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How was the force of gravity (9.81 meters per second squared) determined?


The acceleration due to gravity (g) was derived from observations of falling objects. Galileo observed that all objects fall at the same rate of speed regardless of the object's mass. Over time, scientists were able to put a value on the acceleration due to earth’s gravity as 9.81 m/s2. Mathematically the equation for g is:   

g = G *Me/ r2

g = acceleration due to gravity (units m/s2)

G = the universal gravitational constant, G = 6.673 x 10-11N·m2kg2

Me = mass of a large body (for example, Earth). The mass of the Earth is 5.98x 1024 kg.(10 to the 24 power)

r = the distance from the center of mass of the large body. The radius of the Earth is 6.38 x 10m (10 to the 6 power)

After plugging in all the numbers and solving for g we find that at the earth’s surface the acceleration due to gravity is 9.81 m/s2.(Seconds squared)


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