Tsiolkovsky rocket equation

Tsiolkovsky's rocket equation, named after Konstantin Tsiolkovsky who first derived it, states that for a simple rocket in the absence of gravity or drag forces:

where the mass of the rocket during lift-off, is the mass of the empty rocket without its fuel, but including the payload mass, the initial rocket velocity, the final rocket velocity and the velocity of the rocket exhaust.

The equation is obtained by integrating the equation of motion for a simple rocket that emits mass at a constant rate and velocity for its entire burn, and noting that in this case all the irrelevant constants such as the density of the fuel simply cancel out from the final result. The difference is known as (delta V).

Although an extreme simplification, the rocket equation captures the essentials of rocket flight physics in a single short equation. It happens that delta V is one of the most important quantities in orbital mechanics, that quantifies how difficult it is to get from one trajectory to another.

Clearly, to achieve a large delta V, either must be huge (growing exponentially as delta V rises), or must be tiny, or must be very high, or some combination of all of these.

In practice, this has been achieved by using very large rockets (increasing ), with multiple stages (decreasing ), and rockets with very high exhaust velocities. The Saturn V rockets used in the Apollo space program are a good example of this.

See also

• Spacecraft propulsion
• Specific impulse