While talking to Maverick, Goose indicates that because of the circumstances surrounding Duke's death in Vietnam, Maverick was denied admission to the U.S. Naval Academy.
After the losing engagement at TOPGUN with Viper and Jester, Maverick is shown in his quarters looking at a picture a picture of himself and Duke that Maverick carries in his wallet. Viper also has a picture of himself and Duke on the wall at Viper's house that Maverick sees when he visits Viper.
Viper tells Maverick that Viper served with Duke while both were assigned with VF-51 aboard the USS Oriskany. Viper then reveals then-classified details surrounding Duke's plane being shot down and that Viper witnessed Duke's heroic actions before Duke's F-4 Phantom II was shot down.
It is thought that Duke is a reference to former U.S. congressman Randy "Duke" Cunningham, who is a former TOPGUN instructor and the only U.S. Navy pilot ace in the Vietnam War.