Period Ratios

Period-Square over Radius-Cubed Matches

Two orbit ledgers match the same normalized Kepler ratio. 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 first orbit matches the normalized period law

The first period-square 4 over radius-cubed 8 gives one half.

TA2rA3=48=12\frac{T_A^{2}}{r_A^{3}}=\frac{4}{8}=\frac{1}{2}
First period ratioThe normalized Kepler constant is an explicit checked value.keplerConstant=1/2 s^2/m^3leftRadiusCubed=8 m^3leftPeriodSquared=4 s^2leftRatio=1/2 s^2/m^3rightRadiusCubed=64 m^3rightPeriodSquared=32 s^2rightRatio=1/2 s^2/m^3acceptedBit=1 bit

The second orbit matches the same normalized law

The second period-square 32 over radius-cubed 64 also gives one half.

TB2rB3=3264=12\frac{T_B^{2}}{r_B^{3}}=\frac{32}{64}=\frac{1}{2}
Second period ratioBoth ratio labels are checked against K.keplerConstant=1/2 s^2/m^3leftRadiusCubed=8 m^3leftPeriodSquared=4 s^2leftRatio=1/2 s^2/m^3rightRadiusCubed=64 m^3rightPeriodSquared=32 s^2rightRatio=1/2 s^2/m^3acceptedBit=1 bit