A real-time relativistic clock comparison for NASA's
Artemis II mission — the first crewed flight
to the Moon since Apollo 17 in 1972.
As Orion travels to the Moon and back, its clocks tick at a
different rate than clocks on Earth. Two effects compete:
Gravitational blueshift
Far from Earth, gravity is weaker and clocks run faster. At the Moon's distance, Orion's clocks gain time relative to Earth.
Velocity time dilation
Moving clocks run slower (special relativity). At 10+ km/s during translunar injection, this effect opposes the gravitational gain.
For Artemis II, gravity dominates — the crew ages
slightly more than people on Earth,
accumulating hundreds of microseconds over 10 days.
Worldline metric
The proper time along Orion's worldline in the weak-field limit:
Δτ is accumulated by integrating this metric along
the spacecraft's trajectory at each timestep, comparing
Orion's clock rate to a reference clock on Earth's surface.
Simulation
Trajectory computed via RK4 integration under
Earth + Moon gravity (two-body). Burns are impulsive
Δv maneuvers at the correct mission times. Ascent phase
is interpolated from real SLS performance data. All parameters
cross-referenced with NASA Artemis II mission control.