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The first estimate of Newton’s constant G was made by Maskelyne in 1774 by measuring the angle between the directions of the apparent plumb-line vertical at points on opposite sides of the Scottish mountain Schiehallion (height 1081 m, chosen for its regular conical shape). Find a rough estimate of the angle through which a plumb line is deviated by the gravitational attraction of the mountain, assuming that it is a sphere of radius 500 m and density 2.7 × 10^3 kg m−3.

Attempt at solution:

I'm doubtful of my understanding on how Maskelyne's experiment actually worked. My setup is a sphere of radius r (with uniform density d), and tangent to the bottom of the sphere (a distance z away from the bottom point of the sphere) is the plumb-line. By spherical symmetry, we can consider the sphere as a point mass (with mass m that can be determined with r and d). So, we just need to find the gravitational force between the point mass in the sphere and the one on the plumb-line, and then do some calculation to get the angle of deviation.

First of all, this reasoning seems too simple. Second of all, I'm not sure how I'm supposed to deal with the fact that I don't know the mass of the plumb-line. However, the variable z would end up in my solution anyways. Can someone help me out in terms of setting up the problem correctly?