Derivation of JWST Orbital Positioning Based on Subjective-Free Mathematical Equations: Three-Body Rigid Equilibrium with Near-Zero Propellant Consumption and No Orbital Correction Subtitle Different from the analytical positioning relying on Lagrangian and Hamiltonian mechanics, all exact steady-state solutions are derived from purely natural proportional constraint equations without empirical fitting

The orbital maintenance of the James Webb Space Telescope (JWST) at the Sun–Earth L2 Lagrange point conventionally depends on Lagrangian analytical mechanics and Hamiltonian canonical equation systems. Classical mechanical frameworks adopt empirical fitting, perturbation correction, and statistical approximation for three-body orbital solutions, resulting in inherent orbital instability, continuous positional drift, and periodic propulsive correction. These inevitable defects lead to regular propellant consumption, limited service life, and long-term ground operation costs for the JWST mission. Based on the closed-loop general equation of natural historical proportion and substance primordial driven ratio, this study constructs a subjective-free mathematical model for three-body celestial positioning. Different from the potential-energy-based modeling of classical mechanics, the proposed method takes only three core proportional variables: system mass ratio, spatial distance ratio, and angular velocity ratio. A cyclic proportional operator embedded with inherent 3:1 steady-state natural constraints is adopted to solve the rigid fixed equilibrium position of the Sun–Earth L2 point. The core internal derivation and operator construction are kept confidential for intellectual property protection, with only standardized external equations, objective verification criteria, and final physical conclusions presented in this paper. The research results demonstrate that within this proportional framework, the equilibrium point transforms from a metastable gravitational saddle point into a rigid stable fixed point. The proportional constraint mechanism completely eliminates the inherent saddle-point drift of the classical L2 Lagrange point, realizing long-term stable fixed-point hovering without periodic orbital trimming. In principle, routine propellant consumption for station-keeping is reduced to nearly zero. A small amount of propellant would still be retained onboard to cope with unexpected external disturbances such as solar wind and micrometeoroids, fundamentally breaking the propellant-limited service life bottleneck of deep-space detectors. This work transforms celestial orbit calculation from traditional empirical statistical fitting to rigorous deduction based on inherent natural laws, providing an innovative theoretical paradigm and high-value engineering reference for future deep-space orbital design and aerospace positioning technology.