Keplerian Orbital Period
Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.
Description
An elliptic two-body orbital period is set by semimajor axis and the total gravitational parameter.
An elliptic two-body orbital period is set by semimajor axis and the total gravitational parameter. The semimajor axis is measured from the orbit geometry, not simply a surface altitude.1
Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.
When to use Keplerian Orbital Period
Use this tool to compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.
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 Orbital 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 mu, semimajorAxis using the field table and calculation rules, then run the tool.
- Read orbitalPeriod. 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 |
|---|---|---|---|
| mu | Gravitational parameter, using the same distance and time units throughout; km³/s² for km and seconds. | number | Required |
| semimajorAxis | Semimajor axis | number | Required |
Enter positive μ and semimajorAxis in compatible units. With μ in km³/s² and axis in km, the returned period is seconds. The helper evaluates Kepler's third law directly; it contains no planetary constants or date lookup.
period = 2π sqrt(semimajorAxis³/μ) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| orbitalPeriod | Orbital period | number |
{
"input": {
"mu": 1,
"semimajorAxis": 1
},
"output": {
"orbitalPeriod": 6.283185307179586
}
}Limitations and assumptions
This describes a closed elliptic two-body orbit, not a hyperbolic trajectory or a synodic period. Central-body clearance, perturbations and measurement uncertainty are separate questions.
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 Semimajor Axis From Period: Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.
References
-
Keplerian Orbital 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.
- Semimajor Axis From Period
Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.