Documentation / @interstellar-tools/equations / gravityAssistTurningAngle

Function: gravityAssistTurningAngle()

function gravityAssistTurningAngle(
  rp: number,
  vInfinity: number,
  mu: number
): Radians;

Defined in: manoeuvres/gravity-assist-turning-angle.ts:36

Compute gravity-assist turning angle (flyby deflection) for a hyperbolic encounter.

Equation:

$$\delta =2\arcsin \left(\frac{1}{1+\frac{r_p{v}_{\mathrm{\infty }}^2}{\mu }}\right)$$

Where:

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

Unit consistency is required:

• If $\mu$ is in m³/s², then $r_p$ must be in m and $v_{\mathrm{\infty }}$ in m/s.
• If $\mu$ is in km³/s², then $r_p$ must be in km and $v_{\mathrm{\infty }}$ in km/s.

Parameters

Parameter	Type	Description
rp	number	Periapsis radius $r_p$ (finite, > 0).
vInfinity	number	Hyperbolic excess speed $v_{\mathrm{\infty }}$ (finite, >= 0).
mu	number	Standard gravitational parameter $\mu$ (finite, > 0).

Returns

Radians

Turning angle $\delta$ in radians (range: 0 to π).

Throws

If any input is not finite.

Throws

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

Example

// Example (km-based):
// rp = 7000 km, v∞ = 8 km/s, mu(Earth) = 398600.4418 km³/s²
const delta = gravityAssistTurningAngle(7000, 8, 398600.4418);
// delta is in radians