In October 1957, news of the Soviet Union’s launch of Sputnik 1 reaches the town of Coalwood, West Virginia, where most residents work in the coal mines. As the townspeople gather outside to see the satellite orbit across the sky, Homer Hickam is inspired to build his own rockets to escape Coalwood. His family and classmates’ do not respond kindly, especially his father John, the mine superintendent, who wants Homer to join him in the mines.
Homer teams up with math geek Quentin Wilson, who shares an interest in aerospace engineering; with the support of friends Roy Lee Cooke and Sherman O’Dell, and their science teacher at Big Creek High School, Miss Freida J. Riley, the four construct small rockets. While their first launches fail, they experiment with new fuels and designs and eventually succeed. Though the local paper runs a story about the boys, they are accused of starting a wildfire with a stray rocket and are arrested. After John picks up Homer, Roy Lee is beaten by his abusive stepfather, Vernon. John intervenes and rescues Roy Lee, warning Vernon that he will protect Roy Lee as Roy Lee’s late father would have.
The four abandon rocketry and destroy their launch site. In a mining accident, John is injured rescuing others, and Ike Bykovsky, a mine worker who let Homer use the machine shop for rocketry and transferred underground for better pay, is killed. Homer drops out of high school to work in the mine and provide for his family while his father recovers.
Later, Homer is inspired to read a book on rocket science from Miss Riley, learning to calculate the trajectory of a rocket. Using this, he and Quentin locate their missing rocket and prove it could not have caused the fire. The boys present their findings to Miss Riley and the school principal, Mr. Turner, who determines the catalyst was a flare from a nearby airfield. Homer returns to school by special invitation; the boys return to rocketry and win the school science fair. With the opportunity for one of them to participate in the National Science Fair in Indianapolis, they elect Homer.
The workers’ union goes on strike against John. While the family eats dinner, Vernon shoots into the kitchen but misses John, who dismisses Homer and Jim’s fears, leading to a heated argument with Homer. With the mines set to close and resenting his father’s pressures, Homer storms out of the house, vowing never to return.
At the fair, Homer’s display is well-received, and he enjoys popularity and some sightseeing. Overnight, someone steals his machined rocket part model – the de Laval nozzle – and his autographed picture of Dr. Wernher von Braun. Homer makes an urgent phone call home, and his mother, Elsie, implores John to end the ongoing strike so that Mr. Bolden, Bykovsky’s replacement, can use the machine shop to build a replacement nozzle. John relents when Elsie, fed up with his lack of support for their son, threatens to leave him. With the town’s support and replacement parts quickly sent to Indianapolis by bus, Homer wins the top prize and is bombarded with college scholarship offers. He is also congratulated by von Braun himself, not realizing his idol’s identity until he has gone.
Homer returns to Coalwood a hero and visits Miss Riley, who is dying of Hodgkin’s lymphoma. At the launch of their largest rocket yet – the Miss Riley – John, who never attended any of the launchings, is given the honor of pushing the launch button. The Miss Riley reaches an altitude of 30,000 feet (9,100 m) – higher than the summit of Mount Everest. As the town looks up to the skies, John slowly puts his hand on Homer’s shoulder and smiles, finally showing Homer that he is proud of him.
An epilogue, using real footage, reveals the true outcomes of the main characters’ lives.