Tidal Forces API

Tidal-physics and gravitational-dominance astrophysics as an API, computed locally and deterministically. The tidal-force endpoint computes the tidal (differential) acceleration that stretches a body, a = 2·G·M·r/d³, from the primary mass, the radius (half-size) of the affected body and the centre-to-centre distance — and the force if a body mass is given; tidal effects fall off as the inverse cube of distance, far faster than gravity's inverse square, which is why they matter only close in. The roche-limit endpoint computes the Roche limit, the distance inside which tidal forces tear a satellite apart, for both rigid bodies, d = R·(2·ρM/ρm)^(1/3), and fluid bodies, d = 2.44·R·(ρM/ρm)^(1/3), from the primary radius and the two densities — Saturn's rings sit inside its Roche limit. The hill-sphere endpoint computes the Hill-sphere radius, r_H ≈ a·(1−e)·(m/3M)^(1/3), the region where a body's own gravity dominates so it can keep moons, from the orbital distance, eccentricity and the two masses. Masses are in kilograms, distances and radii in metres and densities in kg/m³, with G = 6.674×10⁻¹¹. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy, astrophysics, planetary-science, simulation and education app developers, ring-system and moon-stability tools, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is tidal and gravitational-dominance physics; for Newtonian gravity use a gravitation API and for orbital periods an orbital-mechanics API.