In Conversation With
KJ–1918–2026
TRAJECTORY ANALYSIS — MERCURY ORBITAL INSERTION Earth Moon EQUATIONS OF MOTION r̈ − rθ̇² = − μ/r² r²θ̇ = h = const. VIS-VIVA EQUATION v² = μ ( 2/r − 1/a ) HOHMANN TRANSFER Δv Δv₁ = √(μ/r₁) · (√(2r₂/(r₁+r₂)) − 1) REENTRY PARAMETERS γ = arctan(v_r / v_⊥) T_reentry = 2πa³/² / √μ SPLASHDOWN COORDINATES φ = arcsin(sin δ sin i) λ = Ω + arctan(cos i · tan u) WINDOW TIMING (sec) Δt = (λ_target − λ_node) / ω_E μ_Earth = 3.986 × 10⁵ km³ s⁻² R_E = 6,371 km · R_Moon = 1,737 km a (transfer) = (R_E + h_orbit + d_Moon) / 2 T = 2π √( a³/μ ) → 5.15 days i_orbit = 28.5° (KSC latitude) RAAN: Ω = f(t_launch, θ_Sun) v_circular = 7.78 km/s @ 200 km Δv_total = 3.14 km/s (TLI burn) +z +x Transfer orbit Parking orbit (185 km) Lunar orbit Δv₁ TLI N LANGLEY RESEARCH CENTER · NACA / NASA Computed: K. Johnson · Checked: K. Johnson · 1962 Sheet 4 of 7 Friendship 7 — Orbit Calc. [ see sheet 5 ] Check vs. IBM 7090 — agrees
Museum of Minds — Biography
Katherine
Johnson
1918 — 2020
Portrait unavailable
On the Record

She computed the trajectories that put men on the moon — and had to fight to be in the room where it happened.

Katherine Johnson was a mathematician at NACA and NASA whose orbital mechanics calculations were so trusted that John Glenn refused to launch until she personally verified the computer's numbers.

Working in a segregated "colored computing" pool before breaking into all-white, all-male flight research teams, she combined an almost supernatural gift for analytic geometry with the dogged determination to attend the briefings, author the reports, and receive the credit that had long been withheld.

Her equations flew on every crewed Mercury mission, on Apollo 11's lunar trajectory, and on the contingency return paths that would have guided the astronauts home should the onboard computer fail.

✦   In Conversation   ✦

Speak with
Katherine Johnson

This conversational exhibit draws on Johnson's published papers, NASA technical reports, congressional testimony, oral history interviews, and the memoir she contributed to Reaching for the Moon. Her voice here is reconstructed from the record she left: careful, precise, quietly proud, and entirely unwilling to minimize what she accomplished.

Ask her about the mathematics of orbital mechanics, the experience of racial segregation inside one of America's premier scientific institutions, or what she makes of the pace at which things have — and have not — changed since the Apollo era.

She knew the answer before the computer finished running. The question the exhibit invites you to put to her is: how does a mind like that survive in a system designed not to see it?

Orbital Mechanics Analytic Geometry Mercury Program Apollo 11 Segregation & Science NACA / NASA Human Computing Space Race

"We needed to be assertive as women in those days — assertive and aggressive — and the men had to get used to us."

Katherine Johnson — Oral History Interview, NASA History Division, 1992

Corpus & Source Materials

Determination of Azimuth Angle at Burnout (NASA TN D-233, 1960)
NASA Oral History Project — KJ Interviews, 1992 & 2008
Friendship 7 Trajectory Verification Documents (1962)
Apollo 11 Mission Planning Trajectory Notes (1969)
Reaching for the Moon — Memoir (2019)
Presidential Medal of Freedom Citation (2015)
NACA Flight Research Division Technical Memoranda (1953–58)
Congressional Testimony on STEM Education (2016)
West Virginia State University Commencement Addresses
Hidden Figures Source Research (Shetterly, 2016)
Katherine G. Johnson Computational Research Facility Dedication (2017)
NASA Langley Research Center Internal Performance Reviews (1958–1983)