Its value is 6.67 times ten

to the minus eleventh power with units cubic meter

divided by kilogram and seconds to the square.

So, this allows us

to determine, for example, the force

that the Earth exerts on the Sun or vice-versa,

the force that the Sun exerts on the Earth.

In this course, we are more interested in what happens

on the Earth, so we will now look at

this case, which is closer to us.

We still have a large mass m2, which is the mass of the Earth,

and a smaller mass m2, which is the mass of a person standing on the Earth.

The forces in presence act like before

along the axis that connects the center of gravity of the person to the center

of gravity of the Earth. We have force F 1 2 which the

body #1 exerts on mass 2 and the force

F 2 1 which the Earth exerts on the person. It must be noted

that we generally do not notice that the force, the gravitational

force which acts on a body is in direction of the center of the Earth. We

rather think, and this

is also true, that it acts vertically, downwards.

But when we say downwards, actually, we need to look not just to

the ground, we have to see that this force acts up to the center of the Earth.

Then, what is the value of this force if we consider a person of mass m1 ?

Let's regroup the constant terms together. F2 1 is equal to G, the universal

gravitation constant, which is obviously constant, multiplied by

the mass of Earth, which is also constant,

divided by the distance between both centers of gravity.

This distance is equal to the Earth's radius plus roughly

one half the height of the man. When we consider that the radius of

Earth is more than six millions of meters, we can see that adding one

meter, maximum one point two meters, is not going to change very much.

Thus we can consider that the distance between both bodies is simply r, where

r is the Earth's radius, multiplied by the mass m1 which is variable.

If we regroup all these elements together and if we take their numerical value,

we will then get the universal gravitation constant, 6.67 times ten

power minus eleven times the mass of Earth 5.985 times ten

power twenty four kilograms divided

by 6378000

meters, to square. If we calculate

this, we get the value of 9.81 with units

meter per second squared

and this is a constant which we call g, which is

the terrestrial gravitation constant.