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Thread: Gravity stronger closer to centre of the earth?

  1. #1 Gravity stronger closer to centre of the earth? 
    Forum Freshman LotusTiger's Avatar
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    Why is this. I think I heard anyway that every particle exibitits it's own gravity on other things. Does this mean the reason things are heavier of the same mass closer to the earth is because the center of the earth is very dense?


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    No, it is the law of gravity. Let's assume the Newtonian approach for simplicity. This law constitutes that the gravitational force between two bodies having a mass depends on the mass and the distance squared. For simplicity, it is often assumed that one mass is much bigger than the other so that the force of the "lighter" body can be neglected. So, the force is higher, the bigger the mass, and lower the more distant it is. Why exactly the law is like this, cannot be answered with this Newtonian approach. The nature of "mass" is still an unanswered question.

    This law is only valid accurately, if the mass is point-like, i.e. without dimension. The closer you get to a real body with a mass the more you will have to consider its size. It is possible, but mathematically more difficult than just multiplication and division of numbers. But the qualitative effect still remains that the force increases, the closer you get.

    This means, the density of a body only determines until which distance the point-like approach is still in good agreement with reality.

    As soon as you get inside the body with the bigger mass, i.e. the earth, the effective gravitational force is reduced the more you advance to the core of the earth. The reason is that the gravitational pull from one side is partially compensated by matter now being on the other side. In the centre of the earth, everything is effectively weightless.


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    Darn, Dishmaster, you beat me to answering it... :wink:
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    Forum Freshman LotusTiger's Avatar
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    Thanks Dishmaster I understand most of what you said?

    But I have a question and correct me if this comes from not understanding a part of what you said correctly. But if you were a quarter way away from the center of the earth on one side in a large opening would you be pulled towards the surface of the earth becasue most particles are above you now? I welcome others too to awnser this question on what dishmaster said too.
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    Quote Originally Posted by Liongold
    Darn, Dishmaster, you beat me to answering it... :wink:
    Sorry.

    Quote Originally Posted by LotusTiger
    Thanks Dishmaster I understand most of what you said?

    But I have a question and correct me if this comes from not understanding a part of what you said correctly. But if you were a quarter way away from the center of the earth on one side in a large opening would you be pulled towards the surface of the earth becasue most particles are above you now? I welcome others too to awnser this question on what dishmaster said too.
    You will be pulled towards the centre. If the earth were hollow, you would bounce around the centre for a while and finally come to rest there. You have to the see the earth as a sphere and not in terms of up and down. Within the sphere, there is also left and right, ahead and back. From the centre, all forces cancel out, because for each particle at a certain distance there is another at the same distance, but in the opposite direction. If you are 1/4 of the earth's radius away from the centre, there is 3/4 above you, but still 4/4 behind the centre to the other direction.
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    Assuming for a moment that the earth is perfectly homogeneous, then as you go down, you will only be pulled towards matter that is at the same depth and deeper than you are. In other words, if you take the mean radius of a perfectly homogeneous billiard ball to be 10000m, if you then descend into a hole down to 2000m below the surface, you would experience gravity as if you were standing on a billiard ball with a radius of 8000m. Also, if you were on the inside of an earth sized ping pong ball, then you would float around in zero gravity, irrespective of how think the plastic is or where on the inside you are.

    This is Newton's Shell theorem.
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    Quote Originally Posted by Dishmaster
    If the earth were hollow, you would bounce around the centre for a while and finally come to rest there.
    I think you are effectively weightless inside a hollow sphere: the gravity cancels out, regardless of where you are inside the hollow earth. While there is more mass at one side, that mass is also further away, and in a nice and homogeneous hollow sphere, it cancels out nicely.

    or what Kalster said...
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    Quote Originally Posted by Bender
    Quote Originally Posted by Dishmaster
    If the earth were hollow, you would bounce around the centre for a while and finally come to rest there.
    I think you are effectively weightless inside a hollow sphere: the gravity cancels out, regardless of where you are inside the hollow earth. While there is more mass at one side, that mass is also further away, and in a nice and homogeneous hollow sphere, it cancels out nicely.

    or what Kalster said...
    I think he meant if you were to jump into a hole that goes straight through. Friction will eventually stop the pendulum.
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    Quote Originally Posted by Dishmaster
    You will be pulled towards the centre. If the earth were hollow, you would bounce around the centre for a while and finally come to rest there. You have to the see the earth as a sphere and not in terms of up and down. Within the sphere, there is also left and right, ahead and back. From the centre, all forces cancel out, because for each particle at a certain distance there is another at the same distance, but in the opposite direction. If you are 1/4 of the earth's radius away from the centre, there is 3/4 above you, but still 4/4 behind the centre to the other direction.
    If the earth was hollow, gravity would be zero everywhere inside it; no matter where you were in the interior, gravity would always perfectly cancel out (assuming it's perfect sphere, etc).

    Edit: Oops, someone else already said it.
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  11. #10 Re: Gravity stronger closer to centre of the earth? 
    Forum Freshman deadcat's Avatar
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    Quote Originally Posted by LotusTiger
    Why is this. I think I heard anyway that every particle exibitits it's own gravity on other things. Does this mean the reason things are heavier of the same mass closer to the earth is because the center of the earth is very dense?
    I thought of this also when first taking an in depth examination into gravity, what I came to understand as being accepted was that the larger a mass is, the more it will affect space/time fabric hence affecting gravity, like a heavy object in the center of the net all lighter objects in a range that can be affected will then will be drawn closer. Now I thought, if this was the case how would people all over the world stay on the planet if one side was down, when reading further into this I learned the objects mass dips into space/time in ALL directions, so the center of the mass would be attract objects from ALL sides.

