be explained from the viewpoint of careful writer in the today's day and age. Another surprising fact is that in the Gospel, Jesus only stays on the earth 24 hours after his resurrection. But in Acts it lasts 40 days!!! The only explanation is the amount of time between the time the Gospel was composed, the first part of Luke's work (written c. A.D. 85-90, and the second part, Acts (written perhaps 20 or 30 years later). Luke, although very biased at times, is both an author and a surprisingly faithful one at that, i.e., faithful to the sources he had at the time, even when they presented contradictory information.
TWH: Regarding the first question, the Scripture reference is Acts 2:33-36: "Therefore, having been exalted to the right hand of God and having received from the Father the promise of the Holy Spirit . . . ." So, the issue that is being raised in the question to Antonio is one of a supposed contradiction. I say "supposed" because it is more a contradiction that is present in the questioner's mind, not a real contradiction. How is it, then that Peter says that Jesus was exalted to the right hand of the Father after his resurrection, yet in Luke he demonstrates (as Matthew does) that Jesus' birth is divine? I'd point anyone who asks this question to Phil. 2:6-11. Jesus is God (Phil. 2:6), but he was willing to humble himself and take on the likeness of humans so that he could give his life as a sacrifice to pay the price for their sins. At the incarnation, we see Jesus taking on human likeness (minus the sin nature that spread to all men through Adam), while retaining his divine nature. Fully God, fully man. What takes place after he dies on the cross and is raised from the dead is described also by Paul in Philippians 2. In v. 9, it says that God the Father super exalted Jesus. We know, of course, that Jesus is headed back to a relationship with the Father that they shared forever (e.g., John 1:1, 18; 14:1-6, 28; 17:5). The exaltation is the fulfillment of a passage that truly teaches the divinity and preexistence of Jesus Christ. Simply look at Psalm 110 and compare that to Matt. 22:41-46 and Acts 2:33-36.
With regard to the issue that Antonio points out, let me offer a couple of thoughts. First, Luke 24:44-49 does not take place immediately following the appearance to the ten assembled disciples. Robert L. Thomas writes:
"It must not be surmised that this meeting was the same as that in [Luke 24:35-44] and therefore took place on the same day as the resurrection. Luke clarifies this point in his second book when he points out that forty days had transpired since the resurrection (Acts 1:3). Hence there was ample time for a journey to Galilee and back" (A Harmony of the Gospels, 262 n.l).Second, the post-resurrection events seemingly being squeezed into such a tight space can be explained by the overall length of the Gospel. Luke's Gospel fit nicely onto one papyri scroll. He put everything together so that it would read smoothly. I'd like to repeat the words of John Wenham: "[T]he charge of irreconcilability brought against the resurrection stories has not been proved. Rather it has been shown that these records exhibit the characteristics of accurate and independent reporting, for while superficially they show great disharmony, on close examination the details gradually fall into place" (John Wenham, Easter Enigma, 124).