Documentation / @interstellar-tools/equations / eccentricitySquaredOblateSpheroid

Function: eccentricitySquaredOblateSpheroid()

function eccentricitySquaredOblateSpheroid(a: number, c: number): number;

Defined in: cartography/eccentricity-squared-oblate-spheroid.ts:39

Compute first eccentricity squared ($e^2$) for an oblate spheroid.

The first eccentricity describes how much an oblate spheroid (ellipsoid of revolution) deviates from a perfect sphere. For equatorial radius ($a$) and polar radius ($c$):

$$e^2=1-\frac{c^2}{a^2}$$

Notes:

• ($e^2$) is dimensionless.
• For a physically valid oblate spheroid with ($a\ge c>0$), ($0\le e^2<1$).
• This quantity is widely used in geodesy and mapping formulas (e.g., planetographic latitude, geodetic coordinates, map projections).

Parameters

Parameter	Type	Description
a	number	Equatorial radius ($a$) (finite, > 0).
c	number	Polar radius ($c$) (finite, > 0).

Returns

number

First eccentricity squared ($e^2$) (dimensionless).

Throws

If a or c is not a finite number.

Throws

If a <= 0 or c <= 0.

Example

// Earth (WGS84-ish radii in meters):
const a = 6378137.0;
const c = 6356752.314245;
const e2 = eccentricitySquaredOblateSpheroid(a, c);

See

• https://en.wikipedia.org/wiki/Eccentricity\_(mathematics)#Ellipses_and_ellipsoids Eccentricity for ellipses/ellipsoids (includes first eccentricity)
• https://en.wikipedia.org/wiki/Reference_ellipsoid Reference ellipsoid (geodesy context; uses a, b and eccentricity)
• https://epsg.org/guidance-notes.html EPSG Guidance Notes (geodesy reference; ellipsoid parameters and derived quantities)