Goodhart entered the Royal Naval College at Dartmouth in the Hawke Term in 1933. He then attended the Royal Naval Engineering College at Keyham, Devonport. He served as an engineering lieutenant, and saw action in the evacuation of Crete in 1941 on which was hit by two bombs. He then served on and saw more action escorting convoys to Malta and the assaults on Italy over the next two years.