Tsiolkovsky rocket equation

He was the first to develop the Tsiolkovsky rocket equation, though it was not published widely for some years.

From this equation one can derive the Tsiolkovsky rocket equation.

This is known as the Tsiolkovsky rocket equation:

In rockets, the total velocity change can be calculated (using the Tsiolkovsky rocket equation) as follows:

Below this speed, motion is approximately described by Newtonian physics and the Tsiolkovsky rocket equation can be used.

It can cause confusion that the Tsiolkovsky rocket equation is similar to the relativistic force equation .

According to the Tsiolkovsky rocket equation, a rocket with higher exhaust velocity needs less propellant mass to achieve a given change of speed.

When is constant, the delta-v that a rocket vehicle can provide can be calculated from the Tsiolkovsky rocket equation:

Using this formula with as the varying mass of the rocket is mathematically equivalent to the derived Tsiolkovsky rocket equation, but this derivation is not correct.

With time reversed we have the situation of two objects pushed away from each other, e.g. shooting a projectile, or a rocket applying thrust (compare the derivation of the Tsiolkovsky rocket equation).

The Tsiolkovsky rocket equation shows that for a rocket with a given empty mass and a given amount of fuel, the total change in velocity it can accomplish is proportional to the effective exhaust velocity.

The Tsiolkovsky rocket equation shows that the delta-v of a rocket (stage), is proportional to the logarithm of the fuelled-to-empty mass ratio of the vehicle, and to the specific impulse of the rocket engine.

The ideal rocket equation, or the Tsiolkovsky rocket equation, can be used to study the motion of vehicles that behave like a rocket (where a body accelerates itself by ejecting part of its mass, a propellant, with high speed).

The conversion constant between the two versions of specific impulse is g. The higher the specific impulse, the lower the propellant flow rate required for a given thrust, and in the case of a rocket the less propellant is needed for a given delta-v per the Tsiolkovsky rocket equation.

The Tsiolkovsky rocket equation, or ideal rocket equation, describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself (a thrust) by expelling part of its mass with high speed and move due to the conservation of momentum.