Boundary and Invariant Scans

Doppler Approach Scaling Three-Row Scan

Three exact rows show signed approach-speed scaling. 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 faster approach gives a larger blueshift ratio

The signed training ratio keeps the approach direction negative; larger magnitude radial speed makes a larger magnitude blueshift.

Δλλ=vc=−26=−13{\Delta\lambda\over\lambda}={v\over c}={-2\over6}=\frac{-1}{3}
Approach Doppler row oneThe sign is bound to the radial-speed source.radialSpeed=-2 m/slightSpeed=6 m/sshiftRatio=-1/3formulaRole=low-speed signed training ratio

A faster approach gives a larger blueshift ratio

The signed training ratio keeps the approach direction negative; larger magnitude radial speed makes a larger magnitude blueshift.

Δλλ=vc=−36=−12{\Delta\lambda\over\lambda}={v\over c}={-3\over6}=\frac{-1}{2}
Approach Doppler row twoThe sign is bound to the radial-speed source.radialSpeed=-3 m/slightSpeed=6 m/sshiftRatio=-1/2formulaRole=low-speed signed training ratio

A faster approach gives a larger blueshift ratio

The signed training ratio keeps the approach direction negative; larger magnitude radial speed makes a larger magnitude blueshift.

Δλλ=vc=−46=−23{\Delta\lambda\over\lambda}={v\over c}={-4\over6}=\frac{-2}{3}
Approach Doppler row threeThe sign is bound to the radial-speed source.radialSpeed=-4 m/slightSpeed=6 m/sshiftRatio=-2/3formulaRole=low-speed signed training ratio