# The Naked Scientists Forum

### Author Topic: What is the force of gravity half way to th earths core?  (Read 15551 times)

#### Andrew K Fletcher

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##### What is the force of gravity half way to th earths core?
« Reply #25 on: 13/07/2008 15:58:21 »
If the gravitational force was 0 gravity at the core and 1 g at the surface, there would be no reason for the denser materials to be attracted towards the core.

#### graham.d

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##### What is the force of gravity half way to th earths core?
« Reply #26 on: 13/07/2008 19:46:11 »
Sophie, the reason for the calculus is only that it is not obvious that the field is zero everywhere inside a spherical shell. Knowing this means you don't need the calculus, but if you need to prove this, then I think you do need calculus.

#### Alan McDougall

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##### What is the force of gravity half way to th earths core?
« Reply #27 on: 14/07/2008 09:39:20 »
sophiec,

Quote
No calculus needed, really.
The force is proportional to the mass of the sphere beneath your feet (which is 4πρr3/3)
ρ is density - we can assume it's fairly uniform.
It's also proportional to 1/r2 because of the inverse square law.
Between the two that makes it proportional to r. QED
.

You answer is the the best and easy to comprehend , but the others also valid

Alan

#### lyner

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##### What is the force of gravity half way to th earths core?
« Reply #28 on: 14/07/2008 11:40:46 »
Sophie, the reason for the calculus is only that it is not obvious that the field is zero everywhere inside a spherical shell. Knowing this means you don't need the calculus, but if you need to prove this, then I think you do need calculus.
I agree.
There is a fairly good 'arm waving' argument. Rather than calculating the force on you (sitting in the middle, somewhere), you think of the force on the surface of the shell (equal and opposite - so it's valid) and equate the gravitational, inverse square law, to the effect of ISL on illumination from a light source.  Two cones with the same solid angle, pointing in opposite directions from you, will ' illuminate' the shell with an equal amount of energy. The light is spread out on the distant bits and less spread out in the nearer bits. The total light flux hitting each end of the 'double cone' will be the same, though, and, by analogy, the total gravitational forces on the two areas formed by the two cones of light will also be the equal and opposite. Forces on the shell and, therefore, also on you, will be balanced in any direction. It's easiest to visualise if you are on a diameter but it works for any position - you don't need to consider the actual shape which the light beams form on the  inside of the shell.
(I made this up on my own and I'm quite pleased with it!)

#### graham.d

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##### What is the force of gravity half way to th earths core?
« Reply #29 on: 14/07/2008 15:27:43 »
Oh yes, Sophie. That's very good and why it works is because a spreading flux and the inverse square law are effectively the same in Euclidean space; hmm, may be the same in other spaces but I am not even going to think about that one. I wonder how it would do as a physics undergrad answer?

#### Bored chemist

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##### What is the force of gravity half way to th earths core?
« Reply #30 on: 14/07/2008 18:48:56 »
If, as has been shown, the force is proportional to the radius then an object dropped into this "idealised" hole (no moon, full of vacuum- the earth being solid with equal density all the way down) would exhibit simple harmonic motion.
The maths for that is well known so I will leave it as an exercise for the reader.

And, Sophie, That's a seriously good proof.

#### lyner

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##### What is the force of gravity half way to th earths core?
« Reply #31 on: 14/07/2008 22:33:44 »
Lovely when you don't have to do anything other than wave your arms about.
I gave it some further thought and , first of all, it seemed that the argument would apply for any shape of shell. Then I realised that the shell has to be spherical if the density is uniform - for
F = Gm1m2/r2
to apply.

I have written this elsewhere (and there was a TNS Podcast, too) but the period would be the same (90 minutes) for small, spherical asteroid and a pea sized object moving through a hole through the centre as long as the average density was the same as the Earth's.  What an experiment to try, one day.
« Last Edit: 14/07/2008 22:36:47 by sophiecentaur »

#### Alan McDougall

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##### What is the force of gravity half way to th earths core?
« Reply #32 on: 15/07/2008 01:31:25 »
Go to my other thread on gravity.It relates to a hollow shell like earth etc

#### The Naked Scientists Forum

##### What is the force of gravity half way to th earths core?
« Reply #32 on: 15/07/2008 01:31:25 »