How this calculator works
Synodic period measures how often the relative orbital angle repeats. For same-direction motion, the relative angular rate is the difference of the two mean rates. Opposite-direction rates add. Inverting the same-direction relation needs a branch because the unknown orbit may move faster or slower than the known orbit. Preset sidereal periods are rounded reference values, not precise predictions of observed conjunction dates in eccentric orbits.
Formula
1/S = |1/P1-1/P2| for the same direction. For opposite directions, 1/S = 1/P1+1/P2. Inverse same-direction rate: 1/Punknown = 1/Pknown plus or minus 1/S.
Worked example
Periods 10 s and 20 s in the same direction give S = 20 s. With reference period 10 s and S = 20 s, the faster inverse branch gives target period 6.666667 s.
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Frequently asked questions
Why does the inverse have two branches?
The same relative rate can arise from an orbit that is faster or slower than the known orbit.
What if both sidereal periods match?
For same-direction motion the relative angle is constant and no finite repetition interval is determined.
Does this predict the date of the next conjunction?
No. You also need an initial phase, and precise predictions require the actual orbital geometry.