Synodic Period & Launch Window Calculator
Find how often launch windows open between two planets, the Hohmann transfer time and the phase angle the target planet must be at when you depart, for Earth to Mars, Venus, Jupiter and more.
Why launch windows repeat
Planets move around the Sun at different speeds, so the geometry between two of them repeats only after the faster one has gained a full lap on the slower. That interval is the synodic period, given by 1/S = |1/T₁ − 1/T₂|, where T₁ and T₂ are the orbital periods. With Earth at 365.256 days and Mars at 686.980 days, the synodic period is 779.9 days, about 2.14 years. That is why Mars missions cluster in windows a little over two years apart, and why a mission that misses its window waits that long for the next. Venus windows come every 583.9 days, and Jupiter, which moves slowly, comes back into position every 398.9 days.
The phase angle
A Hohmann transfer between planetary orbits is half of an ellipse around the Sun, touching the departure orbit at one end and the destination orbit at the other. The calculator uses circular orbits with the semi-major axes in astronomical units, so for Earth at 1.000 AU and Mars at 1.524 AU the transfer ellipse has a semi-major axis of 1.2618 AU. Kepler’s third law in years and AU gives the transfer time directly: half of 1.2618^1.5 years, which is 258.9 days. During that time Mars moves 360° × 258.9 ÷ 687.0 = 135.7° along its orbit. To arrive where Mars is, the spacecraft must depart when Mars is 180° − 135.7° = 44.3° ahead of Earth. That angle is the phase angle the window opens on.
For an inner planet the sign flips. Venus moves fast enough during a 146.1-day transfer that it must be 54.0° behind Earth at departure. Coming home from Mars, Earth must be 75.1° behind Mars, which is why a crew that has just arrived cannot leave at once; on a minimum-energy mission they wait at Mars for roughly 450 days until the geometry comes round.
Limits of the idealised answer
Real orbits are elliptical and tilted. Mars has an eccentricity of 0.093, so the best transfers vary considerably from one window to the next, and planners use porkchop plots computed from ephemerides, charts of launch energy against departure and arrival date. The results here are the textbook figures that every porkchop plot is built around, and they are right to within a few weeks. A common mistake is to treat the synodic period as the travel time. The two are unrelated: the synodic period is how often you can go, the transfer time is how long the trip takes.
How to use it
- Choose the departure planet. The default is Earth.
- Choose the destination. The default Mars gives a synodic period of 779.9 days.
- Read the transfer semi-major axis, the transfer time of 258.9 days and the phase angle of 44.3°.
- A negative phase angle means the destination must be behind the departure planet at launch, which happens for inward transfers.
- Use the Hohmann transfer calculator around the Sun, or the escape velocity calculator, to turn the trip into a Δv budget.
Questions from the flight desk
How often is there a launch window to Mars?
About every 26 months. Earth and Mars return to the same relative position every synodic period of about 780 days, 2.14 years. Each window lasts a few weeks around the best date. Because Mars’s orbit is elliptical, some windows need noticeably less energy than others, which repeats on a cycle of about 15 to 17 years.
What is the synodic period of a planet?
The time between successive identical alignments of two bodies as seen from the Sun, such as two oppositions of Mars. It follows from 1/S = |1/T₁ − 1/T₂|. For Earth and Mars it is 779.9 days, for Earth and Venus 583.9 days, and for Earth and Jupiter 398.9 days.
How long does it take to get to Mars?
A minimum-energy Hohmann transfer takes about 259 days, roughly eight and a half months. Real missions have ranged from about six to ten months depending on the window and how much extra launch energy they could afford. Faster trajectories need a larger departure burn and arrive faster, which also raises the braking requirement at Mars.
What is the phase angle for a Hohmann transfer?
The angle between the departure planet and the destination, measured around the Sun, at the moment of launch. For Earth to Mars it is about 44° with Mars ahead, so that Mars travels the remaining 136° while the spacecraft flies its half ellipse. For Earth to Venus Venus must be about 54° behind Earth.
Disclaimer: Orbital mechanics results are ideal two-body figures with instantaneous burns, computed from the values you enter and the constants stated on each page. They are not mission analysis, flight dynamics or launch safety advice. Real orbits are perturbed by Earth’s oblateness, the Moon, the Sun and atmospheric drag, and real burns carry gravity and steering losses. Never use these numbers to operate a spacecraft or to fly a rocket; follow the safety code of your rocketry association and the advice of qualified engineers.