Orbital parameters¶

Source: AI/Tools/OrbitalParametersTools.cs

Conversions between Cartesian, Keplerian, equinoctial and equatorial representations, anomaly conversions, and closed-form summary quantities.

State-vector conversions¶

ConvertStateVectorToKeplerianElements¶

Parameter	Type
`stateVector`	`StateVector`

Returns the classical orbital elements (semi-major axis, eccentricity, inclination, RAAN, argument of periapsis, mean anomaly, perigee radius).

ConvertStateVectorToEquinoctialElements¶

Parameter	Type
`stateVector`	`StateVector`

Returns equinoctial elements (P, F, G, H, K, L0).

ConvertStateVectorToEquatorialCoordinates¶

Parameter	Type
`stateVector`	`StateVector`

Returns equatorial coordinates (right ascension, declination, distance, epoch). Implicitly transformed into ICRF.

ConvertKeplerianElementsToStateVector¶

Parameter	Type
`keplerianElements`	`KeplerianElements`

Returns the Cartesian state vector in the same frame and center-of-motion as the input.

ConvertEquinoctialElementsToStateVector¶

Parameter	Type
`equinoctialElements`	`EquinoctialElements`

Inverse of ConvertStateVectorToEquinoctialElements.

ConvertStateVectorToTheGivenFrame¶

Transform a state vector into another frame at its own epoch.

Parameter	Type
`stateVector`	`StateVector`
`frame`	`FramesEnum`

{
  "stateVector": {
    "centerOfMotion": "EARTH",
    "epoch": { "dateTime": "2024-01-01T00:00:00", "kind": "UTC" },
    "frame": "ICRF",
    "position": { "x": 7000000, "y": 0, "z": 0 },
    "velocity": { "x": 0, "y": 7500, "z": 0 }
  },
  "frame": "ITRF93"
}

ConvertKeplerianElementsToEquinoctialElements¶

Direct conversion that does not go through a state vector. Same parameter type as the Keplerian → state-vector tool.

ConvertEquinoctialElementsToKeplerianElements¶

Inverse of the previous tool.

Anomaly conversions¶

All four support elliptical (0 <= e < 1), parabolic (e ≈ 1) and hyperbolic (e > 1) regimes. Eccentricity must be non-negative.

Tool	Inputs
`ConvertMeanAnomalyToEccentricAnomaly`	`meanAnomaly` (rad), `eccentricity`
`ConvertEccentricAnomalyToTrueAnomaly`	`eccentricAnomaly` (rad), `eccentricity`
`ConvertMeanAnomalyToTrueAnomaly`	`meanAnomaly` (rad), `eccentricity`
`ConvertTrueAnomalyToMeanAnomaly`	`trueAnomaly` (rad), `eccentricity`

{ "meanAnomaly": 0.5, "eccentricity": 0.1 }

Summary quantities¶

ComputeOrbitalPeriod¶

Orbital period in seconds via Kepler's third law. Only valid for elliptical orbits (a > 0, e < 1).

Parameter	Type
`keplerianElements`	`KeplerianElements`

ComputeMeanMotion¶

Mean motion n = sqrt(mu / a^3) in radians per second. Elliptical only.

ComputeApsides¶

Apoapsis and periapsis radii in meters. Elliptical only.

Returns { apoapsis, periapsis }.

ComputeSpecificOrbitalEnergy¶

Specific orbital energy epsilon = v²/2 − mu/r in J/kg.

Parameter	Type
`stateVector`	`StateVector`

ComputeSpecificAngularMomentum¶

Specific angular momentum h = r × v in m²/s, expressed in the input frame.

Parameter	Type
`stateVector`	`StateVector`