Ellipse From Apsis Radii

Recover ellipse shape parameters from ordered center-referenced periapsis and apoapsis radii, not surface altitudes.

Description

Periapsis and apoapsis radii determine an ellipse's size and eccentricity.

Periapsis and apoapsis radii determine an ellipse's size and eccentricity. These lengths are measured from the central focus rather than from a body's surface.^[1]

Recover ellipse shape parameters from ordered center-referenced periapsis and apoapsis radii, not surface altitudes.

When to use Ellipse From Apsis Radii

Use this tool to recover ellipse shape parameters from ordered center-referenced periapsis and apoapsis radii, not surface altitudes.

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 Ellipse From Apsis Radii 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 periapsisRadius, apoapsisRadius using the field table and calculation rules, then run the tool.
Read semimajorAxis, orbitalEccentricity, 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
periapsisRadius	Periapsis radius	number	Required
apoapsisRadius	Apoapsis radius	number	Required

Enter positive periapsis and apoapsis radii in matching units, with apoapsis at least periapsis. The tool returns semimajor axis, dimensionless eccentricity and semilatus rectum. Equal radii give a circle with zero eccentricity.

a = (rp+ra)/2; e = (ra−rp)/(ra+rp); p = 2rp ra/(rp+ra)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
semimajorAxis	Semimajor axis	number
orbitalEccentricity	Orbital eccentricity	number
semilatusRectum	Semilatus rectum	number

json

{
  "input": {
    "periapsisRadius": 1,
    "apoapsisRadius": 3
  },
  "output": {
    "semimajorAxis": 2,
    "orbitalEccentricity": 0.5,
    "semilatusRectum": 1.5
  }
}

Limitations and assumptions

No gravity parameter, period, orientation or central-body radius is used. It does not infer orbital elements from position measurements or check physical clearance.

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 Elliptic Semilatus Rectum: Calculate the elliptic semilatus rectum from semimajor axis and eccentricity rather than measured apsis radii. For a complementary task, use Keplerian Orbital Period: Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.

References

Ellipse From Apsis Radii — tool.io

Similar or alternative tools

Elliptic Semilatus Rectum
Calculate the elliptic semilatus rectum from semimajor axis and eccentricity rather than measured apsis radii.
Keplerian Orbital Period
Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.