#astrophysics

Black-hole general-relativity maths as an API, computed locally and deterministically. The radius endpoint computes the Schwarzschild radius r_s = 2GM/c² — the event horizon of a non-rotating black hole — from a mass given in kilograms or solar masses, together with the photon sphere at 1.5·r_s and the innermost stable circular orbit (ISCO) at 3·r_s; the Sun would have an event horizon about 2.95 km across and the Earth about 9 mm. The time-dilation endpoint computes the gravitational time-dilation factor √(1 − r_s/r) at a distance r from a mass — a clock deep in a gravity well ticks slower than a far-away clock, and at the horizon time appears to stop. The hawking endpoint computes the Hawking temperature T = ħc³/(8πGMk_B), which is higher for smaller black holes, and the evaporation time, which scales as the cube of the mass — a solar-mass black hole would take about 10^67 years to evaporate. Masses are in kilograms or solar masses and distances in metres, using G, c, ħ and the Boltzmann constant. Everything is computed locally and deterministically, so it is instant and private. Ideal for astrophysics, cosmology, science-communication, simulation and education app developers, black-hole and relativity tools, and physics teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is general-relativity black-hole physics; for special relativity (Lorentz factor, E=mc²) use a relativity API.

api.oanor.com/schwarzschild-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.

api.oanor.com/tidal-api

Stellar magnitude and distance maths as an API, computed locally and deterministically. The magnitude endpoint works the distance modulus, m − M = 5·log₁₀(d/pc) − 5 — give any two of the apparent magnitude m, the absolute magnitude M and the distance and it returns the third, with the distance in parsecs, light-years and astronomical units (the absolute magnitude is the apparent magnitude a star would have at 10 parsecs). The flux endpoint applies Pogson's relation to turn a magnitude difference into a brightness ratio, F₁/F₂ = 10^(0.4·(m₂ − m₁)), where five magnitudes is exactly a hundredfold change in brightness — from two magnitudes, a magnitude difference or a ratio. The parallax endpoint converts a parallax angle into a distance, d(pc) = 1 ÷ p(arcseconds), and back, the geometric method behind the parsec itself. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy-education, planetarium, stargazing and science app developers, observing and astrophysics tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is stellar magnitude and distance; for orbital mechanics use an orbital API and for great-circle distances on Earth a geo-distance API.

api.oanor.com/starmagnitude-api