Documentation / @interstellar-tools/equations / flightPathAngleFromTrueAnomaly

Function: flightPathAngleFromTrueAnomaly()

function flightPathAngleFromTrueAnomaly(nu: Radians, e: number): Radians;

Defined in: orbits/flight-path-angle-from-true-anomaly.ts:30

Flight-path angle ($\gamma$) from true anomaly ($\nu$) and eccentricity ($e$).

Definition

$$\tan \gamma =\frac{e\sin \nu }{1+e\cos \nu }$$

Domain notes

• Elliptic / circular ($0\le e<1$): since $1+e\cos \nu \ge 1-e>0$ for all $\nu$, we have $\gamma \in (-\frac{\pi }{2},\frac{\pi }{2})$.
• Parabolic ($e=1$): at $\nu =\pi$ the ratio is $0/0$; by continuity $\gamma \to 0$ (this function returns $0$ in that limit).
• Hyperbolic ($ e>1$ ): only $\nu$ with $1+e\cos \nu >0$ are physical; when $1+e\cos \nu =0$ the angle tends to $\pm \frac{\pi }{2}$.

Conventions

• Returns ($\gamma$) in radians (positive outbound $0<\nu <\pi$, negative inbound).
• Uses atan2(e sin ν, 1 + e cos ν) for correct quadrant handling and robust behavior near asymptotes.

Parameters

Parameter	Type	Description
nu	Radians	True anomaly ($\nu$) in radians; must be finite.
e	number	Eccentricity ($e$), dimensionless, must be finite and ≥ 0.

Returns

Radians

Flight-path angle ($\gamma$) in radians.

Throws

If inputs are non-finite or ($e<0$). Note: at the parabolic limit ($e=1,\nu =\pi$) this function returns $0$; at hyperbolic asymptotes ($1+e\cos \nu =0$) it tends to $\pm \pi /2$.