My sons father is in prison for domestic abuse against me. He is on the birth certificate and was in my sons life for the first 3 years. I know he would never give up his rights to him. He is sentenced to 5 years and cld get out in 2013 with good behavior. I would like to move on in my life and have plans to move out of state I want to know what rights his father has and what I should to prevent his father from causing us trouble in our relocation.

This is a depends on the state.

First do you have a custody and child visitation order ?
If you do, he has only those rights given to him in those.

If there is no custody order, he has equal rights to the child as you do.

In some states ( like GA where I live) a long term prison sentence can be a reason to ask for his rights to be taken away. ** but you will need an attorney since this is hard to do. And it is not forsure.

But if you wish to limit his visits you will need to either get, or modify your current child custody order