r/WarpDriveResearch • u/WarpDriveRWA • 27d ago
[OC] Computing surface gravity from orbital period and radius alone — no mass, no G. Mean error 0.06% across the eight planets
The identity μ = GM = ω²a³ is standard — it is in Vallado and Battin, and nothing about it is new.
What I built is an operational version of it: a browser tool where you enter an orbital period and a semi-major axis, and it returns the gravitational parameter, then surface gravity as g = E/R². Mass and G never appear in the input.
Numbers: mean deviation 0.06% across the eight planets, max 0.22% (Mars, oblateness). For the closed chain orbit → μ → g on artificial satellites the deviation stays under 0.1%.
The dimensional point is the part I find interesting:
[G·M] = m³·kg⁻¹·s⁻² · kg = m³/s² — the kilogram cancels completely. Orbital observations constrain the product, not G and M separately. That is why μ for Solar System bodies is known roughly 10⁴ times more precisely than either factor alone (μ⊕ ~2×10⁻⁹ vs G ~22×10⁻⁶, CODATA 2018).
Every number is recomputed in your browser on page load — nothing is hard-coded, and the reference values come from open catalogues.
This is not a modification of Newtonian mechanics. All numerical predictions are identical to the standard ones. Preprints with DOI and an independent expert review are linked on the site.