Documentation / @interstellar-tools/equations / escapeSpeed

Function: escapeSpeed()

function escapeSpeed(r: number, mu: number): number;

Defined in: orbits/escape-speed.ts:65

Escape speed ($v_{\text{esc}}$) - minimum speed to escape a central body's gravity from radius ($r$) (ignoring drag/perturbations).

Definition

$$v_{\text{esc}}=\sqrt{\frac{2\mu }{r}}$$

where ($\mu$) is the standard gravitational parameter and ($r$) is the distance from the central body's center.

Units

• Inputs: ($r$) in meters (m), ($\mu$) in m³/s².
• Output: ($v_{\text{esc}}$) in m/s.

INFO

• Relationship to circular speed ($v_c$): ($v_{\text{esc}}=\sqrt{2}{v}_c$).
• This corresponds to parabolic specific energy (($\epsilon =0$)).
• For general (non-escape) orbital speed use visVivaSpeed(r, a, mu).

In practiceLeaving Earth

11.19 km/s

Escape speed at Earth's surface

That's √2 times the 7.91 km/s it takes to orbit just above the surface, which is why a rocket for the Moon or Mars is so much bigger than one for low Earth orbit.

escapeSpeed(6.371e6, 3.986004418e14); // ≈ 11 186 m/s

Parameters

Parameter	Type	Description
r	number	Radius ($r$) (m), distance from the central body’s center (must be finite and > 0).
mu	number	Gravitational parameter ($\mu$) (m³/s²), must be finite and ≥ 0.

Returns

number

Escape speed ($v_{\text{esc}}$) (m/s).

Throws

Error If inputs are non-finite or out of domain.

Examples

// Near Earth's surface (approx.)
const muEarth = 3.986004418e14; // m³/s²
const rSurface = 6378e3; // m
const vEsc = escapeSpeed(rSurface, muEarth); // ≈ 11186 m/s

// LEO ~400 km altitude: r = R_E + 400 km
const muEarth = 3.986004418e14;
const rLEO = 6378e3 + 400e3;
const vEsc = escapeSpeed(rLEO, muEarth); // ≈ 10860 m/s