Hello. In this video, we will review rapidly the principles of universal gravitation and we will see how it applies to gravitation on earth. We will see the effect of masses of the bodies, their distance, we will look at what is gravitation on the Earth and finally we will make some considerations on the units of force that will be used throughout this course. Let's first consider the case of universal gravitation as it applies, for example, between a Sun of mass m2 and a planet, the Earth for instance, with a mass m1. The forces always act along the axis which links the centers of gravity of the two celestial bodies. On the body with mass m2 acts a force F 1 2 due to body number 2, likewise, on the body with mass m1 acts a force F 2 1 which is due to body number 2. Universal gravitation tells us that this force F 1 2 is equal to force F 2 1 and that it is opposed to it, with a value of G times the product of the two masses m1 and m2, divided by the distance between the two bodies to the square. Constant G is called the universal gravitation constant. 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. You can then express again the force F2 1 which acts on the man by g times m1. We also notice that g is approximately equal to 10, 9.81, there is a little error, but for this course we will consider that g is equal to 10 and thus the effect, the force F2 1 is equal to 10 times m1. If we consider a person with a mass of 80 kilograms and if we multiply this mass by 10, we obtain the force F2 1 which isbe equal to 800 kilograms times meters per second squared. This entity, kilograms times meters per second squared, is a new unit of measure which we will call the Newton, with N as symbol. This is the unit of measure of force that we will use mostly in this course. One Newton is the gravitational force corresponding to a mass of one hundred grams. It is a rather small value. We will often work with the kiloNewton, which is equal to one thousand Newtons, that is to say the gravitational force of one hundred kilograms, or even with the megaNewton, which is equal to one million of Newtons, that is to say the gravitational force of one hundred tons, this is the weight of a big locomotive. In this lecture, using the principles of universal gravitation, we expressed the bases of gravitation on Earth. We have seen that the terrestrial acceleration constant g is approximately equal to ten meters per second squared. We have seen that the forces which are exerted will be expressed in Newton, respectively in kiloNewton and megaNewton.
