Documentation / @interstellar-tools/equations / specificAngularMomentumFromElements

Function: specificAngularMomentumFromElements()

function specificAngularMomentumFromElements(
  a: number,
  e: number,
  mu: number
): number;

Defined in: orbits/specific-angular-momentum-from-elements.ts:59

Specific angular momentum ($h$) from orbital elements.

Definition

$$h=\sqrt{\mu a(1-e^2)}$$

where ($a$) is the semi-major axis, ($e$) the eccentricity, and ($\mu$) the gravitational parameter.

Validity by conic

• Elliptic: ($a>0,0\le e<1$) → ($1-e^2>0$) ⇒ radicand ($>0$).
• Hyperbolic: ($a<0,e>1$) → ($1-e^2<0$) and ($a<0$) ⇒ product still ($>0$).
• Parabolic: ($e=1$) is not represented by finite ($a$). Use state vectors or ($h=\sqrt{2\mu r_p}$) (with periapsis radius ($r_p$)).

Units

• Inputs: ($a$) in m, ($e$) dimensionless, ($\mu$) in m³/s².
• Output: ($h$) in m²/s.

INFO

• This returns the magnitude of ($\mathbf{h}=\mathbf{r}\times \mathbf{v}$).
• For numerical robustness, tiny negative radicands from FP cancellation are clamped to zero.

Parameters

Parameter	Type	Description
a	number	Semi-major axis ($a$) (m). Must be finite and ≠ 0 (elliptic ($a>0$), hyperbolic ($a<0$)).
e	number	Eccentricity ($e$) (dimensionless). Must be finite and ≥ 0.
mu	number	Gravitational parameter ($\mu$) (m³/s²). Must be finite and ≥ 0.

Returns

number

Specific angular momentum ($h$) (m²/s).

Throws

Error If ($a$) is non-finite or zero; if ($e$) is non-finite or negative; if ($\mu$) is non-finite or negative; or if ($\mu a(1-e²)<0$) beyond a tiny FP tolerance (invalid element set for this formula).

Examples

// Near-circular LEO-like elements
const muEarth = 3.986004418e14; // m³/s²
const a = 6778e3; // m
const e = 0.001;
const h = specificAngularMomentumFromElements(a, e, muEarth); // ≈ sqrt(μ a)

// Hyperbolic flyby example
const muEarth = 3.986004418e14; // m³/s²
const a = -50000e3; // m (negative for hyperbola)
const e = 1.2;
const h = specificAngularMomentumFromElements(a, e, muEarth);

See

specificAngularMomentum - compute ($h$) from state vectors ($(\mathbf{r},\mathbf{v})$).