Sidereal and synodic periods
A planet’s sidereal period is the time it takes to orbit the Sun once relative to the stars. Seen from Earth, which is moving too, events like oppositions or conjunctions repeat on a different rhythm: the synodic period, the time for the two bodies to return to the same alignment with the Sun.
The formula
1 ÷ S = |1 ÷ P1 − 1 ÷ P2|
where P1 and P2 are the two sidereal periods. The closer the two periods, the longer the synodic period.
Example: Mars
Earth orbits in 365.26 days and Mars in 687 days:
- 1/S = 1/365.26 − 1/687 ≈ 0.001282 per day;
- S ≈ 780 days, about 2 years and 2 months.
That is why Mars is best placed for observation, and for launching spacecraft, about every 26 months.
Other synodic periods seen from Earth
| Planet | Sidereal period | Synodic period |
|---|---|---|
| Mercury | 88 days | 116 days |
| Venus | 225 days | 584 days |
| Mars | 687 days | 780 days |
| Jupiter | 11.86 years | 399 days |
| Saturn | 29.46 years | 378 days |
Distant planets have synodic periods just over a year: Earth catches up with them a little more than once a year.
The Moon’s month
The same formula explains the lunar month. The Moon orbits Earth in 27.32 days relative to the stars, but because Earth moves around the Sun meanwhile, the time from new moon to new moon is:
1/S = 1/27.32 − 1/365.26, so S ≈ 29.53 days, the synodic month.
Other uses
- Satellites: the time between passes of a satellite over a rotating planet.
- Clock hands: the hour and minute hands overlap every 1/(1/1 − 1/12) = 12/11 hours, about every 65.5 minutes.
- Runners on a track: a faster runner laps a slower one at the synodic interval of their lap times.