Ameteur astronamers observing Sputnik 1, October 4 1957, Britannica
It showed how the US reacted from Sputnik 1 and how the USA was planning on building a different satellite to respond to it.“The U.S. is believed to have the technical capability to establish successfully a small scientific satellite of the earth in the fairly near future. Recent studies by the Department of Defense have indicated that a small scientific satellite could be made"(National Security Council Report).The Department of Defense was used to protect the American people from foreign or other countries and to keep the citizens safe from threats. And this is significant because the US didn't know what the Soviet Union was going to use it for. They thought they were going to use it for surveillance and guided missiles.
The Soviets response to the successful launch of Sputnik, was important; they were surprised in some ways of the launch. They would track it day and night making sure it stayed on course and to collect info on how it was holding up. The Soviets were very happy with the successful launch and the fact that the Soviets could gain info on the whole world.
“Scientific stations located at various points in the Soviet Union are tracking the satellite and determining the elements of its trajectory. Since the density of the rarified upper layers of the atmosphere is not accurately known, there are no data at present for the precise determination of the satellite's lifetime and of the point of its entry into the dense layers of the atmosphere. Calculations have shown that owing to the tremendous velocity of the satellite, at the end of its existence it will burn up on reaching the dense layers of the atmosphere at an altitude of several tens of kilometers” (Krieger).
This evidence shows that the Soviets put lots of time and effort into the successful launch and keeping it on course. It talks about how they even set up observation posts to watch its long term trajectory and they calculated how long it would last in the harsh climate of space.