There are two different branches of aerospace engineering: aircraft and spacecraft. Officially, they are called aeronautical engineering and astronautical engineering or rocket science.
The original term was aerospace engineering, but as astronautics branch developed, it was divided into two.
Aerospace engineering dates back to the late 19th century and the beginning of the 20th century. Earlier research has been made from the middle of 18th century to 19th century, by Sir George Cayley, but between his findings were no recorded data of other engineering notable discoveries. He noticed the separated forces of lift and drag, which influence any vehicle than flights. After the flight of the Wright brothers, the engineering world expanded further with the military aircrafts of the World War I.
The first airship to raise awareness on the scientific community was the Sputnik satellite, launched into space on the 4th of October 1957. The next year, on January 31, the U.S. launched its first satellite into space. Later the same year, The National Aeronautics and Space Administration emerged as a need of constant surveillance of the aircrafts during the Cold War.
Project Mercury was one of the first programs to ambition to carry an astronaut o an Earth orbit. As the engineering developed, so did the spacecrafts. The Apollo project was the first aircraft designed to have three astronauts aboard. Amongst the missions of the project were lunar landings, circumlunar flights and transporting the astronauts to a space station.
The studies started in 1960s, with a feasibility study competition between General Dynamics/ Convair, General Electric and Glenn L. Martin Company.
The mission was built around political pressure: the U.S. wanting to achieve technical superiority over the Soviet Union. During the presidency of John F. Kennedy, aerospace technology became a symbol of national pride and technical advancement. The program successfully ended with a manned Moon landing.