What was the goal of the us in the space race?

The US was concerned that domination of space by the USSR would give the Soviets a military or technological advantage over the US during the Cold war. The initial attempts following World War II were expanded by the growth of new nuclear weapons delivery systems, not the altruistic desire for space exploration.

The goal set by President John F. Kennedy in 1961 was to land a man on the Moon before the end of the 1960s, to demonstrate the superior scientific ability of the US (and generally free-enterprise, and the democratic system of government). By achieving this on July 20, 1969, the US gained substantial prestige in international affairs.