Understanding The Concept Of Gravitational Force
Everything in human experience, in human history or better still or as per human civilization experience, everything seems to fall to the earth. Water particles (that are large enough and cannot be held in the wind) fall. People cannot just flow around, they fall. You do not have taxi cabs that flow around, they fall. Hold a needle a then release the force you are using to hold it, it will fall. This stuff is fundamental to everything that we have experienced.
Image from Pixabay - Public Domain (CCO Licensed)
Isaac Newton, the greatest among the greatest
So, we believe that that is just how things are. Things will always fall to the earth surface. We believe that is just how the universe is and to think otherwise will be crazy. And that is why this guy I am going to mention here is one of the greatest geniuses of all time. He did many more things than just the things I am going to describe in this post. Each and any of those things would have earned its place in history.. We are talking about the man you have probably known. Yes, Isaac Newton! One of the greatest geniuses in human history.
One of Isaac Newton's big insight about this whole things falling down is do they have to fall down? Is this just something that we should assume about the universe that things just have to fall down. And we were told that he did tell the people that he was somewhat inspired to come upon this way of thinking by observing an apple falling from the tree. It is probably not true what you have seen in some cartoons on TV that the apple hit his head while he was sleeping and gave him the idea.
To most people, it is just the normal for an apple to fall from the tree. Like, it is just the way of the universe in which we live. But for Isaac newton, at least on that fateful day, he was like "why did that happen". This to some degree is some example of out of box thinking because, something that for thousands of years, human being has always been taken for granted. Like that has been how things are meant to be.
That question took Isaac Newton down to entire line of reasoning that set up the basis for all of classical mechanism which for the most part we still use today. For most purposes, like engineering things or dealing with things on the surface of the planet, we can still use the Mathematics that Isaac Newton came up with from this simple question. He was able to kind of thing that there was something that might be pulling things to the earth. Like some kind of force acting on that apple that pulled it to the earth surface.
Understanding the law of gravity
So he formulated an entire law around this stuff. The thing that Isaac Newton believes brought the apple to the earth is non-other than gravity. And so he formulated the universal law of gravitation. Or the law of universal gravitation, either way. In it, he theorized that the force between two objects and its affected quantity is always going to attract the two objects to each other. So, the force of gravity between two objects is going to be equal to this big G which is just a small number multiply by the mass of the first object, multiply by the mass of the second object, (and the two objects) divided by the distance (between the two objects) squared. Let me give you a mathematical expression of this so we can all get the big picture here.
So, if you are talking about the force of gravity on earth, we pick one of the masses to be earth (m2 for instance) and the second (m1) to be the mass of the object. So R is the distance between the object and the earth. So when we see this, something will surely be raising up in our brains that the way Isaac Newton defines the gravity or simply the formula above is saying that we have gravity between any two objects. So we will be like okay I am looking at the computer screen or my phone right now reading this post, so how come the computer screen or the mobile does not fly into my face.
And the answer to that is that the force is really small. There actually is some force of attraction between you and the computer screen. it is just that it is more than over compensated for. The friction between the computer and the desk, the friction between you and your seat and which is frankly being caused by the force between you and the earth and the force of gravitation between the computer and the earth. Both of you and the computer suck more masses than you really can notice. This is really negligible as being overpowered by other forces that is keeping the computer from even drifting into your face or your face drifting into the computer.
So just to get a sense of that, the G that is causing the proportionality, get the sense of how small it is. This is approximately equals to:
The units are there this way: Think of the N otherwise known as Newton as the unit for the force of gravitation (G). m is Meter which is the unit for measuring distance and of course, kg represents the masses involved. But i want to make it clear that these are super small numbers. Tenth to the negative of 11 which is 0.00000000001. So it is the same thing as ``6.67x0.00000000001`. You see how small that is. And that is why when you multiple it with not so large number (think of yourself and the computer screen, which is not so large compared to that of earth and the computer desk), you are going to end with a super small force. The reason the computer screen does not drift in your face.
When you think about really massive bodies like the earth, the force of gravity starts to become noticeable. Very noticeable. I am not going to give you the mass of earth in tis post, but if you put in the mass of earth as your m2and the distance from the surface of the earth to the center of the earth for r and so you multiply the r by G and m2 (which is the mass if the earth), all of these simply to what is sometimes called g`. So, you can use that as thegravitational field of the surface of earth, the same thing asacceleration of gravity near the surface of earthand that comes out to be9.8m/s'2. And then you are left with just the other mass,m1``.
So for simplicity, if something is close to the surface of the earth, the distance does matter, but we can say the force of gravity is going to be this little g multiply by whatever the mass that is close to earth m1.
For example, let us take me. If I weigh 70kg, that means I have a mass of 70kg. Weight is actually force. We will talk about that later. Then we can calculate te force at which the earth is pulling down on me with my weight. So, in this situation, the force is going to be g which is 9.8 m/s'2 x 70kg and that gives us 686 kg.m/s'2 or this is exactly the same thing as 686 Newton. So, my weight on earth which is the same thing as the force that earth is pulling down on me or the gravitational attraction between me and earth is 686N.
Conclusion
Now i will ask you an interesting question. We already know that the earth is pulling down on me with a force of 686N. Now my question is am I pulling on the earth with any force? Or am I pulling on the earth with a lager force than it is pulling on me? Your reaction might be "oh the earth is so huge and the earth is pulling on @harmudahola than @harmudahola is pulling on the earth".
Unfortunately, that is not the case. The earth is pulling on me at 686 N and I am also pulling on the earth with a force of 686N. So @harmudahola is also pulling on the earth with a force of 676N and that makes me so powerful, don't you think? But you might say that does not make any sense. If i have a building and you to jump from the top of the building, the force of gravity is going to start acting on you and you are going to start accelerating downwards. It does not seem like the earth is accelerating to you. The way to think about that is the force are the same.
F = m * a (Force is equal to mass multiply by acceleration
Well, we are talking about 686 N in term of the force that hold the gravitational attraction between myself and the earth. And that will equals to 68kg * a. So if we solve for a, we are going to get 9.8m/s'2. Now, if we do the same thing for earth, I already said it that we are pulling at each other at 686N.
Reference
Thank you for reading. I hope to see you here next time.
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