The Universe is governed by the laws of physics that cannot be changed by us. As such, there are hard limits to what we can do with rockets and how we build them. The working of rockets is governed by the Tsiolkovsky rocket equation, named after the rocket scientist Konstantin Tsiolkovsky.

Tsiolkovsky Rocket Equation

The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the conservation of momentum.

The forces on a rocket change dramatically during a typical flight. During powered flight, the propellants of the propulsion system are constantly being exhausted from the nozzle. As a result, the weight and mass of the rocket is constantly changing. Because of the changing mass, we cannot use the standard form of Newton's second law of motion to determine the acceleration and velocity of the rocket.

It basically says that the increase in speed of a spacecraft is:

v_e ln (m_i/m_f)

where v_e is the exhaust velocity or velocity of the expelled gases, and m_i/m_f is the ratio between initial and final mass.

In the case of a rocket leaving the Earth, part of the thrust is expended in pushing against gravity.

From the ideal rocket equation, 90% of the weight of a rocket going to orbit is propellant weight. The remaining 10% of the weight includes structure, engines, and payload. So given the current state-of-the-art, the payload accounts for only about 1% of the weight of an ideal rocket at launch. Rockets are terribly inefficient and expensive.

Applicability

The rocket equation captures the essentials of rocket flight physics in a single short equation. It also holds true for rocket-like reaction vehicles whenever the effective exhaust velocity is constant, and can be summed or integrated when the effective exhaust velocity varies. The rocket equation only accounts for the reaction force from the rocket engine; it does not include other forces that may act on a rocket, such as aerodynamic or gravitational forces. As such, when using it to calculate the propellant requirement for launch from (or powered descent to) a planet with an atmosphere, the effects of these forces must be included.

In what has been called the tyranny of the rocket equation, there is a limit to the amount of payload that the rocket can carry, as higher amounts of propellant increment the overall weight, and thus also increase the fuel consumption.

Stages

In the case of sequentially thrusting rocket stages, the equation applies for each stage, where for each stage the initial mass in the equation is the total mass of the rocket after discarding the previous stage, and the final mass in the equation is the total mass of the rocket just before discarding the stage concerned. For each stage the specific impulse may be different.