Tisserand Orbital Parameter
Compute a circular restricted-three-body Tisserand parameter in the supplied planet frame; no universal comet taxonomy cutoff is embedded.
Description
The Tisserand parameter combines a small body's orbital size, eccentricity and inclination relative to a planet in a circular restricted three-body approximation.
The Tisserand parameter combines a small body's orbital size, eccentricity and inclination relative to a planet in a circular restricted three-body approximation. The reference planet and the inclination frame are therefore part of the supplied model.1
Compute a circular restricted-three-body Tisserand parameter in the supplied planet frame; no universal comet taxonomy cutoff is embedded.
When to use Tisserand Orbital Parameter
Use this tool to compute a circular restricted-three-body Tisserand parameter in the supplied planet frame; no universal comet taxonomy cutoff is embedded.
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 Tisserand Orbital Parameter 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 semimajorAxis, eccentricity, inclinationDegrees, planetSemimajorAxis using the field table and calculation rules, then run the tool.
- Read tisserandValue. 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 |
|---|---|---|---|
| semimajorAxis | Semimajor axis | number | Required |
| eccentricity | Eccentricity | number | Required |
| inclinationDegrees | Inclination degrees | number | Required |
| planetSemimajorAxis | Planet semimajor axis | number | Required |
Enter positive body and planet semimajor axes in matching distance units, eccentricity from 0 inclusive to 1 exclusive, and inclination from 0 through 180 degrees. The helper converts inclination to radians and evaluates the dimensionless expression. A circular coplanar orbit with equal semimajor axes gives 3.
T = a_planet/a + 2 cos(i) √[(a/a_planet)(1−e²)] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| tisserandValue | Tisserand value | number |
{
"input": {
"semimajorAxis": 1,
"eccentricity": 0,
"inclinationDegrees": 0,
"planetSemimajorAxis": 1
},
"output": {
"tisserandValue": 3
}
}Limitations and assumptions
This does not read orbital elements, propagate encounters or apply a universal comet-classification threshold. Hyperbolic/parabolic body elements are outside the accepted domain. Frame mismatches or inconsistent distance units invalidate interpretation even if numeric validation succeeds.
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 State Eccentricity Vector: Derive the eccentricity vector and mathematical conic class from a nonradial two-body Cartesian state; floating values near one require physical uncertainty assessment. 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
-
Tisserand Orbital Parameter — tool.io
Similar or alternative tools
- State Eccentricity Vector
Derive the eccentricity vector and mathematical conic class from a nonradial two-body Cartesian state; floating values near one require physical uncertainty assessment.
- Semimajor Axis From Period
Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.