Period Ratio Acceptance Cross-Scan - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

Three exact rows show accepted and rejected period ratios. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The period ratio must match the law source

The checked source divides period square eight by radius cubed sixteen, giving one half, so the acceptance bit is one.

\frac{T^{2}}{R^{3}}=\frac{8}{16}=\tfrac{1}{2},\quad \text{accept}=1

Same ratio accepts; nearby wrong ratio rejects

Two rows preserve the one-half law. The last row changes period square alone, so the ratio no longer matches.

\begin{array}{c|c|c|c}T^{2}&R^{3}&T^{2}/R^{3}&\text{accept}\\4&8&\frac{1}{2}&1\\8&16&\frac{1}{2}&1\\9&16&\frac{9}{16}&0\\\end{array}