Isaac Newton is probably most famous for the falling apple story, which supposedly led to his development of the Law of Gravitation. This states that for two masses, m and M, separated by a distance r, the gravitational force exerted by one mass on the other is:
F = -GmM/r2
G is the universal gravitational constant.
G = 6.67 x 10-11 N m2 / kg2
The minus sign in the force equation indicates that the force is attractive, and the unit vector indicates that the force is along the line connecting the two masses.
The masses exert equal and opposite forces on one another.
Since the gravitational field g = F/m, in general g has a magnitude of GM/r2 and points toward M. This gives us the value of 9.8 m/s2 we've been using all along:
M = mass of the Earth = 5.98 x 1024 kg
R = radius of the Earth = 6.37 x 106 m
g = 9.83 m/s2