Wrong Period-Square Breaks the Ratio - Rotational Dynamics and Orbital Mechanics Step by Step

For a shared central mass only the true period closes the T^2 / r^3 ratio; a wrong period-square leaves it unmatched, so the candidate is rejected. The verdict is exact only for the stated periods, radii, and central mass in the ideal circular two-body model. Real orbits add eccentricity, inclination, perturbations, central-mass uncertainty, finite-body effects, and measurement uncertainty.

A wrong period-square renders as a rejected Kepler ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A wrong period-square can still be displayed honestly

Try period-square 36 with radius-cubed 64.

\frac{T_B^{2}}{r_B^{3}}=\frac{36}{64}

Nine sixteenths does not equal one half

The checked candidate ratio is 9 over 16, so the accepted bit is 0.

\frac{9}{16}\ne\frac{1}{2}