Principles of Jet Propulsion: a non-standard analysis of the basic formulas for rocket propulsion leads to surprising results

We have found a law that connects the speed variation of a body to the throw of part of its mass, using the principle of conservation of momentum. Starting from a situation in which a child on a cart throws rocks in the same and opposite directions of its motion, we derived the formulas in relativistic and Galileian conditions. We then used our results to prove that to accelerate is easier than to decelerate. In fact, given the same initial conditions, the variation in velocity in acceleration is greater than the one in deceleration. Our formulas can be applied in several different situations involving rockets and jet propulsion, for example, to find between multiple paths the best one that grants a higher final velocity.