A New Kinetic Theory of Particle Collisions

The kinetic theory of gasses is used in deep space navigation for modeling small forces acting on a spacecraft. Acceleration of a spacecraft occurs as a result of the energy and momentum transfer from molecules leaving the spacecraft through evaporation or gas leaks or from molecules impacting the spacecraft from an external source. In performing analysis of these events, a model of molecules in a closed container was developed. This model revealed a probability distribution of molecular velocity magnitudes that differs from the Maxwell-Boltzmann distribution. At first it was assumed that the model is not correct. However, further analysis has not revealed an error source. The difference is small but can be detected by direct measurement. A definitive measurement performed in 1955 confirms a small error which was attributed to the apparatus. The error is consistent with the computer model developed for navigation and seems to confirm that the Maxwell-Boltzmann theory is not correct. Over the years, considerable evidence has been developed that supports the computer model. However, there has been no independent confirmation. Furthermore, it seems to upset settled science and questions the application of entropy to molecules in a container. The absence of mathematical proof hinders acceptance of the computer model, but has not hindered its application to deep space navigation. Finally, a mathematical proof has been developed and is the subject of this paper. The complete probability distribution is not described as a closed form mathematical equation. The proof only applies to a single point where the error is greatest. However, the approach developed here may lead to a new mathematical function to replace the Maxwell-Boltzmann distribution