Skip to 0 minutes and 14 seconds So we left with Galileo identifying the law of free fall of material objects. And now let us introduce Sir Isaac Newton. But before we do that, let us say that, after Galileo, Johannes Kepler identified the laws of motion of planets. But it is really Newton who realised that planets, stars, celestial objects are moving in the same way– they are falling in the same way as material objects, like this apple. According to the legend, it is through an apple falling from a tree on his head, or through watching an apple fall on a clear night where there was moon shining, that he realised this fact.

Skip to 1 minute and 7 seconds We’re going to use, again, a thought experiment, this time due to Newton, which is called the “cannonball experiment.” So I’m here standing– let’s imagine this is at a five-meter height. I’ve chosen five metres because it takes an apple one second to fall to the ground. And so let me drop this apple to the ground, in principle, in, let’s say, one second.

Skip to 1 minute and 37 seconds Now I will repeat the experiment with a wooden ball. And this time I will communicate the ball an horizontal velocity of two metres per second. So that means that, during the time that the ball will be falling, the one second it takes the ball to fall to the ground, the ball will move horizontally two metres. And so it will fall two-meter distance from me.

Skip to 2 minutes and 14 seconds Now I could repeat the experiment with a steel ball– with a petanque ball– communicating the ball a velocity of five metres per second. Instead of doing that, I will go immediately to a much faster velocity. Let me imagine that I’m throwing this ball at 7,900 metres per second. For safety reason, let me do that on the blackboard below.

Skip to 2 minutes and 44 seconds And so we have been throwing the steel ball at a velocity of 7,900 metres per second. I’ve chosen this velocity in such a way that one second later the ball is still at the height of 5 metres, because of the curvature of the round surface of the Earth. And so that means that, of course, if I’m ignoring friction, then the ball will continue to fall around the Earth. And will be starting to orbit around the Earth. Of course, in reality, there is friction. And if I was able to throw a ball at this velocity, it would immediately melt, because of the friction against the atmosphere– against the air. But let’s imagine that there is no friction– no air around.

Skip to 3 minutes and 49 seconds Then I’ve just set this ball in orbit. And so you see this cannonball experiment– so that’s the cannonball of the name of the thought experiment proposed to us by Newton– shows that the motion of this ball is identical to the motion of the moon, for example. So the moon is falling around the Earth in exactly the same way as a cannonball, and so it obeys the same laws as the law of free fall of massive objects, like the apple. And similarly for satellites. The International Space Station, for example, is orbiting around the Earth, again according to the same laws as the law of an apple falling from a tree.

Skip to 4 minutes and 47 seconds So the force of gravitation is universal. It applies to material bodies, like balls or apples, or celestial bodies, like stars or planets. And it is also Isaac Newton who identified this universal force and the properties of this force. So if we have two bodies of specific masses, then the force between these two bodies is proportional to the mass of each of the two bodies and inversely proportional to the distance squared between the two bodies. If you have massive objects, like spheres, with spherical symmetry, like the Earth, then everything is as if the mass– the full mass– was localised at the centre of these spheres.

Skip to 5 minutes and 41 seconds So that means, for example, the attraction between ourselves and the Earth– everything is as if the mass– the total mass– of the Earth was localised at its centre. Now what characterises the strength of gravitational attraction is a constant– a universal constant which is known as the “gravitational constant,” or “Newton’s constant,” which we call “G” and which is quite small. The value in standard units is 6 times 10 to the minus 11, which means– we’ll come back to powers of 10, but that means 1 over 100 billion. So a very tiny number which shows the gravitational force is extremely weak. And we’ll come back to that. It turns out that the gravitational force is the weakest of all fundamental forces.

Skip to 6 minutes and 48 seconds So we can now return to the difference that we made between the concept of mass and the concept of weight. Let me remind you that the mass measures the inertia, so it measures resistance to changes of motion. Whereas a weight is the force exerted by the gravitational attraction of the Earth. So this means that, in a different context, the mass will be the same, whereas the weight will be different. If we take, for example, the weight of this kilogramme of sugar at an altitude of 6,300 kilometres– I’ve chosen the altitude in such a way that this is exactly the double of the distance to the centre of the Earth. So the radius of the Earth is 6,300 kilometres.

Skip to 7 minutes and 46 seconds So if we are at an altitude which is, you know, the same as the distance to the centre of the Earth, we are at a distance twice the same. And so that means that attraction is divided by 2 squared, so that’s divided by 4. That’s what it means. The weight of this kilogramme of sugar will be divided by 4. We could go also to other planets. We could go to the Moon. In the case of the Moon, the attraction of the Moon, because of the mass of the Moon is much smaller– a factor 81– but also the radius of the Moon is smaller, so you’re closer to the centre of the Moon.

Skip to 8 minutes and 27 seconds When you add the two effects– lighter mass, smaller radius– then you end up with a weight which is approximately one sixth of the weight of the same kilo of sugar– kilogramme of sugar– on Earth. So you see that, depending on where you are, the weight is different, but the mass, which measures the quantity of matter, remains the same.

Skip to 8 minutes and 57 seconds Since I’ve just mentioned the Moon, let us take the opportunity of watching a very famous video– an historical one. It is in the context of the Apollo 15 mission that Capt. Dave Scott made the experiment of trying to let a feather and a hammer fall on the surface of the Moon. There is no atmosphere, no friction, and so the idea was to check that a feather and a hammer are falling in the same way at the surface of a moon. So let’s watch this video.

Skip to 9 minutes and 35 seconds We copy. […….] solar wind and, uh, [………] in the ETB.

Skip to 9 minutes and 45 seconds Not quite yet. I haven’t put the solar wind in yet, but I will shortly. I want to watch this. –a good picture, there. I’ve got, uh– Beautiful picture, Dave.

Skip to 9 minutes and 57 seconds Well, in my left hand I have a feather; in my right hand a hammer. And I guess one of the reasons we got here today was because of a gentleman named Galileo, a long time ago, who made a rather significant discovery about falling objects in gravity fields. And we thought that, uh, where would be a better place to confirm his findings than on the Moon? And so we thought we’d try it here for you. The feather happens to be, appropriately, a falcon feather, for our Falcon. And I’ll, uh, drop the two of them, here. And hopefully they’ll hit the ground at the same time. How ‘bout that? [BEEP] Mr. Galileo was correct in his findings!

Skip to 10 minutes and 42 seconds [BEEPS] So let us summarise the concepts introduced in this sequence. We have identified the gravitational force as a universal force which applies to all objects– either material, like an apple, a sugar lump, a ball– or celestial objects, like planets and stars. The force is proportional to the mass of each body and inversely proportional to the square of the distance between the two bodies. And the weight of a material body is the gravitational force which is exerted by the Earth, or another planet, on this body. And so let me conclude by asking you a question. I have here a box of sugar lumps. I’ve been insisting on the distinction between mass and weight.

Skip to 11 minutes and 44 seconds So let us imagine that we are on the space station, in a weightlessness.

Skip to 11 minutes and 51 seconds This box of sugar is floating around in the space station. And my question is, how would you test whether this box of sugar lumps is full or empty?

# Newton and the Moon falling

It is Isaac Newton who realized that the law of the universality of the free fall of material objects was also valid for celestial objects like the Moon, the planets and the stars. Discover why we can say that the Moon keeps falling in the gravitational attraction of the Earth, just as the astronaut in the space station keeps falling as well. And follow Newton when he identifies the universal law of gravitation.

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