Re: Who were the first to try and calculate how much the Earth weighs?

Hello, Nicolaj!

If someone calculated the mass of the earth early on, I can't find a record
of it in any of my books or on the web.  Certainly the diameter of the Earth
had a good estimate, circa. 250BC, by Eratosthenes (see, e.g. the "Cambridge 
History of Astronomy", pg. 39), and I suppose anyone after that could posit 
a density estimate (but couldn't prove it right) and multiply by the volume 
of the planet. But if they did this, they didn't leave any trace that I 
could find of what they estimated.

"Decent" (whatever that means...) numbers for the mass of the Earth followed 
after the determination of the universal constant of gravitation [the G in
F = GMm/(r^2)] just around 1800 by Cavendish. Indeed, it is said that when
asked why he was taking the measurement, Cavendish replied that he was 
"weighing the Earth."  (He should have known better...it was the mass he was 
determining, not the "weight"...but I suppose it sounds better his way).

Measurement of the gravitational constant turns out to be a fairly difficult
thing to do, because the gravitational force is so small that measuring it
in a laboratory gets tangled with myriad sources of experimental noise 
(slight temperature changes, vibration from trucks driving by, very slight 
air movements, etc). Here's a web site that talks about the recent 
determinations of G at the University of Washington:

     http://npl.washington.edu/eotwash/gconst.html

The formulas used, once G and the Earth's radius are known, are pretty 
straightforward applications of Newton's force laws and law of gravitation, 
and how it's done can be found in an introductory physics text...unless it 
is left as a homework problem for the student to solve!  (I also found this 
is a favorite physics lab. exercise when perusing web pages on the 
subject.).