Documentation / @interstellar-tools/equations / circularSpeed

Function: circularSpeed()

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

Defined in: orbits/circular-speed.ts:55

Circular speed ($v_c$) for a body in a circular orbit at radius ($r$).

Definition

$$v_c=\sqrt{\frac{\mu }{r}}$$

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

Units

• Inputs: ($r$) in meters (m), ($\mu$) in m³/s².
• Output: ($v_c$) in m/s.

INFO

• This is the special case of the vis-viva equation for circular orbits (($a=r$)).
• If you need a non-circular orbit, use visVivaSpeed(r, a, mu).

In practiceThe International Space Station

7.66 km/s

Circular speed at 420 km altitude

That's about 27 600 km/h, fast enough to circle Earth every 93 minutes.

circularSpeed(6.371e6 + 420e3, 3.986004418e14); // ≈ 7661 m/s

Parameters

Parameter	Type	Description
r	number	Orbital radius ($r$) (m), must be finite and > 0.
mu	number	Gravitational parameter ($\mu$) (m³/s²), must be finite and ≥ 0.

Returns

number

Circular speed ($v_c$) (m/s).

Throws

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

See

visVivaSpeed

Example

// LEO ~400 km altitude around Earth
const muEarth = 3.986004418e14; // m³/s²
const r = 6378e3 + 400e3; // m
const v = circularSpeed(r, muEarth); // ≈ 7670 m/s