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The first order effect (distance) is the difference frequency. The second order effect (velocity) is the change in frequency.

Noise (SNR, distance to the ball, aperture) will determine how well this works, since too much integration could muddy the signals.

It’s worth a try! Good luck.

It comes down to power supply and distance, you could, but you would probably need numerous sensors and would probably be better off with a longer wave and bigger power source

Ainstein demonstrated this with tiger woods. The raw output is very dense and contains range and Doppler information.