"g" and Universal Law of Gravitation?

Question

Question 1:
Drill a hole all the way down to a depth 0.5 metre above the centre of earth. For that we need a long casing to stop sloughing and ground water into the hole. This is an ideal closed end casing which is strong enough to withstand high pressure and temperature inside the earth. Now put a sphere of 1 kg mass of 1 metre diameter at/ on the base of hole. The distance between the centre of the earth and the centre of the sphere is 1 metre.

Now apply the same universal law of gravitation to the two masses. Can I calculate the value of “g” (as Newton drive for his equation on the surface of the earth ) at this point by the following equation.

F = G M m/R^2 g = GM/R^2 , Where R = 1 metre, therefore R = GM, g= 3.98 x 10^14 m/sec^2. So Weight of this mass at o.5 metre above centre of earth =mg = 3.98 x 10^14 N. If not, please explain and why g = 10.7 m/sec^2 in inner core?

Question 2:
Now push the casing further down and past the centre of earth by half a metre. Now Again put a sphere of 1 kg mass of 1 metre diameter at/ on the base of shaft such that the centre of the earth and the centre of the sphere coincides. (Just like white and yolk of boil egg)
Apply the same universal law of gravitation to the two masses. What will be the value of “g” and the gravitational force?
F = G M m/R^2 g = GM/R^2 , Where R = zero metre, therefore g= 0 m/sec^2 or infinity & F=zero or infinity
If not, please explain why?

What is the value “g” at the centre of gravity of the earth?

Question 3:

Now push the casing further down and past the centre of gravity of earth by one km. Now remove the sphere and drop a stone from ground surface or the top of casing. So where will be the resting position of stone, centre of gravity of the earth or at the base of hole?

Answer 1

I believe the "universal law of gravitation" only works for point-masses, that is where you can have no containment.

in question 2, the sphere will have 0 gravitation due to the earth because the gravity from the earth cancels itself out all around it. This basic idea of the gravity cancelling out is the root question in all of those questions.

Answer 2

question 1,
no you can't use the eq in it's basic form. it is accurate as long as the objects are essentially points compared to the distance between them.
with the sphere being below the outer diameter of the earth, to be accurate you would have to sum the gravitaional forces for all the particles of mass in the earth. you can visualize that if the the earth were treated as a popcorn ball each piece would have a pull on the sphere. gravitational effect would be much more complicated than assumed.

question 2,
as question one, there would be a complicated grav effect. a better assumption would be that the earth is two halves. if the sphere were right in the middle then net g would be balanced and zero. if the sphere moves away 1m, the net g would be a result of R 0.5m and M=a 1m thick slice of the earth.

qu 3
it would come to rest at the center of earth, where g forces are balanced.

Answer 3

So actual, pumpkin! The sunlight basically has a negligible effect on earth. Heliocentrists do in comparison to data and cutting-facet technology getting in the way of their nineteenth century theories. And heliocentrism and gravity are basically theories - they have not graduated yet.