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Assuming a spherical Earth of radius, R = 6,371,000 m, and a latitudinal (N-S) arc length, a = 1m, then the latitudinal arc angle, dφ = a / R = 0.000000157 rad = 0.0000089932 deg, but note what others have said about the fact that a longitudinal (E-W) arc length of 1m will have a longitudinal arc angle that increases as you move away from the equator.

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