how can we calculate the mass of the earth?
Find the period and distance of a satelite and use Kepler's law
By measuring the rate of gravitational acceleration at the surface. The limiting factor is the accuracy of Newton's constant G, which has been measured now to about 4 significant figures.
Cheers -- sylas
Sylas' method is rather old school. It is confounded not only by the relative low accuracy in our knowledge of G but also by the Earth's rotation, the Earth's non-spherical shape, and local variations in g due to local variations in density. Nonetheless, that is how scientists estimated the Earth's mass prior to the space age.
The Earth's non-spherical mass plus the fact that a satellite is also subject to gravity from the Moon, the Sun, Jupiter, Venus, etc. means that a simple Keplerian model (post #2) will also give erroneous results. The current best estimate of G*Me is obtained by observing satellites over a long period of time and removing all those confounding effects. The product of G and the Earth's mass is now known to almost nine places of accuracy thanks to satellite observations. However, because the universal gravitation constant G is only known to about four decimal places, the mass of the Earth is also known to only four decimal places.
Bah. Young people these days don't show no respect. :tongue2: That aside... you are quite correct. My old fashioned post crossed with the ever up to date mgb_phys, who is the better guide in these modern times.
Do you know how they obtain estimates for G? I'm guessing it is by measuring accelerations of known masses in a laboratory, but I've not checked.
Cheers -- sylas, who is just a tad younger than the space age
Bah right back atcha! Your parting remark ("Cheers -- sylas, who is just a tad younger than the space age") makes me my flatulence more chronologically challenged than yours.
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