Henry Cavendish · The density of Earth
Can you weigh the Earth?
That time, that place
Newton's law of gravitation contained a constant, G, and nobody knew its value. You could work out how many times heavier one planet was than another, but not what the Earth actually weighed.
The geologist John Michell designed an apparatus to measure it, then died. The apparatus passed to Cavendish.
Why this question
Hang two small lead balls at the ends of a rod, suspend the rod from a fine wire. Bring large lead balls alongside, and the gravity between them should twist the rod — very slightly.
The problem is how slight. A breath, a draught from a temperature difference across the room, a footstep — anything at all is larger than this force.
What was found
Cavendish put the apparatus in a sealed room and stayed outside it. He read the scale through a telescope aimed at a hole in the wall — so that he would not have to enter.
The twist was tiny. He measured it over and over and averaged.
Result: the mean density of the Earth is about 5.48 times that of water. Today's figure is 5.51. He was within one percent, more than two centuries ago.
With that one number in hand, the masses of the Sun, the Moon and the planets followed.
The mass of the Earth was thought to be beyond reach
Repeated readings of the torsion balance's tiny rotation, taken through a wall
It became the first measured value behind G, and the masses of the solar system followed