|MadSci Network: Astronomy|
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.).
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