Documentation / @interstellar-tools/equations / rocketDeltaVFromIsp

Function: rocketDeltaVFromIsp()

function rocketDeltaVFromIsp(
  Isp: number,
  m0: number,
  mf: number,
  g0?: number
): number;

Defined in: manoeuvres/rocket-delta-v-from-isp.ts:45

Compute ideal delta-v from the Tsiolkovsky rocket equation using specific impulse.

$$\mathrm{\Delta }v=g_0{I}_{sp}\ln \left(\frac{m_0}{m_f}\right)$$

Where:

• $I_{sp}$ is the specific impulse (s)
• $g_0$ is standard gravity (m/s²)
• $m_0$ is initial (wet) mass before the burn (kg)
• $m_f$ is final (dry / post-burn) mass after the burn (kg)

Units

• Inputs: Isp in s, g0 in m/s², masses in kg.
• Output: $\mathrm{\Delta }v$ in m/s.

Notes

• This is the ideal rocket equation (no gravity/drag losses, finite burn effects, steering losses, etc.).
• g0 defaults to 9.80665 m/s² (standard gravity).
• Requires mf < m0 to yield a positive delta-v.

Parameters

Parameter	Type	Default value	Description
Isp	number	undefined	Specific impulse $I_{sp}$ in seconds (finite, > 0).
m0	number	undefined	Initial mass $m_0$ in kg (finite, > 0).
mf	number	undefined	Final mass $m_f$ in kg (finite, > 0 and < m0).
g0	number	9.80665	Standard gravity $g_0$ in m/s² (finite, > 0). Defaults to 9.80665.

Returns

number

Ideal delta-v $\mathrm{\Delta }v$ in m/s.

Throws

If any input is not a finite number.

Throws

If Isp <= 0, g0 <= 0, m0 <= 0, mf <= 0, or mf >= m0.

Example

// Example:
// Isp = 320 s, m0 = 1200 kg, mf = 800 kg
const dv = rocketDeltaVFromIsp(320, 1200, 800);
// dv ≈ 9.80665 * 320 * ln(1200/800) ≈ 1270 m/s

See

https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation Tsiolkovsky rocket equation (background and derivation)