Coordinate conversions

Rotate a vector between frames

GetFrameRotationMatrix returns a 3×3 rotation matrix. Use it to rotate any vector expressed in one frame into another at a specific epoch.

{
  "fromFrame": "ICRF",
  "toFrame": "ITRF93",
  "datetime": "2024-01-01T00:00:00"
}

For state vectors (position + velocity) use GetFrameStateRotationMatrix to get both R and dR/dt. They form the 6×6 state-transition matrix [[R, 0], [dR/dt, R]].

Transform a state vector directly

If you already have a StateVector, the simplest path is ConvertStateVectorToTheGivenFrame, which does the rotation and the velocity correction for you.

{
  "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"
}

Equatorial coordinates (RA / Dec)

For astronomical pointing, ConvertStateVectorToEquatorialCoordinates returns right ascension (rad), declination (rad), distance (m), and the epoch. The state vector is implicitly rotated into ICRF first.

Body-fixed Cartesian ↔ planetodetic

Working on the ground? Use ConvertPlanetodeticToCartesian and ConvertCartesianToPlanetodetic — both pick up the body's equatorial radius and flattening automatically.

{
  "body": "EARTH",
  "latitude": 0.7853981633974483,
  "longitude": 0.0,
  "altitude": 0.0
}

Time-scale conversions

Same idea on the time axis. ConvertDateTime switches between UTC, TDB, TAI, TDT, GPS and Local. ConvertToJulianDate, ConvertToModifiedJulianDate, and ConvertToEphemerisTime are also available. See Time.