Question

The mass of the earth was experimentally determined for the first time by

Answer 1

Cavendish was the first one to have determined Newton's theory was correct. Newton's gravitational constant and accurately measured the Earths mass and density. So it was Newton.

Answer 2

The mass of earth was first calculated back in the 1770s in Perth.  

M⊕ = 5.9722×1024 kg is the current estimated mass of the Earth.

The Schiehallion experiment was the experiment that was done with the funding of Royal Society to determine the mass of earth. The experiment was conducted near a Scottish mountain named Scheihallion.  The mass of the earth is considered as the standard astronomical unit of mass to find the mass of other planets of the solar system.

Later the Cavendish experiment was conducted to determine the correct value where the Schiehallion experiment posed some defects.