Orbits and elements

The server lets you cross between Cartesian, Keplerian and equinoctial representations and ask for summary quantities (period, mean motion, apsides, energy).

From state vector to Keplerian elements

{
  "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 }
  }
}

Tool: ConvertStateVectorToKeplerianElements. Returns { semiMajorAxis, eccentricity, inclination, rightAscensionOfAscendingNode, argumentOfPeriapsis, meanAnomaly, perigeeRadius, … }.

From Keplerian to state vector

The inverse direction is ConvertKeplerianElementsToStateVector. ISS-like LEO:

{
  "keplerianElements": {
    "centerOfMotion": "EARTH",
    "epoch": { "dateTime": "2024-01-01T00:00:00", "kind": "UTC" },
    "frame": "ICRF",
    "semiMajorAxis": 6778000,
    "eccentricity": 0.0001,
    "inclination": 0.9006,
    "rightAscensionOfAscendingNode": 0.0,
    "argumentOfPeriapsis": 0.0,
    "meanAnomaly": 0.0
  }
}

Period and mean motion

{
  "keplerianElements": {
    "centerOfMotion": "EARTH",
    "epoch": { "dateTime": "2024-01-01T00:00:00", "kind": "UTC" },
    "frame": "ICRF",
    "semiMajorAxis": 6778000,
    "eccentricity": 0.0001,
    "inclination": 0.9006,
    "rightAscensionOfAscendingNode": 0,
    "argumentOfPeriapsis": 0,
    "meanAnomaly": 0
  }
}

Tools: ComputeOrbitalPeriod (seconds), ComputeMeanMotion (rad/s), ComputeApsides (apoapsis/periapsis in meters). All require elliptical orbits (a > 0, e < 1).

Equinoctial elements

Equinoctial elements are well-defined at zero eccentricity and zero inclination — useful for low-eccentricity or near-equatorial orbits. The conversions are ConvertStateVectorToEquinoctialElements, ConvertEquinoctialElementsToStateVector, ConvertKeplerianElementsToEquinoctialElements, ConvertEquinoctialElementsToKeplerianElements.

Anomalies

To navigate between mean / eccentric / true anomaly without going through a state vector, use ConvertMeanAnomalyToEccentricAnomaly, ConvertMeanAnomalyToTrueAnomaly, ConvertEccentricAnomalyToTrueAnomaly, ConvertTrueAnomalyToMeanAnomaly. All support elliptical, parabolic and hyperbolic regimes.

Specific energy and angular momentum

ComputeSpecificOrbitalEnergy and ComputeSpecificAngularMomentum work from a single state vector. The angular momentum vector is expressed in the same frame as the input.