What this equation says is that the force due to gravity is equal to a number, G, (called the gravitational constant) times the mass of both objects divided by the square of the distance between the objects.
Scientists have been able
to measure the gravitational
constant to be
G = 6.67 x 10^{-11} m^{3} kg ^{-1} s^{-2}
which is a very small number...
G = 0.0000000000667 m^{3} kg ^{-1} s^{-2}
Let's see if these numbers make sense. Can we calculate what the force of gravity felt by an object with a mass of 1 kg is when it is near the Earth's surface?
In this case:
Force = G x (mass of Earth) x (mass of object)
-------------------------------------------------
(distance between them)^{2}
Now there is **one really big catch** here. The fact that the object is on the Earth's surface does not mean that the distance between them is zero (or even just a few centimetres). When calculating the force of gravity for roughly spherical objects like the Earth we need to work as if all the mass was concentrated at the centre. This is not just a convenient 'fiddle'. There is a very good reason for this, but it's a bit too complicated to explain here. Anyway this means that in our example the distance between the objects is actually the radius of the Earth! So now we can plug in some numbers to Newton's equation.
Force =( 6.67 x 10^{-11}) x( 5.976 x 10^{24}) x 1
--------------------------------------------
(6.374 x 10^{6})^{2}
Where the masses are in kilograms and the distance in metres. Working out the numbers gives the answer 9.81 - and what is force measured in? Newtons! So it all works out correctly, a mass of 1 kg on the Earth's surface feels a gravitational force of 9.81 newtons. For convenience we often round-off the value and say the weight of a one kilogramme mass is 10 newtons. |