Documentation / @interstellar-tools/equations / hyperbolicPeriapsisSpeed

Function: hyperbolicPeriapsisSpeed()

function hyperbolicPeriapsisSpeed(
  vInfinity: number,
  rp: number,
  mu: number
): number;

Defined in: orbits/hyperbolic-periapsis-speed.ts:35

Compute hyperbolic periapsis speed for a flyby/escape hyperbola.

Equation:

$$v_p=\sqrt{v_{\mathrm{\infty }}^2+\frac{2\mu }{r_p}}$$

Where:

• $v_{\mathrm{\infty }}$ is the hyperbolic excess speed (m/s or km/s)
• $\mu$ is the standard gravitational parameter of the central body (m³/s² or km³/s²)
• $r_p$ is the periapsis radius measured from the body's center (m or km)

Unit consistency is required:

• If $\mu$ is in m³/s², then $r_p$ must be in m and speeds are in m/s.
• If $\mu$ is in km³/s², then $r_p$ must be in km and speeds are in km/s.

Parameters

Parameter	Type	Description
vInfinity	number	Hyperbolic excess speed $v_{\mathrm{\infty }}$ (must be finite, >= 0).
rp	number	Periapsis radius $r_p$ from the central body's center (must be finite, > 0).
mu	number	Standard gravitational parameter $\mu$ (must be finite, > 0).

Returns

number

Periapsis speed $v_p$ in the same speed units as vInfinity.

Throws

If any input is not finite.

Throws

If vInfinity < 0, rp <= 0, or mu <= 0.

Example

// Earth example (km-based):
// mu = 398600.4418 km³/s², rp ~ 6678 km (LEO-ish), v∞ = 3.2 km/s
const vp = hyperbolicPeriapsisSpeed(3.2, 6678, 398600.4418);