Synodic Period Calculator (Time Between Oppositions and Conjunctions)
How often two bodies line up again as seen from the star or planet they orbit — the time between Mars oppositions, Venus conjunctions or two full moons — from their two orbital periods.
Results
The dashed line marks the value you entered.
What this tool does
The synodic period is the one you actually observe: the faster body gains a lap on the slower one every 1 ÷ |1 ÷ P₁ − 1 ÷ P₂|, which is longer than either orbit when the periods are close. Mars is at opposition from Earth about every 780 days — roughly 26 months — and Venus returns to the same place in our sky every 584 days. The Moon's cycle of phases, 29.53 days, is longer than its 27.32-day orbit for the same reason: the Earth has moved on around the Sun in the meantime.
Formula
1 ÷ S = |1 ÷ P₁ − 1 ÷ P₂| (S = time between two alignments)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
p1 | Orbital period of the first body | d |
p2 | Orbital period of the second body | d |
S | Synodic period | d |
SY | Synodic period in years | yr |
G | Angle one body gains on the other each day | °/d |
Worked example
- Orbital period of the first body365.256 d
- Orbital period of the second body686.98 d
- Synodic period779.93 d
- Synodic period in years2.135 yr
- Angle one body gains on the other each day0.4616 °/d
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.