Evans, Craig A., Isobel A. H. Combes, Daniel M. Gurtner. The Bible Knowledge Background Commentary: Acts-Philemon, Volume 2. Chicago: David C. Cook, 2004, Page 77 - 78 (Google Books, Accessed 2/14/2016).)
With that background, look at what God did to prepare Peter for Cornelius. Acts 9:1 – 23 describes the process. Cornelius had a vision while praying instructing him to send for Peter, so he sent three men. The next day as the men were on the way to find Peter in Joppa, Peter is praying and sees the three sheets vision. While he is perplexed about what he sees the men Cornelius sent show up. The Spirit then instructs Peter to greet and accompany them.
We are going to unwrap this fully because there is a lot here. First, Peter’s world view, the view shaped by his understanding of what he thinks is the Law is wrong. We know that God can confront. He confronted Paul in Chapter 9. Here though God is taking Peter thorough a process, gracefully and gently re-instructing him about what God really wants. He uses the time of Peter’s personal prayer and worship, to give him instruction through both the vision and a direct word from the Holy Spirit. This was a shock to Peter. By his response it is clear that he is hesitant to break what he sees as the law.
Keep this in mind as we move through this passage. As I said there is much more here. More tomorrow.