Synodic Period Calculator
Find how often two bodies line up as seen from a common center, see the real dates of their recent and upcoming conjunctions, and for three or more, the synodic period of every pair. To find when planets actually line up, use the Planetary Alignment Calculator.
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Calculator
Pick a body from the list, or choose Custom… to type your own period. The period box stays grayed out and only becomes active when you choose Custom…. Add as many bodies as you like.
How often do the planets line up?
Every planet returns to the same alignment with Earth and the Sun on its own steady beat, its synodic period: how often a faster inner planet laps us, or how often we lap a slower outer planet. Here is how often each one lines up with Earth, worked out from the orbital periods in the table further down with the formula 1 / S = | 1 / P₁ − 1 / P₂ |:
| Planet | Synodic period (days) | In years | How often it lines up with Earth |
|---|---|---|---|
| Mercury | 115.88 | 0.32 | About every 4 months |
| Venus | 583.92 | 1.60 | About every 1.6 years |
| Mars | 779.93 | 2.14 | About every 2.1 years (about 26 months) |
| Jupiter | 398.88 | 1.09 | About every 13 months |
| Saturn | 378.09 | 1.04 | About every 12.4 months |
| Uranus | 369.66 | 1.01 | About every 12.1 months |
| Neptune | 367.49 | 1.01 | About every 12.1 months |
These are synodic periods relative to Earth, the time from one Earth line-up to the next. The outer planets all settle near a little over one year, because Earth laps each of them roughly once per Earth year. For any other pair, or three or more bodies at once, use the calculator above.
All the planets gathering at once is a different question. A single planet lines up with Earth on a clockwork schedule, but the planets never form a perfectly straight line, and several bright ones bunching into the same patch of sky (a planet parade) is much rarer. For the real upcoming groupings and where to look, see the Planet Parade Tracker; for the exact date a specific set of planets next lines up, use the Planetary Alignment Calculator.
What this calculator answers: how often two bodies line up, on average. That average gap between line-ups is the synodic period. For the real dates they line up, use the Planetary Alignment Calculator.
Reference tables
Synodic cycle table
Every pair's synodic period, how often the two bodies return to the same alignment, computed from their sidereal periods with the formula 1 / S = | 1 / P₁ − 1 / P₂ |. Read across a row and down a column to find a pair; the diagonal is blank because a body has no synodic period with itself. Choose a unit:
Synodic period in years (1 year = 365.25 days).
These ten are the classic set. For custom periods or extra bodies (Ceres, Chiron, Eris, the lunar nodes), use the calculator above.
Standard sidereal periods
Mean values used by the picker. The lunar nodes entry is the retrograde nodal cycle, included for cycle work.
| Body | Sidereal period (days) | Years |
|---|---|---|
| Mercury | 87.969 | 0.2408 |
| Venus | 224.701 | 0.6152 |
| Earth | 365.256 | 1.0000 |
| Mars | 686.980 | 1.8808 |
| Jupiter | 4,332.589 | 11.8620 |
| Saturn | 10,759.220 | 29.4571 |
| Uranus | 30,688.500 | 84.0205 |
| Neptune | 60,182.000 | 164.7693 |
| Pluto | 90,560.000 | 247.9398 |
| Moon (sidereal) | 27.322 | 0.0748 |
| Ceres | 1,681.630 | 4.6041 |
| Chiron | 18,413.000 | 50.4120 |
| Eris | 203,830.000 | 558.0561 |
| Lunar Nodes (regression) (retrograde nodal cycle, not an orbit) | 6,798.380 | 18.6130 |
How the synodic period is calculated
For the models, accuracy and data behind these figures, see the methodology and sources page.
The synodic period is the time for two orbiting bodies to return to the same relative alignment (for example, two planets lining up again as seen from the Sun). From their sidereal periods P₁ and P₂ it is:
1 / S = | 1 / P₁ − 1 / P₂ |
The faster body laps the slower one, and the absolute value makes the order of the two bodies irrelevant. The result is shown in both years and days (1 year = 365.25 days). If the two rates are equal there is no synodic period, because they never lap each other.
Synodic period vs sidereal period
These two are easy to mix up. The sidereal period is the true orbital period: the time a body takes to go once around the Sun against the fixed stars. The synodic period is the time between repeats of a configuration, such as one planet catching up to another as seen from a shared center. The calculator takes sidereal periods as input and returns a synodic period.
| Property | Sidereal period | Synodic period |
|---|---|---|
| Measured against | The fixed stars | Another moving body |
| Describes | One full orbit | Return to the same alignment |
| Mercury example | About 87.969 days | About 115.88 days from Earth |
| Used here as | Input (P) | Output (S) |
The synodic value can be longer or shorter than either orbit. Two bodies with nearly equal periods crawl past each other and take a long time to realign, while a fast inner body laps a slow outer body briskly. That is why Mercury's synodic period with Earth, about 115.88 days, is longer than its 87.969 day orbit.
Retrograde bodies (the lunar nodes)
Most bodies travel prograde. The lunar nodes travel retrograde, so when paired with a planet their relative speed is the sum of the two rates: 1/S = 1/P₁ + 1/P₂. For example, Jupiter and the lunar nodes realign about every 7.24 years, not the 32.7 years a plain difference would suggest.
