Universal Application of Cosmic Gravitational Signature: Validating Cosmic Architectures via Saini Limit (SL)

This research paper presents the detailed quantitative validation of the Deepak Gravitational Signature (S = G·g = G²·m/r³) across various complex astronomical configurations and specific exoplanetary systems, firmly establishing the universal consistency of the Saini Limit (SL = 2.0 × 10⁻¹⁰ m⁴/(kg·s⁴)). While contemporary astronomy continues to rely on qualitative or empirical metrics for celestial classification, this study delivers a scale-invariant mathematical framework tested against 4 specific cosmic architectures. Key Validations: 1. Dwarf and Binary Systems: Verification of surface gravitational binding and celestial captivity limits through the Pluto-Charon system. 2. Exoplanets & Satellites: Mathematical analysis of independent existence versus satellite dynamics using specific data from the Kepler system (Kepler-22b and satellite Kepler-1625b I). 3. Lagrangian Mechanics: Applied to invisible geometric Lagrangian points (L1 to L5), proving how net signatures dictate stable versus unstable orbital gradients. 4. Aerospace Application: Confirmation of critical orbital insertion and capture limits using real interplanetary trajectory boundaries verified by Mars (validated by ISRO MOM and NASA MRO missions) and Venus planets. Conclusion: The numerical outcomes establish that physical dimensions do not govern orbital independence; instead, the computed gravitational signature uniformly characterizes spacetime stability fields, orbital insertion boundaries, and systemic captivity limits. *** Keywords: Saini Limit, Deepak Gravitational Signature, Orbital Mechanics, Lagrange Points, Exoplanets, Interplanetary Trajectories, ISRO MOM, NASA MRO, Spacetime Stability, Celestial Classification.