It's very interesting that the definition of a metre the length of a
2-second pendulum would be so close to the definition of a metre as 10
millionth of the meridian along a quadrant. So I asked myself whether
this coincidence is unique to the earth or if it would happen in other
planets.
It turns out that what is unique about the earth is its density. Any
planet, whether big or small, will have the same close relationship
between the two definitions of metre, as long as it has the same density
as the Earth. In a big planet, the metre would be longer, but the two
definitions of metre would still agree if the planet's density is right.
I would provide a full formal derivation, but that might be off-topic :-)
Daniel.
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