Low Speed Doppler Shiftcan be expanded by the binomial expansion and only the first two terms of the expansion used
When expressed in terms of the frequency shift, this becomes

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Doppler Expression ExpansionTo get a simplified expression for the Doppler frequency expression, the square root in the expression can be expanded using the binomial expansion as For low speeds where v << c, the first two terms give a good approximation of the Doppler shift:

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Doppler Calculation 
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