Newtonian Tidal Acceleration

$$\Delta a = \frac{2GMR}{d^3}$$

Status: Proven.

This is the standard first-order (leading-term) approximation for the differential gravitational acceleration across an extended body of radius $R$, caused by an external mass $M$ at distance $d$. It follows directly from a Taylor expansion of Newton’s law of gravitation, $F=GMm/r^2$, comparing the pull at the near and far sides of the body — the difference (not the pull itself) is what raises tides, distorts orbits, and can shred a body that ventures inside another’s Roche limit.

Real, independent confirmation: this is the textbook derivation behind ocean tides (the Moon and Sun’s differential pull on Earth), tidal locking, and tidal disruption events observed in astronomy (e.g., stars torn apart by black holes). It’s standard, undergraduate-level celestial mechanics, not a contested or novel result.

Used in: Paper 1, applied to estimate the Moon’s tidal bulge on Earth (~0.7 m). This is a direct, unmodified application of the real formula — nothing PBT-specific about the equation itself here.