Relative weights and elevations

[RenaissanceChemist]

The science channel had a physicist who travels the world measuring to a hundredth of a gram the weight of a plaster gnome.

He demonstrated that the gnome loses 2 hundredths of a gram from the ground floor to the 108th floor of a high rise.

His error was in claiming that the closer you get to the center of the earth, the heavier your weight will be.  Quite impossible, no?

So I created a crude representation of how weight changes with below grade elevation, but can't quite manage to determine the depth at which measured weight is maximized.   A very neat problem in my opinion.

[swansont]

There’s a curve given here that has numbers on the axes: https://physics.stackexchange.com/questions/439639/the-acceleration-in-earths-gravity

[mathematic]

Assuming uniform density for the earth, the maximum will be at the surface.  However, the interior density is higher, so a curve as shown may be more accurate.

[RenaissanceChemist]

1 hour ago, mathematic said:

Assuming uniform density for the earth, the maximum will be at the surface.  However, the interior density is higher, so a curve as shown may be more accurate.

WHERE "at the surface"?

You failed to add the condition of perfectly spherical shape, which of course is not the case.  Masses weigh more at the poles, where they are closer to the center.

I submit that further decreasing elevation relative to the center will increase measured weight to an optimum, where it will reverse and get lighter until it goes to 0 weight at the center.