    That's a pretty crazy point you bring up though because the closer to the center of the mass your get the steeper the decline would be, therefore making a greater force of gravity, unless I'm missing something, but I guess that's the whole point of LotusTiger's question.

    The one thing I still don't understand about gravity though is how it can "slingshot" objects, you think they would just collide.
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  12. #11 Re: Gravity stronger closer to centre of the earth? 
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    Quote Originally Posted by deadcat
    The one thing I still don't understand about gravity though is how it can "slingshot" objects, you think they would just collide.
    You could describe an orbiting satellite to be constantly falling towards earth, but missing it.

    In short: all objects have momentum. You change the momentum by pulling on them, but only gradually. This means it's not because gravity pulls one object straight to another that that other object will instantly change its course towards the first.
    At the same time, both objects are moving, with the result that the gradually changing direction of movement of the second object will never actually go directly at the first, but keeps on missing it.
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  13. #12 Re: Gravity stronger closer to centre of the earth? 
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    Quote Originally Posted by Bender
    Quote Originally Posted by deadcat
    The one thing I still don't understand about gravity though is how it can "slingshot" objects, you think they would just collide.
    You could describe an orbiting satellite to be constantly falling towards earth, but missing it.

    In short: all objects have momentum. You change the momentum by pulling on them, but only gradually. This means it's not because gravity pulls one object straight to another that that other object will instantly change its course towards the first.
    At the same time, both objects are moving, with the result that the gradually changing direction of movement of the second object will never actually go directly at the first, but keeps on missing it.
    Ok, that makes more sense, I'm sure things collide too, just didn't understand the slingshot effect, that makes sense though.
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    The largely unsung hero of planetary exploration is Gary Flandro. It was his work at JPL that made possible the paradigm changing journeys of Pioneer 11 and the Voyager spacecraft.

    In 1925 Walter Hohmann was the first to propose, in Die Erreichbarkeit der Himelskorper, multi-planet trajectories, which used the slingshot effect. (Today he is better known as the originator of the Hohmann minimum energy transfer orbit.) G.A. Crocco discovered that the slingshot effect could be used to maintain a continual looping around the inner planets in what he called the Grand Tour. He announced this in Rome in 1956 at the Seventh International Astronautical Conference.

    Joe Cutting at JPl, who had been one of the team that engineered the close approach to Mercury of Mariner 10 by approaching Venus en route, directed Flandro, in 1965, to look for ways of using gravity assist from Jupiter to explore the outer planets.

    Flandro, using incredibly primitive calculating methods (including manual ones) worked out over one thousand trajectories and determined that a Grand Tour of the outer planets would be possible if launched in the late 1970s. The next such opportunity would not occur for for over one hundred and seventy years. The Pioneer and Voyager programs were born.

    It is one of those interesting coincidences that the man who coined the term Grand Tour and the man who made possible the greatest achievement of space exploration in the 20th century both have the intials G.A.

    References:
    Litmann, M. "Planets Beyond: discovering the outer solar system" John Wiley and Sons pp 95-98

    Snyder, A.P. "NASA and Planetary Exploration" http://spacescience.nasa.gov/admin/pubs/history/

    Harland, D.M. "Mission to Saturn" Springer-Praxis Chap. 2

    Flandro, G.A. "Fast Reconaissance Missions to the Outer Solar system Utilizing Energy Derived from the Gravitational field of Jupiter", Acta Astronautica 12 1966
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  15. #14 Re: Gravity stronger closer to centre of the earth? 
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    Quote Originally Posted by deadcat
    missing something, but I guess that's the whole point of LotusTiger's question.

    The one thing I still don't understand about gravity though is how it can "slingshot" objects, you think they would just collide.
    Gravity is used to transfer momentum from one object to another. It is similar to when a ball hitting a bat imparts some of its momentum to the ball, but instead of colliding, the objects whip around each other in hyperbolic orbits.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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    Forum Radioactive Isotope MagiMaster's Avatar
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    Just thought I should point out that during a slingshot maneuver, the ship gains speed because it steals some from the planet's orbit. (Of course, the difference in mass means that the ship is now going significantly faster and the planet doesn't even notice.)
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    Quote Originally Posted by MagiMaster
    Just thought I should point out that during a slingshot maneuver, the ship gains speed because it steals some from the planet's orbit. (Of course, the difference in mass means that the ship is now going significantly faster and the planet doesn't even notice.)
    And it can be used the other way too; you can remove velocity from the ship and give some to the planet.
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    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  18. #17  
    Universal Mind John Galt's Avatar
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    Two points of detail here that I am 85% certain about.
    1. Magimaster, the angular momentum transfer is 'stolen' from the rotation of the planet about its axis, not from the its orbital velocity.
    2. Janus, there is no way of transfering energy to from the spacecraft to the planet. If the appropriate trajectory is chosen the craft can be directed sunwards at an increased velocity, rather than outwards, but the planet loses in both instances.
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