The rhetorical appeal that Kennedy is using to persuade the audience to change their perspective on space exploration is logos, as he is using facts to convince them of the need to fund a space program.
He argues that the exploration of space will go ahead, with or without the United States, and that no nation can expect to be a leader if it falls behind in the race for space. This logical argument is intended to convince the audience that the United States needs to invest in space exploration in order to maintain its position as a world leader.