Documentation / @interstellar-tools/equations / periApoapsisRadii

Function: periApoapsisRadii()

function periApoapsisRadii(a: number, e: number): PeriApoRadiiType;

Defined in: orbits/peri-apoapsis-radii.ts:65

Peri/apoapsis radii from semi-major axis ($a$) and eccentricity ($e$).

Definitions

$$r_p=a(1-e),r_a=a(1+e)$$

Conic validity

• Elliptic / circular: ($a>0,0\le e<1$) → ($r_p>0$) and ($r_a>0$).
• Hyperbolic: ($a<0,e>1$) → ($r_p=a(1-e)=|a|(e-1)>0$), no apoapsis (unbounded), so ($r_a=null$).
• Parabolic: ($e=1$) is not defined with finite ($a$). Use the parabolic form (e.g. ($r_p=\frac{p}{2}$)) or state vectors.

Units

• Inputs: ($a$) in meters (m), ($e$) dimensionless.
• Output: ($r_p,r_a$) in meters (m).

In practiceMolniya orbit

545 km / 39 913 km

Altitude at perigee and apogee

With e = 0.74, a Molniya satellite races through perigee and spends most of its 12 hour orbit slowly crossing apogee, high above the northern latitudes it serves.

periApoapsisRadii(26600e3, 0.74);
// rp = 6 916 km, ra = 46 284 km from Earth's centre

Parameters

Parameter	Type	Description
a	number	Semi-major axis ($a$) (m). Must be finite and ≠ 0.
e	number	Eccentricity ($e$) (dimensionless). Must be finite and ≥ 0.

Returns

PeriApoRadiiType

Object with periapsis rp and apoapsis ra (or null if undefined for hyperbolic).

Throws

Error If inputs are invalid or the ($(a,e)$) pair does not correspond to an ellipse/circle or hyperbola with finite ($a$).

Examples

// Elliptic example (LEO-like)
const a = 7000e3; // m
const e = 0.01;
const { rp, ra } = periApoapsisRadii(a, e); // rp ≈ 6930 km, ra ≈ 7070 km

// Hyperbolic flyby (no apoapsis)
const a = -50_000e3; // m
const e = 1.2;
const { rp, ra } = periApoapsisRadii(a, e); // rp = |a|(e-1) = 10,000 km, ra = null