Earth and Mars orbit the Sun at different rates, so their relative geometry repeats on a ~26-month synodic period. A low-energy Hohmann transfer only works when Mars is a specific ~44° ahead of Earth at departure — arriving exactly opposite the launch point, half a transfer-ellipse later, just as Mars gets there.
For every launch date on the slider this simulator solves Lambert's problem (universal-variable formulation) across a spread of transfer durations, keeps the lowest-delta-v solution, and draws that exact conic trajectory. Near the window the winning ellipse is close to the classic 180° Hohmann arc. Off-window, the only trajectories that still reach Mars's actual future position sweep a distorted arc with a steeper approach — and cost far more delta-v.
Δv(t) = min over T of
|v1(t,T) − v_Earth(t)| + |v_Mars(t+T) − v2(t,T)|
- Launch date — scrub across ~7.4 years; the chart below shows the full recurring pattern of cheap valleys (windows) and expensive ridges.
- Zone badge — green near a window, red once required propellant makes the launch impractical; wait ~26 months for the next valley.
- Propellant mass — the rocket equation is exponential in delta-v, so a modest timing miss detonates the propellant budget long before delta-v itself looks dramatic.