Documentation / @interstellar-tools/equations / planetocentricLatitude

Function: planetocentricLatitude()

function planetocentricLatitude(x: number, y: number, z: number): number;

Defined in: cartography/planetocentric-latitude.ts:37

Compute planetocentric latitude (${\phi }_c$) from body-fixed Cartesian coordinates.

Planetocentric latitude is defined as the angle between the body's equatorial plane and the radius vector from the body's center of mass to the point:

$${\phi }_c=\arctan \left(\frac{z}{\sqrt{x^2+y^2}}\right)$$

Implementation note:

• This uses atan2(z, hypot(x,y)) for numerical stability and correct quadrant handling.

Parameters

Parameter	Type	Description
x	number	X coordinate in a body-fixed frame (finite).
y	number	Y coordinate in a body-fixed frame (finite).
z	number	Z coordinate in a body-fixed frame (finite).

Returns

number

Planetocentric latitude (${\phi }_c$) in radians (range: ($[-\pi /2,\pi /2]$)).

Throws

If any input is not a finite number.

Example

// Point directly above the equator on +X axis:
const phi = planetocentricLatitude(1, 0, 0);
// phi === 0

// Point on +Z axis:
const northPole = planetocentricLatitude(0, 0, 1);
// northPole === Math.PI / 2

See

• https://en.wikipedia.org/wiki/Planetary_coordinate_system Planetary coordinate system (definitions of planetocentric vs. planetographic latitude)
• https://planetarynames.wr.usgs.gov/Page/Website USGS Planetary Names (planetocentric latitude definition)
• https://pds.nasa.gov/datastandards/pds3/standards/sr/Chapter02.pdf NASA PDS Standards Reference (planetocentric latitude defined as angle to the center-of-mass vector)
• https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/individual_docs/17_frames_and_coordinate_systems.pdf NAIF SPICE tutorial: Frames and Coordinate Systems (planetocentric/body-fixed frame conventions)