Semimajor Axis From Period
Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.
Description
Kepler's third law connects a positive elliptic orbital period with semimajor axis in a two-body model.
Kepler's third law connects a positive elliptic orbital period with semimajor axis in a two-body model. The gravitational parameter should describe the relevant combined gravity rather than assuming a hard-coded central body.1
Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.
When to use Semimajor Axis From Period
Use this tool to invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.
Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Semimajor Axis From Period and understand its results
- Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter mu, orbitalPeriod using the field table and calculation rules, then run the tool.
- Read semimajorAxis. 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 |
| orbitalPeriod | Orbital period | number | Required |
Enter positive μ and orbitalPeriod with compatible distance/time units. The tool divides the period by 2π, squares it, multiplies by μ and takes the cube root. For μ in km³/s² and period in seconds, the result is km. It returns one positive-model semimajor-axis estimate rather than an orbital state.
semimajorAxis = cubeRoot[μ(period/(2π))²] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| semimajorAxis | Semimajor axis | number |
{
"input": {
"mu": 1,
"orbitalPeriod": 6.283185307179586
},
"output": {
"semimajorAxis": 1
}
}Limitations and assumptions
This does not apply a repeating period to parabolic or hyperbolic motion and does not model perturbations or an observed synodic period. It does not verify central-body clearance or derive eccentricity and inclination. Choose the appropriate total gravitational parameter.
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 Specific Orbital Energy: Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety. For a complementary task, use Tisserand Orbital Parameter: Compute a circular restricted-three-body Tisserand parameter in the supplied planet frame; no universal comet taxonomy cutoff is embedded.
References
-
Semimajor Axis From Period — tool.io
Similar or alternative tools
- Specific Orbital Energy
Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety.
- Tisserand Orbital Parameter
Compute a circular restricted-three-body Tisserand parameter in the supplied planet frame; no universal comet taxonomy cutoff is embedded.