Launch Window Calculator

The synodic period is the time between successive alignments of Earth and another planet, as seen from the Sun. For an outer planet (farther from Sun than Earth), synodic period = 1/(1/P_Earth - 1/P_planet). For an inner planet, 1/(1/P_planet - 1/P_Earth). Mars synodic period = 779.9 days, Venus = 583.9 days, Jupiter = 398.9 days.

You must wait for the next synodic period. For Mars, that is about 26 months. Some missions have missed windows due to launch vehicle problems (Fobos-Grunt, 2011, which suffered a propulsion failure and could not execute its trans-Mars injection burn). In the worst case, a missed Mars window means the spacecraft burns up or drifts aimlessly in heliocentric orbit.

No. Mars and Earth orbits are slightly elliptical, so the transfer geometry varies from window to window. Every 15-17 years, a particularly favorable perihelic opposition brings Mars close to Earth, reducing the required delta-v. The 2003 opposition was the closest Mars-Earth approach in 60,000 years. Launch windows near perihelic opposition are most efficient for mission planning.

A porkchop plot shows total delta-v (or C3 launch energy) as contour lines over a grid of departure date versus arrival date. The minimum-delta-v region has a shape resembling a porkchop, giving the plot its name. Mission planners use porkchop plots to identify the optimal launch window and how the required delta-v changes for nearby dates.

C3 (characteristic energy) = v_infinity^2, where v_infinity is the hyperbolic excess velocity when leaving Earth's sphere of influence. It is the launch energy required above and beyond Earth escape velocity. Positive C3 means the spacecraft can reach heliocentric orbit (interplanetary missions). Larger C3 means faster travel to the target but requires more propellant.

A direct trajectory (Hohmann-like) goes from Earth's orbit directly to the target in the shortest efficient path. An indirect trajectory uses gravity assists from other planets to save delta-v or enable trajectories not possible with direct flights. Voyager, Galileo, and Cassini all used gravity assists from Jupiter to reach the outer planets.

For Earth orbital launches, the launch window is determined by the launch site latitude and the target orbital inclination and right ascension of ascending node (RAAN). The launch site passes through the orbital plane twice per day as Earth rotates. For ISS supply missions, the window is typically 5-10 minutes. Missing the window requires waiting for the next pass, typically 12 hours later.

A free return trajectory is an Earth-Moon or Earth-Mars trajectory that naturally returns to Earth if the main engine fails partway through. Apollo 13 used a free return trajectory to limp home after its oxygen tank explosion. Free return trajectories are planned as abort contingencies for crewed missions because they require no additional propellant to return home.

Interplanetary launch windows are planned years in advance. NASA identifies planetary window opportunities decades into the future for mission concept studies. The actual launch date within a window is determined by launch vehicle readiness, spacecraft readiness, and range safety considerations. For Mars missions, the window typically spans 3-4 weeks, allowing some scheduling flexibility.