Elliptic Semilatus Rectum
Calculate the elliptic semilatus rectum from semimajor axis and eccentricity rather than measured apsis radii.
Description
The semilatus rectum is the conic's scale in its polar radius equation.
The semilatus rectum is the conic's scale in its polar radius equation. For an ellipse it is smaller than or equal to the semimajor axis, with equality at zero eccentricity.1
Calculate the elliptic semilatus rectum from semimajor axis and eccentricity rather than measured apsis radii.
When to use Elliptic Semilatus Rectum
Use this tool to calculate the elliptic semilatus rectum from semimajor axis and eccentricity rather than measured apsis radii.
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 Elliptic Semilatus Rectum 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 semimajorAxis, orbitalEccentricity using the field table and calculation rules, then run the tool.
- Read semilatusRectum. 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 |
| orbitalEccentricity | Orbital eccentricity | number | Required |
Enter positive semimajor axis and eccentricity from 0 inclusive to 1 exclusive. The tool computes the elliptic scale directly and returns it in the axis's unit. Zero eccentricity returns the semimajor axis.
semilatusRectum = semimajorAxis × (1−eccentricity²) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| semilatusRectum | Semilatus rectum | number |
{
"input": {
"semimajorAxis": 2,
"orbitalEccentricity": 0.5
},
"output": {
"semilatusRectum": 1.5
}
}Limitations and assumptions
This does not estimate elements from measured radii or support parabolic/hyperbolic semimajor-axis conventions. Surface altitude must not be substituted for a center-referenced orbital element.
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 Ellipse From Apsis Radii: Recover ellipse shape parameters from ordered center-referenced periapsis and apoapsis radii, not surface altitudes. For a complementary task, use Conic Flight Path Angle: Compute the conic flight-path angle with a physical positive-radius anomaly constraint for elliptic, parabolic, or hyperbolic eccentricity.
References
-
Elliptic Semilatus Rectum — tool.io
Similar or alternative tools
- Ellipse From Apsis Radii
Recover ellipse shape parameters from ordered center-referenced periapsis and apoapsis radii, not surface altitudes.
- Conic Flight Path Angle
Compute the conic flight-path angle with a physical positive-radius anomaly constraint for elliptic, parabolic, or hyperbolic eccentricity.