Plot: Approximately one year (early 1961 to early 1962) - what is the height of the American-Soviet space race - in the life of three female friends who worked in the female African-American computing section of NASA at Langley, is presented. Their largely unheralded at the time contributions to the advancement of the American space program are dramatized, their contributions which they were able to achieve despite facing both gender and race issues, the latter as much of the US, including NASA, was still segregated. Mary Jackson, assigned to the space capsule heat shield team, is encouraged by one of the engineers on the team to apply for one of the more senior engineering positions, he seeing her expertise. In what ends up being the Catch-22, Mary does not have the necessary qualifications for the promotion, and cannot get those qualifications as the extension courses are not taught in any high school accessible to African-Americans in Hampton where she lives. Her struggles are exacerbated by her husband Levi Jackson, a civil rights activist who only sees the advancement of African-Americans in a narrow view. Dorothy Vaughan has been acting supervisor of the section, only having the responsibilities but not the title or the associated pay. Dorothy believes not getting that promotion is largely the doing of her Caucasian supervisor, Vivian Mitchell. With the first IBM mainframe computer just having been purchased at NASA, Dorothy, with the odds stacked against her, tries to learn as much as she can on her own about its workings to make herself and the entire African-American female computing section relevant in this changing time. And widowed mother Katherine Gobel is the mathematical genius whose expertise in analytical geometry gets her assigned to the Space Task Group under the lead of Al Harrison, a no nonsense man who wants the job done at any cost. To get to Harrison, Katherine has to go through lead engineer Paul Stafford, who sees her as an irrelevant underling, he always falling on the excuse of clearance to quash Katherine's ability to do her job effectively. Her burgeoning romance with National Guardsman Jim Johnson is also dramatized, their relationship despite their rocky start.
Alternative Plot: Three brilliant African American women at NASA -- Katherine Johnson, Dorothy Vaughan and Mary Jackson -- serve as the brains behind one of the greatest operations in history: the launch of astronaut John Glenn into orbit, a stunning achievement that restored the nation's confidence, turned around the Space Race and galvanized the world.