Tsiolkovsky Rocket Equation

\[\Delta v=v_e\ln\left(\frac{m_0}{m_f}\right)\]

Variables

Dvdelta-v capability (m/s)

veeffective exhaust velocity (m/s)

m0initial mass including propellant (kg)

mffinal mass after propellant consumption (kg)

Description

What is this formula?

The Tsiolkovsky Rocket Equation calculates the theoretical change in velocity (delta-v) that a rocket can achieve based on its mass ratio and effective exhaust velocity.

It is one of the most fundamental equations in astronautics and rocket engineering.

When to use it

Use this equation when estimating spacecraft performance, rocket staging requirements, mission feasibility, or propellant requirements.

It is widely used in launch vehicle design, orbital mission planning, and deep-space mission analysis.

Example

A spacecraft has:

Initial mass = 50000 kg

Final mass = 10000 kg

Effective exhaust velocity = 3000 m/s

Formula:

Δv = ve × ln(m0/mf)

Substitution:

Δv = 3000 × ln(50000/10000)

Δv = 3000 × ln(5)

Δv = 4828 m/s

Result:

Delta-v = 4.83 km/s

Applications

Rocket design

Space mission planning

Launch vehicle analysis

Propellant budgeting

Spacecraft performance estimation

Astronautics

Note

The Tsiolkovsky Rocket Equation assumes ideal rocket operation in vacuum and neglects gravity losses, aerodynamic drag, steering losses, and engine performance variations. Real missions generally require more propellant than predicted by the ideal equation. Multi-stage rockets apply the equation separately to each stage.