Tidal Force Calculator

Ordinary gravitational pull falls off with distance squared, but tidal acceleration in this calculator's formula, a_tidal = 2GM×r/d³, has distance cubed in the denominator. Halving d multiplies the result by 2³ = 8, which is why moons and planets that migrate closer to their star or host planet experience tidal stress that grows explosively rather than gradually — it's a much steeper relationship than everyday gravity.

It's simplified: the code uses rocheLimit = 2.456 × (secondary body's radius), which assumes the primary and secondary have similar densities. The complete Roche limit formula also scales with the cube root of the ratio of the two bodies' densities, so for a real system where the primary and secondary have very different densities (a rocky moon near a gas giant, for instance), the true limit would differ from what this simplified version reports.

The Roche limit is about whether tidal forces can rip a loosely-bound body apart; the Hill sphere is about whether the secondary body's own gravity can hold onto something orbiting it, like a moon of a moon. The calculator computes it as distance × (secondary mass / 3×primary mass)^(1/3) — the region around the secondary where its own pull beats the primary's tidal pull. A small Hill sphere means the secondary can't sustain distant satellites of its own.

Treat it as an order-of-magnitude estimate only. The formula scales with (distance/radius)⁶ times the orbital period, which captures the extreme sensitivity of locking time to distance, but real tidal locking rates depend heavily on a body's internal composition and energy dissipation — factors this simplified model doesn't include. It's useful for comparing scenarios (closer orbits lock far faster) but not for predicting an exact locking date for a real body.