Launch Window Calculator

Synodic Period comes from 1/T_syn = the absolute difference between 1/Origin Orbital Period and 1/Target Orbital Period -- so when the two periods are nearly equal, that difference shrinks toward zero and Synodic Period grows very large, because two bodies orbiting at nearly the same rate take a long time to drift back into the same relative alignment. Earth and Mars, with fairly different periods (365 vs 687 days), realign roughly every 26 months; two bodies with nearly identical periods could take decades.

It assumes a standard 180-degree Hohmann transfer -- the minimum-energy path between two circular, coplanar orbits around the Sun, which sweeps exactly half of an ellipse connecting the two orbits. Transfer Time is derived from Kepler's third law: each orbital period converts to a semi-major axis (T² = a³ in AU/year units), the transfer ellipse's semi-major axis is the average of the origin and target values, and its full orbital period -- halved for the one-way trip -- gives Transfer Time. Other transfer strategies (faster, higher-energy trajectories) would take less time but require more propellant.

A Hohmann transfer only departs correctly when the target body sits at one specific phase angle ahead of the origin at launch -- arrive too early or too late relative to that angle and the spacecraft and target won't meet at the transfer orbit's far end. Wait Time to Launch measures how long, given today's Current Phase Angle, it takes the two bodies' relative motion to drift into that required alignment, which only recurs once per Synodic Period.

Yes -- if Current Phase Angle happens to already be close to the phase angle a Hohmann transfer requires, Wait Time to Launch will be small, meaning a launch window is opening very soon. If the bodies have just passed that ideal alignment, Wait Time to Launch will instead be close to a full Synodic Period, since the next opportunity won't recur until the bodies drift all the way back around.

Yes, holding Origin Orbital Period fixed: a longer Target Orbital Period implies (via Kepler's third law) a larger target semi-major axis, which pushes the transfer ellipse's own semi-major axis and orbital period up, so Transfer Time always increases as Target Orbital Period increases. This is why crewed Mars missions, with Mars's 687-day period, plan for many-month transfer times (around 259 days for an Earth-to-Mars transfer at default values), while a transfer to a closer target with a shorter period completes faster.