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PlasmaSphere
#4
Jan4-08, 03:19 AM
P: 78
Gravity inside the Earth

Quote Quote by Fizzicist View Post
This is only true if you assume that the density of the earth is uniform, which is not the case.
that is very true, it would not be uniform. It should still derease to zero as you get to the centre though, as at the COG it cancels out in every direction.

I just find it odd that there is no data on this. There are plenty of deep caves and pipelines about the earth, some that go over thirty miles down, so i would have thought that at least some experiments would have been carried out to see what gravity is doing inside the earth. there must be some experiments that have been conducted. can anyone find any? i certainly cant

Quote Quote by Andre View Post
For a homogenouos sphere it can be determined that g(r)=GM(r)/r2. M(r) being the mass within of the sphere with radius r. - G gravitational constant and rho density (Sorry, not proficient with that excellent formula tool)

The total mass outside that radius is cancelling each other. Since M(r)=4/3 * rho * pi *r^3 it follows that g(r)=4/3 * G * rho * pi * r. In other words the gravity inside a homogenouos sphere is directly proportional to the distance to the centre.

Now assuming that the density rho is linear decreasing from value a with increment b, we replace rho with rho(r)=a-br. Substitute it in the first formula to get only a simple square formula, so intergrating is basic.

However we have five discontinuing layers: inner core, outer core, lower mantle, upper mantle, lithosphere. Each with their own numbers r-min, r-max, rho-a and b

So a practical approach is numerical intergration in a spreadsheet with the advantage having the graph visible immediately. I used 100 km increments for each shell. Cross checking it with the real Earth data (mass and g) the numbers in that link appeared to be off by 1,6%.
A fine piece of work! i had not thought about this before, and to be honest the maths was beyond me, until i saw that.

Now who wants to predict what my graph shows?
i would like to see that graph, it doesn't seem to work.

Q1 Where is gravity of the Earth the strongest?

x C – SOMEWHERE ABOUT HALFWAY DOWN TO THE CENTRE OF THE EARTH. 10,62 ms-2 at a dept of about 2890 km
That surprises me somewhat. I would have thought it was stongest at the surface, as the further down you go the more mass cancels out. hmmm..... i'm missing something.