 Hi, I'm Zor. Welcome to Unisor Education. Continuing talking about gravity as part of the course called Physics 14 presented on Unisor.com I do suggest you to watch this lecture from the website. There is a very detailed menu, so you can actually take the course in sequence of topics, the way how they're logically following each other. Also on the same website you can find other courses, like for instance Mass 14 or US Law 14s. Now the site is free, there are no advertising, so it's just the source of good knowledge. Now, so one of the things about gravity is that this is the source of the weight which we all know what it is, obviously. Well, do we? Well, let's start with the definition of what is actually weight. Weight is the force of gravity of the planet, which when it attracts certain objects, so that's what the weight of this object is. Again, the weight of the object is the force of the gravity of the planet extended towards this particular object. So, it's a function of two things, the object itself and the planet. If you change the planet of the same object, put it on a different planet, it will weight differently. So, that's very important to understand. Weight is not absolute. Weight is always related to certain planet, this weight is positioned upon. Now, just for example, if you will take the same object on Earth and put it on the moon, the weight on the moon will be about six times less because the gravity of the moon is about one-sixth of the gravity of the Earth. Next, now, do we feel weight? Well, some people might say yes, but actually the answer is not exactly. We don't really feel the weight which is a gravity. We feel the result of this. Whenever we are standing on the floor, for instance, we feel the reaction of the floor. If there is no floor, we will just fall down and during our fall we will not feel any weight. For instance, just imagine yourself in the elevator and elevator all of the sudden just break all these cables and it just falls down by itself. You will feel that you are falling down, but you will feel no weight because there is nothing which supports you from below and pushes you up. So, whenever you think that you are feeling the weight, you are actually feeling the reaction of the gravity force caused by the gravity and reaction is necessary for you to stand in place. So, I am standing right now on the floor. I feel the floor actually pushing up to my feet. At the same time, every organ is also in place. It doesn't move up or down, which means that whatever the weight of this organ is, this gravity is always reacted upon by something from below it, from muscles, from skeleton, etc. So, the whole sensation of weight is actually the sensation of the reaction to the gravity, not the gravity itself. We don't feel gravity. We can be within the gravitational field of the earth, but if we are falling down, like parachutes for instance, before the parachute is open, then we don't feel any weight. We feel weightless. So, that's actually what weightless means. Weightless means not the absence of the gravity. It's absence of the sensation of gravity and the sensation of gravity is always caused by certain reaction of the force from below actually. Well, if I can say below, considering your planet is down there. So, always the reaction force which we feel. We feel tactile things but not the gravity itself. Gravity is not, we don't have a sense of gravity. We have a sense of touching. We have sense of smell, etc. but no sense of, no sense of gravity. Okay, next. Let's talk about the weightlessness in the spaceship. So, we can consider a spaceship which is circulating around the earth and people feel weightless there if there are no engines running, obviously. So, we just launch this particular spaceship on the orbit. Let's say it's an international space station which everybody knows is somewhere there in the sky. So, this international space station is circulating on a relatively constant orbit around the earth and people on this station feel weightless. Why? Here is a very simple explanation. If you understand that if you are in a falling elevator that you don't really feel weight. With the spaceship it's exactly the same thing. Here is the earth. How about this? Here is the earth, the blue planet. Now, here is our spaceship which is circulating on the circular orbit. This is the orbit. Now, what happens? If engines are not running this spaceship participates in two different motions. One motion is inertial motion. It just goes tangential to the orbit. Another motion caused by the gravity is just falling down towards earth. So, simultaneously when these two things are happening, when on one hand it's tangentially moving by inertia tangential to the orbit and at the same time falling down to the earth, that's what makes this orbit circular. So, if you will consider infinitesimal moment of time, during this moment of time it goes tangential to the circle of the orbit and at the same time falling a little bit down. That's what makes this orbit circular. So, both of these things do not have anything like reaction which we can feel. Obviously, if we are moving by inertia tangential to a circle there is no reaction, nothing pushes on to us. And when we are falling down, as we know like for instance in the falling elevator, we don't feel. So, there is no support which we actually can feel with our style feelings. So, that's why everybody feels weightless in the spaceship. It's basically constantly falling towards the earth and only its linear speed helps to keep the distance from the earth constant. So, we are falling down and moving tangentially and as a result we have this. Obviously, these two movements are related in such a way that the distance from the earth remain the same. And we have already made certain calculations about how to do it. What kind of speed is necessary it was one of the previous lectures. What kind of speed is necessary to maintain the same distance from the earth. So, that's basically the source of weightlessness in the spaceship. Okay, now let's go back to some more mathematical aspects of this thing. So, let me remind you again the law of universal gravity. There is a gravitational constant and we know that the force of gravity is proportional to mass of, let's say, planet times mass of the object. It is inversely proportional to the radius of the planet if our object is on the surface of the planet and we are assuming obviously that the planet is spherical and there is such a weight. So, this is basically the weight. Weight is the force on the planet when the planet attracts the object of mass m. Okay, that's fine. Now, obviously from this we see that different planets with different m and r attract the same object m differently. So, that's why the weight is different. It depends on the planet. Now, from this, since we know the weight we can definitely determine what's the acceleration of the free fold on the surface of this particular planet. It's w divided by m. This is acceleration and it's gm divided by r squared. Now, this is the constant for a planet. For planet Earth, for instance, well, g is a constant unconditionally. m we know the mass of the Earth and r we know the radius of the Earth. Again, we are assuming that this is relatively circular, spherical kind of form. And