I show simple and unquestionable mathematical proof that the formula defining kinetic energy is in error by using rockets as a substitute for gravity. Experiments cannot determine the correct definition of energy, because elastic force cannot be separated from inelastic force in experimental results. So pure mathematics is needed. In rocket analysis, the inelastic force is constant for constant powered rockets eliminating the problem.

In 1686, Gottfried Leibniz sort of showed that force times distance equals mass times velocity squared (Fd = mv²). So he said, therefore, mv² is kinetic energy, which was then being called vis viva (living force). Living force meant the force would accelerate a mass, unlike stress force, which would not.

later, the awareness developed that force times time equals mass time velocity unsquared (Ft = mv). So why would not mv be kinetic energy? This quantity became known as momentum.

After realizing that both relationships exist, a method was needed to determine which one should be kinetic energy. The issue was argued for 200 years and supposedly resolved by James Joule stirring water in a wooden bucket in 1845. The problem is that there is no theoretical possibility of getting a proof from Joule's experiment, besides the fact that he contrived and lied about procedures which he had no ability to produce. Stirring water will not distinguish between elastic and inelastic force. Only inelastic force produces heat, while elastic force produces linear stress on the container. Yet physicists use Joule's experiment with later refinements to determine the relationship between kinetic energy and heat.

For these reasons, a mathematical proof is needed which does not depend upon the difference between elastic and inelastic force. A rocket engine serves the purpose, because it can be analyzed through accelerating force with no concern given to the inelastic force which produces heat. It shows the relationship between the chemical energy of fuel and the kinetic energy of motion.

In using rocket analysis, the chemical energy in fuel is taken care of by the fact that a constant powered rocket uses fuel at a constant rate and produces a constant force. Therefore, the force and rate of fuel use are the same in all comparisons, and force can be arbitrarily given for the examples. I use a hypothetical rocket that produces a force of 10 Newtons for the comparisons.

The correct definition of kinetic energy is, that which is conserved through transformations. Conserved means the same amount of energy exists before and after a transformation. The test of being conserved is to re-arrange the component elements and see if the total stays the same after the transformation as before. Leibniz did this in rearranging the components and sort of showing that the totals remain the same. But he could only show that force times distance and mv squared are conserved relationships; he could not show that they are kinetic energy.

Leibniz's error was in starting with the wrong relationships, Fd and mv², not realizing that Ft and mv were alternatives. The first is a meaningless abstaction with accidental relationships, while the second is kinetic energy. The second is now days called momentum, while the meaningless abstraction is called kinetic energy. Both are mathematically conserved, but only the second is transformed into other forms of energy.

Experimental measurements cannot show which alternative is transformed into other forms of energy due to the inability to separate elastic force from inelastic force in some cases and the inability to capture the heat in other cases. Rocket math does not have these problems. The heat is ignored, and the only force of concern is the easily discernable force which is constantly accelerating the rocket.

Rocket math might sound complex, but it reduces to simple calculus which could be verified by a high school student who has taken calculus and physics courses, which means any engineer or physicist and most biologists. Except that incompetents have been taking over science and shoving out real scientists. The incompetents can't add and subtract. Something similar might be happening in engineering, except that the end result tests the methods and demands correct procedures for producing competitive products. Engineering products straighten out the errors, while there is nothing to straighten out errors in science besides moral character and external accountability. These demands haven't been straightening out the errors in recent decades, and in physics, corruption overwhelmed real science starting with Joule's fake experiment in 1845. Since the difference between elastic and inelastic force could not be understood or measured, corruption overwhelmed real science in the evaluation of Joule's measurement.

What the rocket math does is use a constant powered rocket for making comparisons. The chemical energy used is proportional to the time of burn. So burn time can be used to represent the amount of chemical energy being transformed into kinetic energy. Then a Leibniz type analysis can be used to compare the two alternatives to see which end result is conserved when the component elements are re-arranged.