Three or more bodies
For three or more bodies the calculator lists every pairwise synodic period, because that is what is well defined: each pair keeps its own rhythm. A single combined period for the whole group is not meaningful, since the bodies return to the exact same arrangement only on astronomical timescales. To find when a set of planets actually lines up in the sky, use the Planetary Alignment Calculator.
Worked example: Earth and Mars
Earth is about 365.256 days, Mars about 686.980 days.
1/S = |1/365.256 − 1/686.980| = 0.001282, so S is about 779.9 days, roughly 2.135 years. That matches the familiar 26 month spacing of Mars oppositions.
More worked examples
Each uses sidereal orbital periods and the formula above, with results rounded for readability.
Venus and Earth
Venus is about 224.701 days, Earth about 365.256 days.
1/S = |1/224.701 − 1/365.256|, so S is about 583.9 days, roughly 1.6 years. This is the rhythm behind Venus appearing as the morning and evening star.
Mercury and Earth
Mercury is about 87.969 days, Earth about 365.256 days.
1/S = |1/87.969 − 1/365.256|, so S is about 115.88 days, roughly 0.32 years. Because Mercury is fast and close to the Sun, it laps Earth several times a year.
Jupiter and Saturn: the great conjunction
Jupiter is about 4332.59 days, Saturn about 10759.22 days.
1/S = |1/4332.59 − 1/10759.22|, so S is about 7253 days, roughly 19.86 years. This is the great conjunction interval: the two largest planets line up about once every twenty years, most recently in December 2020.
Why synodic periods matter
A synodic period answers a practical question: how often does a sky event come back around? A few of the things it governs:
- Oppositions and conjunctions. An outer planet reaches opposition, its closest and brightest approach to Earth, once per synodic period. Mars does this about every 779.9 days, the familiar roughly 26 month spacing of good Mars viewing.
- Retrograde loops. A planet appears to slow, reverse, and loop backward against the stars once each synodic period, near opposition for outer planets. See which planets are retrograde right now.
- Launch windows. Mission planners aim for the part of the synodic cycle when two planets are best placed for a transfer, which is why Mars missions cluster about every 26 months.
- Long term cycle studies. Pairings such as Jupiter and Saturn realigning about every 19.86 years are used to study long rhythms in the solar system. For when several planets line up at once, see the Planetary Alignment Calculator.
In short, the sidereal period tells you how a body moves on its own, while the synodic period tells you how often you will see something happen.
Frequently asked questions
What is the difference between a synodic and a sidereal period?
The sidereal period is one full orbit against the fixed stars. The synodic period is the time for a body to return to the same alignment relative to another moving body, such as the Sun and Earth. This calculator takes sidereal periods in and gives a synodic period out.
Why can a planet's synodic period be longer than its orbit?
Because both bodies are moving. While the faster body completes an orbit, the slower one moves on too, so the faster body has to keep going to catch up to the same alignment. For bodies with close orbital speeds this takes a long time, which can make the synodic period far longer than either orbit.
What are the synodic periods of Venus, Mars, and Mercury?
As seen from Earth, Venus is about 583.9 days, Mars about 779.9 days, and Mercury about 115.88 days. You can reproduce any of these by entering the two sidereal periods above.
Why are Mars launch windows about 26 months apart?
Earth and Mars return to the same favorable alignment once per synodic period, about 779.9 days, which is roughly 26 months. That is when a transfer between the two planets needs the least energy, so missions cluster around it.
Are synodic periods exact?
No. Orbital periods are not whole numbers and vary slightly over time, so a synodic period is a mean value. Real intervals wobble around it, which is why successive Jupiter and Saturn conjunctions can fall anywhere from about 18 years 10 months to 20 years 8 months apart.
How often do all the planets line up?
The planets never line up in a perfectly straight row. Loose gatherings of several bright planets in the same part of the sky, often called a planet parade, happen roughly once a year; getting five or six naked-eye planets bunched together is rarer, about once or twice a decade. A tight alignment of all eight planets effectively never happens on human timescales. For the actual upcoming groupings, see the Planet Parade Tracker.
Do the planets ever line up in a straight line?
No, not a literal straight line. The orbits are tilted by a few degrees and the planets move at different speeds, so they spread out along the ecliptic rather than stacking into a row. A planetary alignment in the news means the planets appear loosely in the same region of the sky, not that they are geometrically in a line.
When is the next time all the planets align?
There is no meaningful date when all eight planets align, because a tight line-up of all of them does not happen on human timescales. What you can actually see are planet parades, when several bright planets gather in the same part of the sky. The next ones, with dates and where to look, are on the Planet Parade Tracker.
Keep exploring
Synodic vs Sidereal Periods
The two ways to time an orbit and the lapping formula behind every synodic period.
CalculatorPlanetary Alignment Calculator
When several planets gather in the same part of the sky, and how often it happens.
ConvergenceCycle Convergence and Resonance
How cycles drift in and out of phase, with any pair's beat period and nearest commensurability.
LearnRetrograde Motion
Why planets appear to loop backward as Earth and the planet lap one another, an effect of the synodic cycle.