According to A Short History Of Nearly Everything by Bill Bryson, Henry Cavendish made the first attempt at measuring the mass of the earth in 1798. He calculated it using something called a torsion balance, which had 2 balls of known mass and size, one of which was very large and the other very small. He then hung them next to each other with absolutely no interaction of any kind, in a perfectly windless room. He then measured the displacement of the small ball, therefore calculating the gravitational constant of the Earth, and knowing the size of the earth and the gravitational field strength he could calculate the mass of the Earth. This would not provide a completely 100% accurate answer but it is very very close. He got a reading of 6 billion trillion tons, and if I am right the most recent idea is that it is 5.9742 × 10^24 kilograms which is pretty close.

Newton's rings are a kind of interference pattern produced by light waves interacting with a curved and flat surface. It's explained at this Harvard website.