The Hasan Dipole Model: Gravitational Torque Equilibrium of the Solar System and Prediction of a Dark Stellar Companion

This paper presents the Hasan Dipole Model — a mathematically derived framework predicting the existence of a secondary stellar-mass object (the "Dark Sun") in the outer Solar System, derived exclusively from NASA planetary data without assuming its existence.Key Findings:The gravitational fulcrum of the 9-planet solar system falls at 7.522 AU — between Jupiter and Saturn — verified to three decimal places. Inner 5 planets (Mercury–Jupiter) and Outer 4 planets (Saturn–Pluto) produce identical torques of 750.928, with a net difference of 0.000. Including the Sun and the predicted Dark Sun, the complete system fulcrum holds at 7.5222 AU with a torque balance ratio of 1.000040.Three independent methods converge on the same prediction:Method 1 (Gravitational Fulcrum): Dark Sun mass = 77,373 Earth units (0.2324 Solar masses) at ~39.89 AU. Method 2 (Moon Thermal Ratio): Moon's temperature extremes (+127°C / -23°C / -173°C) yield a 7:6 ratio predicting Dark Sun radius = 127× Earth (809,117 km). Method 3 (Outer Planet Encoding): The four outer planets' combined mass (~127) and radius (÷1000 ≈ 109) encode both solar radii independently.Falsifiable Prediction: A dark sub-stellar object of 0.17–0.23 Solar masses exists in the antisun direction at 39–50 AU, detectable in infrared by WISE, Spitzer, or the James Webb Space Telescope.