I am interested in a timeline for the history of measuring the mass of the Earth from the first estimates to the currently accepted value, and in references containing more details.


Newton's gravity law says that acceleration of gravity on the Earth surface is $\gamma Mr^{-2}$, where $\gamma$ is the gravitational constant, $M$ is the mass of the Earth, and $r$ is the radius of the Earth. Radius is easy to measure (by astronomical means) and the acceleration is also easy to measure. One can use instead the distance to the Moon and Moon's acceleration, for which you only need astronomical observations, which are usually more precise than any measurement on the Earth). This shows that the problem of measuring the mass is EQUIVALENT to the problem of finding the gravitational constant: once you measure one of them you obtain the other.

The gravitational constant was measured for the first time directly by Cavendish (1798) with the result: $6.754×10^{−11} m^3⋅kg^{−1}⋅s^{−2}$. (Modern value is $6.672×10^{−11} m^3 kg^{−1} s^{−2}$. So Cavendish's error was $1.2\%$.

Actually Cavendish actually stated his result in terms of the mass of the Earth, (or the average density of the Earth) rather then in terms of the gravitational constant. There is no much to say about measurements between the time of Cavendish and present (see Wikipedia ("gravitational constant") which explains why it is difficult to measure). I do not think there is another reliable method of accurate measurement of the mass of the Earth, except the direct measurement of the gravity constant. (Any method based on the knowledge of what is the Earth made of will be much less accurate. Actually it works in the opposite direction: we guess the composition of the Earth using the knowledge of its mass).

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