Thanks!
Questions about gravity...
Author
A couple of years ago I took Physics I in college but learned little from it. I've recently decided to start studying it on my own from a physics textbook. I've learned that the effect of gravity varies slightly depending where you are on the surface of the Earth. How would does gravity vary as you get closer to the center of the Earth? Like in Journey to the Center of the Earth. Intuitively, I feel that the effect of gravity would become more intense as you got closer and closer to the Earth's core. This isn't a homework question, it's just something I was thinking about after reading more about gravity in my physics book. I apologize if this question has an obvious answer that I have overlooked.
Thanks!
Thanks!
I think the closer you get to the center of the earth, you have less and less gravity. Because it becomes equally in all other directions.
Author
I think the closer you get to the center of the earth, you have less and less gravity. Because it becomes equally in all other directions.
So, if the center of the Earth were hollow and you were inside of it, you would be floating? Or have I misunderstood what you were saying? Thanks for replying!
You are still attracted to every particle in the universe, and the attraction is proportional to the distance. You are closest to Earth so those particles have the biggest attraction.
If you were in the center of the Earth your net attraction to the particles of the Earth would be roughly zero, because you would be roughly at its center of mass. You would be pulled roughly in equal amounts in each direction by them.
As you approached the center of the planet, your next biggest attractors would be the Sun and moon. You have those attractions already, you just don't notice them. Human bodies aren't really meant to detect that type of forces.
If you were in the center of the Earth your net attraction to the particles of the Earth would be roughly zero, because you would be roughly at its center of mass. You would be pulled roughly in equal amounts in each direction by them.
As you approached the center of the planet, your next biggest attractors would be the Sun and moon. You have those attractions already, you just don't notice them. Human bodies aren't really meant to detect that type of forces.
You might want to look up Gauss' Law. It's usually described for electric charges and electric fields, but it also works for masses and gravitational fields.
Simply, the flux of the gravitational field across a closed surface is proportional to the amount of mass contained within the surface. Now, consider a sphere, centered at the center of the earth, with a radius less than the earth's. Assuming a constant density of the Earth (which isn't true, but go with it), you can compute the mass enclosed, and figure out the flux. Then you can divide this by the area of the sphere, to figure out the flux per unit area, and hence the strength of the field. You'll see how the field drops as you approach the center. In fact, try plotting this as a function of distance from the center of the earth. You'll get that the field is zero at the center, increases linearly until you reach the surface, and then drops off as 1/r^2. It would probably be a good exercise to work out the details yourself!
Simply, the flux of the gravitational field across a closed surface is proportional to the amount of mass contained within the surface. Now, consider a sphere, centered at the center of the earth, with a radius less than the earth's. Assuming a constant density of the Earth (which isn't true, but go with it), you can compute the mass enclosed, and figure out the flux. Then you can divide this by the area of the sphere, to figure out the flux per unit area, and hence the strength of the field. You'll see how the field drops as you approach the center. In fact, try plotting this as a function of distance from the center of the earth. You'll get that the field is zero at the center, increases linearly until you reach the surface, and then drops off as 1/r^2. It would probably be a good exercise to work out the details yourself!
While Gauss' law is nice, you actually should be checking out Newton's Shell Theorem.
Fancy rabbits with oversized egos.
Fancy rabbits with oversized egos.
(If the density of the Earth would be constant) the absolute value of the gravity is a linear function.
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Ahh, beaten by Emergent...
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Ahh, beaten by Emergent...
szecs, you know I love you... but seriously. Newton died quite some decades before Gauss was even born. Please refrain from skewing history through your misinterpretations. It is crackpottery.
szecs, you know I love you... but seriously. Newton died quite some decades before Gauss was even born. Please refrain from skewing history through your misinterpretations. It is crackpottery.
what??
[quote name='taby' timestamp='1303220324' post='4800348']
szecs, you know I love you... but seriously. Newton died quite some decades before Gauss was even born. Please refrain from skewing history through your misinterpretations. It is crackpottery.
what??
[/quote]
Again, I love you, and I am still very sorry that I didn't get you a gdnet Christmas present like I was supposed to.
However, you didn't beat emergent to anything.
Newton couldn't publish his Principia until he finished his shell theorem. It was the crowning jewel, and he struggled with it for years -- co-discovering calculus along the way in order to finally succeed.
Gauss knew that, and so should you guys. To ignore it is very disrespectful to Newton. That said, I rated emergent ++ last night just to prove that I'm not trying to be a jerk out of spite. This is very important history.
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