The Hansen family emigrated from Denmark in 1864. They sailed on the General McClellan, and arrived in New York on 23 June 1864. In some sources Hansen is sometimes spelled as "Hanson." At some point the Hansen family changed the surname to Peterson.
Peter appears as "Per Hansen" on the ship passenger list. His name on his gravestone is engraved as "Peder Hanson Peterson."
More research is needed to confirm his date of birth.