The history of Sputnik is tied to the history of the science of rocketry. Rocket science began to flourish between World War I and World War II. At the conclusion of World War I, Germany was forced to comply with the Treaty of Versailles, which among other things forbade Germany from building artillery. German military officials felt that rockets carrying explosives had the potential to replace artillery. The Treaty of Versailles didn't address rockets.
During World War II, rockets played a small part in Germany's plans. Hitler had hoped rocket attacks on cities would cause countries to panic and submit to Germany's demands. Although Germany did use rockets in several attacks, they didn't perform up to expectations. But the stage was set for further developments in rocketry.
Both the United States and the Soviet Union began to take an interest in rocketry. Several German engineers, including Werner von Braun, surrendered to the United States with the hope of continuing their research. Meanwhile, the Soviet Union began its own rocketry program.
In many ways, the rocketry programs in the Soviet Union and the United States were parallel. Both countries were eager to develop the most advanced rockets in the world. And both countries focused more on military applications of rocketry than anything else. In both the Soviet Union and the United States, the scientific applications for rocketry would have slipped through the cracks if it weren't for a few dedicated individuals.
In the Soviet Union, these individuals included Mikhail Klavdievich Tikhonravov and Sergei Pavlovich Korolev. Tikhonravov was a Soviet Air Force Academy graduate and expert in rocket science. He was responsible for many of the advances in multi-stage rockets in the Soviet Union. The multi-stage rocket made it possible for a rocket to reach orbit. Korolev was one of the founders of the Soviet space program. He was adept at leveraging political contacts to help fund the space program. He also understood the political importance of beating the United States into space.
Tikhonravov and Korolev both led teams that helped develop the Sputnik program. Tikhonravov concentrated mainly on designing a multi-stage rocket that could reach Earth orbit. The concept was simple: as the first stage of the rocket reached peak speed, the rocket would jettison it and the second stage would fire. The rocket would build on its speed, going even faster. As the second stage peaked, the rocket would jettison it and the third stage would fire. Korolev was also instrumental in many design decisions. Some of those decisions were politically motivated. For example, in 1955, U.S. President Eisenhower announced that the United States would launch a satellite during the International Geophysical Year (IGY). The IGY spanned from July 1957 to December 1958. Shortly after Eisenhower's announcement, an official from the Soviet Union said that the U.S.S.R. would also launch a satellite during IGY. Korolev was under political pressure to beat the Americans into space.
While the Soviets had planned to launch a scientific research satellite into orbit, the design and production process was lengthy. In order to ensure that the Soviet Union launched its satellite first, Korolev decided to build a much simpler, smaller satellite. The result was Sputnik, a somewhat primitive device that still fulfilled the definition of a manmade satellite.