On Fri, 12 Nov 2004, Jason S wrote:

> The mass of the Earth has been fairly accurately known for a few centuries.
>
> Kepler's Third Law of Planetary Motion is that the mean orbit radius cube
> divided by rotation time squared for any object in a stable orbit around a
> mass is directly proportional to the mass of the object.
>
> The contant of proportionality depends only on the universal gravitational
> contant (mentioned earlier on this thread and known since Netwon's time),
> and pi.
>
> Since we can measure how far the moon is from the earth and how long it
> takes the moon to orbit the earth, we know the mass of the earth to the same
> level of accuracy.
>
> The mass of the moon wasn't known very accuratly until the mid 20th century
> when we put a satellite in orbit around it.
>
> I don't think you can directly measure g at sea level and 71 km up more
> accuratly than you can measure the earth-moon distance and how long it take
> the moon to orbit the earth.

g can be measured to 1 part in 10^12 or so. The satellite based 
measurement has a small flaw: it uses the mass of the satellite as 
reference, and that is measured with a scale on earth, and the scale 
depends on g.

To really know the mass and density of something the only way would be to 
use something like a mass spectrometer to depose a counted number of atoms 
of it on a scale. This allows mass and density to be computed (with some 
accuracy). *Then* you have a reasonable mass standard and can weigh the 
satellite which can weigh the earth and the moon etc.

And because of the 1/r^2 part in the law of universal gravitation you need 
to measure r to N^2 decimals to find mass with N decimals. And the 
distance from earth to moon in femtometers is ...

Peter
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