Period Law Source Three-Row Scan - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

A period-law-source scan holds the central mass fixed and varies the radius across three rows, checking that T^2 traces back to the same cited source constant T^2/r^3 row by row. The arithmetic is exact only for the stated periods, radii, source values, and rows in the ideal circular two-body model. Real observations add cadence, bandpass, stellar variability, limb darkening, detector calibration, background/noise, finite precision, and measurement uncertainty.

Three exact rows show different cited law constants accepting. 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 cited law accepts its matching ratio

The law source is part of the rendered case, so acceptance is computed against the cited constant rather than a hidden default.

\begin{array}{c}K=\frac{1}{2}\\{T^{2}\over R^{3}}={8\over16}=\frac{1}{2}\\\text{accept}=1\end{array}

The cited law accepts its matching ratio

The law source is part of the rendered case, so acceptance is computed against the cited constant rather than a hidden default.

\begin{array}{c}K=\frac{1}{3}\\{T^{2}\over R^{3}}={9\over27}=\frac{1}{3}\\\text{accept}=1\end{array}

The cited law accepts its matching ratio

The law source is part of the rendered case, so acceptance is computed against the cited constant rather than a hidden default.

\begin{array}{c}K=\frac{2}{3}\\{T^{2}\over R^{3}}={6\over9}=\frac{2}{3}\\\text{accept}=1\end{array}