2MG/r2And notice "r" = 100 meter not 50 meter
"2" = because also part of the mass of the Earth contributes to encircles a central point of space, between the building and the Earth.
I said 'from your measurements'.
OK, I 'll explain because otherwise, this never ends. Follow this carefully, because I will not repeat it (anymore).
1) The actual COG. We can't calculate it from the dimensions of the building, because the mass distribution is certainly not even. If the building was floating in space, we could measure it. It would be the point where gravitational pulls were the same in all directions. So in that point we would measure a virtual zero gravity.
2) Measuring on Earth. We can, as Bjarne demonstrated, measure the gravitational pull on each floor. We will then get a positive gravity on all floors, because Earth's gravitational field is far stronger than that of the building. We will also get a gravity that gets lower as we rise into the building, because Earth's gravity diminishes with elevation (the free air gradient).
3) Calculating. Now we can start to subtract the influences that are not from the building. The scientists making measurements for Bjarne already corrected for tidal force, so we can forget about that. Since we know the approximate hight of each floor, we can also subtract the free air gradient. Now we have a list of values that show the gravity pull of the building plus the gravity of Earth. We will notice that gravity pull is largest at the top floor (Earth + building) and least on the bottom floor (Earth - building.). Between those points, we see a fairly smooth slope (as we have discussed, there are bumps, but that is a secondary matter).
4) COG? Now, to find the exact COG, all we have to do is subtract Earth's gravity from all the values, and the COG will be where the slope crosses zero, just like in space. There is just one small problem: We don't know the exact value for Earth's gravity pull, in that exact spot. Of course, we know the general value, but in real life, it varies from place to place, due to a number of reasons. And, unfortunately, those variations are a good deal larger than the total gravitational pull of a large building. If someone had taken the trouble to measure and record the gravity constant in the spot
before they started to excavate foundations and erecting the building, we might have had luck. But nobody did, and actually, I don't even think sufficiently precise instruments were available at the time.
....
So how can Bjarne deduct the position of the COG, from his measurements? Answer: He can't. Nobody can, because there is insufficient information. What we can see is that there is a gradual slope from top to bottom, which is consistent with the law of gravity. Presumably this crosses the baseline gravity at some spot, but without a sufficiently precise figure for the baseline gravity, we cannot know where.
End of story.
So Bjarne, if you want to make a new experiment, make sure you obtain the baseline gravity. Otherwise you are wasting time and money.
Now, if you had designed a proper protocol, as I told you to do, you would have realized this in advance.
OK, you can now pretend this did not happen.
Hans