Period Ratios

Wrong Period-Square Breaks the Ratio

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.

TB2rB3=3664\frac{T_B^{2}}{r_B^{3}}=\frac{36}{64}
Wrong period-square candidateThe candidate ratio is shown before rejection.keplerConstant=1/2 s^2/m^3leftRadiusCubed=8 m^3leftPeriodSquared=4 s^2leftRatio=1/2 s^2/m^3rightRadiusCubed=64 m^3rightPeriodSquared=36 s^2rightRatio=9/16 s^2/m^3acceptedBit=0 bit

Nine sixteenths does not equal one half

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

916≠12\frac{9}{16}\ne\frac{1}{2}
Rejected period ratioThe rejection is exact ratio arithmetic.keplerConstant=1/2 s^2/m^3leftRadiusCubed=8 m^3leftPeriodSquared=4 s^2leftRatio=1/2 s^2/m^3rightRadiusCubed=64 m^3rightPeriodSquared=36 s^2rightRatio=9/16 s^2/m^3acceptedBit=0 bit