The first man-made object to orbit the Earth looks impudently inconsequential 50 years later: a drab metal ball with four tapered, antenna-like spikes and no snazzy gizmos. But as “Sputnik Mania,” a new documentary opening Friday at the IFC Center, enthusiastically shows, the important thing about Sputnik was where it went. The pioneering Soviet satellite awed average Americans, alarmed elected Americans, and brought the Cold War home for all in new and frightening ways.

“Mania” is a good word not just for reactions at the time, but also for the mercurial, immersing account by the veteran documentarian David Hoffman. Bathing us in varied archival footage, voices from the beyond, and hokey satellite ditties from the period, “Sputnik Mania” hard-sells the nail-biting and wonder that followed the historic launch on October 5, 1957. The lapel-grabbing settles down later on, but for a while, the film’s simplicity and insistence betray its earlier, retail incarnation as a curriculum aid.

The satellite was big news, no question — what else could transfix a world that had already seen the atom bomb? “Sputnik Mania” recounts the amazement of ordinary Americans during the weekend after the Friday launch, and then the inevitable paranoia as the threatening implications emerged. President Eisenhower, seen in press conference footage, seems evasive at best, but Senator Johnson of Texas and others strike a besieged note immediately.

The film quickly becomes a tennis match of events and aftershocks. Shamed by its second-fiddle status, America fast-tracked its own orbital projects, while Nikita Khrushchev released gloating propaganda about his nation’s success. More hand-wringing ensued when the Soviets shot a stray dog into space just one month later; the American follow-up, a satellite launch attempted in December, was a fiery failure.

Doling out the chronology of the space race, “Sputnik Mania” gives a stirring sense of the inexorable chain reaction of possibilities created by Sputnik. The logic fueled by military and scientific thought was swift and brutal: Humans can broach the heavens, so humans can put weapons there, so humans can put atomic weapons there. As we hear from President Johnson’s diary, the skies suddenly felt “alien,” and one feels panicky even now watching how the baby steps of the space race shrank the world down to size for ballistic missiles.

But Mr. Hoffman drives away the doom with liberal dips into contemporary pop culture and news, from songs to television shows such as “Name That Tune” and “Youth Wants To Know.” Walter Cronkite, Edward Murrow, and David Brinkley all turn up to intone in clips; in other clips, we get a sense of Eisenhower’s screen presence — likable, possessing a certain boyishness despite his baldness, and at times bristly. (Missing, however, is Roger Corman’s response: the B-movie “War of the Satellites,” which was released mere months after Sputnik.)

Spoiler alert: The Americans eventually hurl their own vessel (the Explorer) into space once Eisenhower reluctantly turns the project over to the military. The former general gets full due here as being cautious and sensible about the risks of militarization, a role he’s played increasingly in documentaries (“The Corporation,” “Why We Fight”). Khrushchev, whose naturalized American son turns up as raconteur, also gets a bit of burnish via complaints shared with Eisenhower over bellicose army advisers.

The mastermind of the Explorer turns out to be the ex-Nazi rocket scientist Wernher von Braun, who had been spirited out of Germany near the end of World War II. But the movie, condensed from Paul Dickson’s book “Sputnik: The Shock of the Century,” doesn’t dwell on the irony of von Braun’s provenance. (“Once the rockets are up, who cares where they come down?” Tom Lehrer sang of the globe-trotting scientist in 1965’s “Wernher von Braun.”)

After cycling through dueling bomb tests, “Sputnik Mania” ends on a delicate note of wistful pacifism that is incongruous with the movie’s bouts of hyperbole and sweeping claims. Mr. Hoffman pushes and pulls his story around more than he needs to. But even so, his movie helps explain why one Soviet engineer cheekily compared Sputnik to nothing less than Christopher Columbus’s arrival in America.