While not constant but varying depending on
latitude and
altitude, the numerical value of the
acceleration caused by Earth's gravity on the surface lies between 9.74 and 9.87
m/s2, which is quite close to 10. This means that as a result of
Newton's second law, the weight of a kilogram of mass on Earth's surface corresponds roughly to 10
newtons of force exerted on an object.
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This is related to the aforementioned coincidence that the square of pi is close to 10. One of the early definitions of the metre was the length of a pendulum whose half swing had a period equal to one second. Since the period of the full swing of a pendulum is approximated by the equation below, algebra shows that if this definition was maintained, gravitational acceleration measured in metres per second per second would be exactly equal to
π2.
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𝑇≈2𝜋𝐿𝑔
The upper limit of gravity on Earth's surface (9.87 m/s2) is equal to π2 m/s2 to four significant figures. It is approximately 0.6% greater than
standard gravity (9.80665 m/s2).