What is the force of gravity in the center of the earth?
Newton was sitting under his own apple tree in Lancashire. Concerned. Suddenly an apple fell on his head. And that is what history is made of. We all know that history. Whether the story is true or not, the way Newton discovered the law of the gravitational ball, this discovery changed the history of the world.
Assuming, Apple's gossip is true. Assuming that the fall of the apple really opened Newton's eyes. He thought, why did the apple fall down? Why did not go up? This is the question that confused Newton's world of thought.
Suppose Newton thought a little differently. Why didn't the apple fall further down?
The apple did not fall further due to soil erosion.
Well, if there were no soil barrier, if there was a deep tunnel where the apple fell, what would have happened if the tunnel had gone to the center of the earth?
The apple could reach the center of the earth at one time by reading through that tunnel. But the speed of the apple would slow down as it crossed the surface and went a little deeper. This is because the value of gravitational acceleration g is highest at the surface. And the higher you go from the surface, the lower the value of g will be. The value of g will decrease even if it goes down from the surface.
Newton said in his law of gravitation that every object in the universe is attracted to each other. As the distance between two objects increases, the value of their gravitational ball decreases. As the distance decreases, the value of the gravitational ball increases. But where is this distance calculated from two objects?
The calculation of distance comes from the center. That is, one object attracts another object to its center. If that is the case, then why is the value of the gravitational ball at the center of the earth zero?
1. When an apple is on the surface, the mass of the whole earth is active for the gravitational ball, in
fact the Newtonian gravitational force depends on the mass of the object. How much force a falling apple will feel depends on the mass of the earth. Apple's mass is so low that it does not fall into the category. The distance from the center of the earth to the center of the apple also plays a big role in the formula of the gravitational ball.
As the distance between two centers of two objects decreases, so does the value of the gravitational ball attracted between them. The closer an apple is to the center of the earth, the less the distance between the center of the earth and the center of the apple. The logic then is that the more the apple moves toward the center of the earth, the greater the force of attraction between them.
In fact, when the apple falls from the tree to the ground, it feels a greater force of gravity as the distance decreases before it touches the ground. But as the tunnel moves towards the center of the earth, the attraction of the gravitational ball decreases. This is because the force of gravity does not depend solely on the distance between the two objects. There is also the matter of the product of the mass of the two objects.
The picture shows an apple placed inside the tunnel. As much as the mass from the center of the earth to the apple is mass, only that mass participates in the action of gravity.
The darker part of the image is the region of the active mass. The mass of the earth in the light part of the mass does not take any use to attract apples.
The question is, does the product of mass decrease as it passes through the center of the earth through the tunnel?
In order to reduce the product, the mass of any one or two objects should be reduced. If the mass of the earth or the apple is not decreasing, then why the product of mass will decrease?
Um, of course, yes, I know this, why it's something known in advance. Yet the product of mass is decreasing.
How?
Suppose the depth of the tunnel is 100 kilometers. The apple will go to the bottom of the 100 km tunnel and stop. Then its distance from the center of the earth will decrease. The size of the sphere, the mass of the set, up to a depth of 100 km from the earth's surface, will not take part in the gravitational action. This means that as far as the apple goes deep, the size of the earth, the mass in that volume, will not be able to attract the setuku apple. So the product of the mass of the apple and the earth will be reduced a lot. On the other hand, the amount of force required to reduce the mass is much greater than the amount of force required to increase the force due to the reduction of distance. So as the apple moves toward the center of the earth, the force of gravity decreases.
And if it reaches the center of the earth, then there is no distance between the apple and the earth. The center of both is then at one point. Therefore, there is no region of the active mass of the earth to act as a gravitational force. Due to this the value of the gravitational ball in the center of the earth is zero.
1. Gravity / George Gamo
II. The Ascent of Gravity / Marcus Kaun