Resonant Physics of Space Missions: Moon, Sun, Mars. Empirical Link between Spacecraft Mass, Orbital Period, and Mission Success

This work presents an empirical analysis of the relationship between spacecraft mass, orbital period, and mission success for missions to the Moon, Sun, and Mars. Based on data from 34 missions (including Apollo-11, Chang'e-6, Perseverance, Parker Solar Probe, and others), a consistent correlation is identified: successful missions exhibit orbital periods that are close to or multiples of the reference resonant periods of the target celestial bodies: 1.73 min (Moon), 0.66 min (Sun), and 3.47 min (Mars). These values are derived from the α-Triad – a three-dimensional geometric invariant linked to the tetrahedral structure of spacetime and the fundamental frequency f0=400/7=57.142857f0=400/7=57.142857 Hz. A parametric resonance compatibility criterion (ΓΓ) is proposed, allowing the prediction of future mission success at the design stage. It is shown that spacecraft with periods deviating from the reference by more than 20% (Γ∉[0.85,1.15]Γ∈/[0.85,1.15]) statistically fail more often or require significant corrections. The methodology can be used to optimize mass, trajectory, and launch windows. The work also includes predictions for upcoming missions (Artemis III, Luna-26, Solar Cruiser, Mars 2028) and recommendations for correcting design parameters.