we can basically calculate it. Now, if we calculate this value, we can always find the weight as mass times this particular acceleration of the free fold. Now, traditionally the acceleration of the free fold on Earth is symbolized by letter g and it's approximately 9.8 or 7 meters to second square. So, I can use g here and this is the weight on the planet Earth of an object of mass m, lowercase m. Well, usually this even abbreviated even shorter to 9.8 or even 10 sometimes just to make things more rounded. But 9.8 probably would be a good approximation. Alright, now, this is on Earth 9.8. How about other planets? Well, I will give you a couple of numbers but obviously for each planet it has its own mass and its own radius and obviously we will have different acceleration of the free fold which means different acceleration results in different weight, right? Since weight is equal to mass times this acceleration so different acceleration which is a characteristic of the planet. You see, this is weight is a characteristic of both functions. It's a function of both arguments, mass of the object and characteristic of the planet, mass and the radius. Now, but we are talking about a concrete planet. We can characterize the planet just by planet's characteristics and then the weight will be just the multiplication of the mass by this free fold acceleration. So, on Sun, Sun is big, right? And very heavy, obviously. So, on Sun this particular acceleration approximately equals to 274 times 1 meters to second square which is about 28 times greater than on Earth which means that every object on Sun would weight 28 times greater than on Earth but before it burns out, obviously Sun is too hot to have any object on it. Now, on Jupiter, well, Jupiter is a very big planet, much bigger than Earth. However, don't forget this very important fact if you are expanding the planet geometrically, so it has a greater radius, let's say it doubles the radius Now, it's mass, well, considering you have the same density, it's mass is increasing by the factor of 8, right? 2 to the 3rd degree, the cube function right? Double the size, 8 times greater the volume and therefore the mass, if density is the same. So, this is increased by 8 if we double the size Now, but radius is also increased by the factor of 2, right? We're talking about geometrically growing so r square would be 2 square which is 4 so mass is increasing by the factor of 8 radius is increasing by the factor of 4, so the result will be 8 divided by 4 2, so it looks like the force of gravity is proportional to the geometrical size right? So, we double the size, 8 times the mass, 4 times the r square and the result is again 2, the same as I have increased the geometrical proportion So, Jupiter is much greater than Earth, actually more than twice I don't remember, but maybe more than 3 or 4 times even but maybe there is a different density, so it's kind of difficult to say based on just these if we don't know the contents of the density of the Jupiter. Well, the calculations show anyway that this is approximately 25 times 93 meters per second square, which is about 2.6 times, so it's almost well, less than 3 times heavier than on Earth so any object will be heavier on Jupiter because it's a giant planet much bigger than Earth, but not that much as I personally would expect it, I would expect like 10 times greater no, it's only 2.6 times, again because not just the mass which is important, the radius is also important, so on the surface of the Jupiter you are further from the center, and that's why your gravity is decreasing when you are moving outside, the further you are from the center, the less the force of gravity so mass is one thing, radius is another, but as a result we have this particular ratio, and the last number I have is for moon it's 1.625 which is approximately 1.6 of the 9.8 of Earth, so this number acceleration of the freefall is about 1.6 of that of the Earth so things will be lighter by factor of 6 on the moon than on the Earth. Alright, fine that is done, now let's think about how do we measure the weight, we know all these formulas of course, this is great, but what these formulas are usually give you is the weight as the force and the force in the system C is measured in newtons, right so G has something like 6, 6.74 if I'm not mistaken newton divided by kilograms square meters square, right, so this is kilogram and kilogram that would cancel this one and the meters square would cancel this one, so if my mass is in kilograms and my radius is in meters and my G is, my universal constant is this, the result will be the weight in newtons now, who measures weight in newtons nowadays we don't, so let's talk about units of measurement of weight, fortunately or unfortunately, it doesn't really matter, the fact is the weight is measured in pounds and kilograms, right, however that's, especially about kilograms, that's not exactly the correct way of doing it, because kilogram was introduced as the unit of mass not the unit of weight, so we are talking not just about any kilogram, we are talking about kilogram of force kilogram of force and this is abbreviation, not KG, but KGF and this is the weight of earth, of object of one kilogram of mass which is actually one kilogram times 9.8 meter second square, which is 9.8 newtons, so one kilogram of force is equal to 9.8 newtons, so the weights, if the weights are in kilograms then this is basically your conversion, but again there are no weights actually, which have a scale in newtons, there are weights in kilograms or in pounds now about pounds, now one pound is basically 0.454 of the kilogram of force, again this is the unit which is popular in the United States, this is the unit which is popular in Europe and other countries, and to tell you the truth, very rarely people are using this abbreviation, they are using KG, it's assuming that this is actually a kilogram of force, which is the gravity with which earth, our planet earth, not Mercury or any other planet, which with earth attracts an object of mass of one kilogram of mass, right, so sometimes it's this, sometimes I remember using this with a G, capital G also another way, even rarer than this one, so this one is more scientific I would say, definition of the kilogram of force and again in our everyday life we just say kilogram, assuming that this is the weight of an object of a mass of one kilogram, which is kilogram of force, but we're saying just kilogram and there are some other units of measurements more even rarer used in everyday life, and I don't think it's very interesting anyway, so what's interesting is that we are using pounds and kilograms of force, and the game pounds is about this from the kilogram of force, and kilogram of force is 9.8 newtons, so that's how you can transfer all these units into newtons for some kind of scientific calculations, or otherwise if you get some answer in newtons, because you're using system C for all other components of your calculations, and if at the very end you have to really convert it into kilograms of force, you're just using this conversion okay, so that's it for today, I do recommend you to read all the notes for this lecture, they are presented in unison.com in physics 14's lecture that's it, thank you very much, and good luck