This is a meaningless physical quantity, since we have added the magnitudes of four vector quantities, each of which has a different direction (indeed, the vector sum is zero). Newton knew what he was doing, though, and his subsequent argument was sound (see Herivel (1960), Brackenridge (1995), pp. 42-54).

proportional to v2/r, and thus to 1/r2. Hence, gravity, which balances this, must vary as the inverse square of the distance. Since the Earth-Moon distance is about 60 Earth radii, the pull of gravity on the Moon must be about 3600 times smaller than the gravitational force at the surface of the Earth.

To test this, Newton conducted his so-called 'Moon-test'. Basing his observations on an inaccurate value for the diameter of the Earth, he calculated that the effect of gravity on the Moon was actually a little over 4000 times greater

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