3 ms·

Wild guess: you don't measure a second. A second is defined as 1/86400 of a day, or 246060. Lets say a pendulum can swing for about 2 minutes. You just take a

Wild guess: you don't measure a second. A second is defined as 1/86400 of a day, or 246060. Lets say a pendulum can swing for about 2 minutes. You just take a 2 minute hourglass, make a bunch of pendulums of different lengths, and assign someone to count the number of swings between the moment you turn the hourglass and the moment the sand has passed trough. The one closest to 120 is the correct length. Now this solution is mathematically elegant but comes with a lot of problems. First you must rely on a less-than-perfect time measurement device which may suffer from day to day variations due to temperature. On the contrary, to calculate the distance from the poles to the equator, all you need is a good angle measurement device, from which you can triangulate a distance.

defrost 3y ago
> On the contrary, to calculate the distance from the poles to the equator, all you need is a good angle measurement device, from which you can triangulate a distance. Can you expand on how this can be done please? Particularly the bit where you measure the semi-major axis and semi-minor axis of the Earth's ellipsoid and how you settle on a particular ellipsoid out of the many that predate WGS84. https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Ear... "All you need" appears to bury a lot of detail in some hand waving. It's unclear to me whether you intend to measure a distance along the Geoid (gravitational equipotential surface), along the Ellipsoid (the rotated ellipse of best fit), or the actual suurface (the path that would be walked, floated, traversed from equator to pole). A complication with the Geoid path family and surface path family, of course, is that these vary by what line of longitude you might follow.
- numpad0 3y ago
  Eratosthenes did that in his time with spherical Earth model, and it was precise enough for ~2k years. A lot that can be hand waved with that route as opposed to relying on availability of a well defined and calibrated precise time measurement device, whether it's 1 second or 2 minutes.
  - defrost 3y ago
    Eratosthenes who now? Sorry, couldn't help myself, unlike yourself. Just recall we're in a thread about precise definitions of reference units, the title posed refers to tens of trillions of oscillations as the definition of a second. When the kilometer was first coarsely defined by an Earth arc it was already a thousand+ years post shadow of a stick guy. Once that kind of definition gets refined further the "arc of the earth" approach hits all of the hurdles I outlined .. for the benefit of the person I replied to who somehow believed it was a simple straightforward task to make it "better". Hand waving a reference is all very well ... until you hit cases that require actual precision finer than the error bars on the hand wavy seat of the pants cowboy antics. That bar was crossed some decades past.

defrost 3y ago

> On the contrary, to calculate the distance from the poles to the equator, all you need is a good angle measurement device, from which you can triangulate a distance. Can you expand on how this can be done please? Particularly the bit where you measure the semi-major axis and semi-minor axis of the Earth's ellipsoid and how you settle on a particular ellipsoid out of the many that predate WGS84. https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Ear... "All you need" appears to bury a lot of detail in some hand waving. It's unclear to me whether you intend to measure a distance along the Geoid (gravitational equipotential surface), along the Ellipsoid (the rotated ellipse of best fit), or the actual suurface (the path that would be walked, floated, traversed from equator to pole). A complication with the Geoid path family and surface path family, of course, is that these vary by what line of longitude you might follow.

numpad0 3y ago
Eratosthenes did that in his time with spherical Earth model, and it was precise enough for ~2k years. A lot that can be hand waved with that route as opposed to relying on availability of a well defined and calibrated precise time measurement device, whether it's 1 second or 2 minutes.
- defrost 3y ago
  Eratosthenes who now? Sorry, couldn't help myself, unlike yourself. Just recall we're in a thread about precise definitions of reference units, the title posed refers to tens of trillions of oscillations as the definition of a second. When the kilometer was first coarsely defined by an Earth arc it was already a thousand+ years post shadow of a stick guy. Once that kind of definition gets refined further the "arc of the earth" approach hits all of the hurdles I outlined .. for the benefit of the person I replied to who somehow believed it was a simple straightforward task to make it "better". Hand waving a reference is all very well ... until you hit cases that require actual precision finer than the error bars on the hand wavy seat of the pants cowboy antics. That bar was crossed some decades past.