Orbital Synodic Period
Compute a synodic alignment period from two same-direction sidereal periods; equal periods have no finite relative cycle.
Description
A synodic period describes the repetition of relative alignment between same-direction cycles.
A synodic period describes the repetition of relative alignment between same-direction cycles. It is governed by the difference of their cycle frequencies rather than the difference of their periods.1
Compute a synodic alignment period from two same-direction sidereal periods; equal periods have no finite relative cycle.
When to use Orbital Synodic Period
Use this tool to compute a synodic alignment period from two same-direction sidereal periods; equal periods have no finite relative cycle.
Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Orbital Synodic Period and understand its results
- Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter firstSiderealPeriod, secondSiderealPeriod using the field table and calculation rules, then run the tool.
- Read synodicPeriod, relativeCyclesPerTime. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| firstSiderealPeriod | First sidereal period | number | Required |
| secondSiderealPeriod | Second sidereal period | number | Required |
Supply positive sidereal periods in the same time unit. The tool subtracts their reciprocal frequencies and returns the positive magnitude and its reciprocal. Equal periods, or frequencies that become numerically indistinguishable, are errors because no finite relative cycle is represented.
relativeFrequency = |1/P1−1/P2|; synodicPeriod = 1/relativeFrequency Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| synodicPeriod | Synodic period | number |
| relativeCyclesPerTime | Relative cycles per time | number |
{
"input": {
"firstSiderealPeriod": 2,
"secondSiderealPeriod": 3
},
"output": {
"synodicPeriod": 5.999999999999999,
"relativeCyclesPerTime": 0.16666666666666669
}
}Limitations and assumptions
This assumes same-direction cycles and does not handle opposite-direction frequency addition or changing periods. It does not predict a dated conjunction.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Keplerian Two Body Period Ratio: Compare orbital periods around possibly different gravitating systems using semimajor axes and total gravitational parameters. For a complementary task, use Keplerian Orbital Period: Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.
References
-
Orbital Synodic Period — tool.io
Similar or alternative tools
- Keplerian Two Body Period Ratio
Compare orbital periods around possibly different gravitating systems using semimajor axes and total gravitational parameters.
- Keplerian Orbital Period
Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.