Keplerian Two Body Period Ratio
Compare orbital periods around possibly different gravitating systems using semimajor axes and total gravitational parameters.
Description
Keplerian period ratios depend on both orbital sizes and gravitational parameters.
Keplerian period ratios depend on both orbital sizes and gravitational parameters. The familiar semimajor-axis power law alone applies only when the two systems share the same gravity parameter.1
Compare orbital periods around possibly different gravitating systems using semimajor axes and total gravitational parameters.
When to use Keplerian Two Body Period Ratio
Use this tool to compare orbital periods around possibly different gravitating systems using semimajor axes and total gravitational parameters.
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 Keplerian Two Body Period Ratio 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 firstSemimajorAxis, secondSemimajorAxis, firstMu, secondMu using the field table and calculation rules, then run the tool.
- Read secondFirstPeriodRatio. 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 |
|---|---|---|---|
| firstSemimajorAxis | First semimajor axis | number | Required |
| secondSemimajorAxis | Second semimajor axis | number | Required |
| firstMu | First mu | number | Required |
| secondMu | Second mu | number | Required |
Enter positive semimajor axes in a shared distance unit and positive total gravitational parameters in matching distance/time units. The tool returns the dimensionless second-to-first period ratio. Equal axes and equal parameters yield one.
P2/P1 = (a2/a1)^1.5 × sqrt(μ1/μ2) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| secondFirstPeriodRatio | Second first period ratio | number |
{
"input": {
"firstSemimajorAxis": 1,
"secondSemimajorAxis": 4,
"firstMu": 1,
"secondMu": 4
},
"output": {
"secondFirstPeriodRatio": 4
}
}Limitations and assumptions
This compares two-body elliptic periods rather than synodic alignments. Perturbations and uncertainties are not propagated, and different unit systems cannot be mixed.
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 Orbital Period: Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup. For a complementary task, use Orbital Synodic Period: Compute a synodic alignment period from two same-direction sidereal periods; equal periods have no finite relative cycle.
References
-
Keplerian Two Body Period Ratio — tool.io
Similar or alternative tools
- Keplerian Orbital Period
Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.
- Orbital Synodic Period
Compute a synodic alignment period from two same-direction sidereal periods; equal periods have no finite relative cycle.