Regarding the diameter of the earth

  1. is the equatorial diameter of the Earth measured at sea level?
  2. If the Earth was all smoothed out like a billiard ball, mountains leveled and holes filled in, would the diameter be much different?

Don’t know the answer to #1, but as for #2 - the Earth is a more perfect sphere than any billiard ball.
Up until recently, it was more perfectly spherical than any man-made object, but the new kilogram standard is more precise.

I think it was smoother, but not more spherical - the oblateness is a fair bit greater than the roughness.

It’s smoother than a billiard ball, but more oblate than most of them. And I’m pretty sure there have been smoother spheres, for precise experiments, before the new kilogram standard.

  1. I assume you meant circumference rather than diameter. Either way it depends on who measures. The Wikipedia article on Earth for instance uses two different sources for equatorial radius and equatorial circumference and the two don’t match up perfectly. If you calculate the circumference from the radius you get a number a few hundred meters shorter.

  2. When giving a single number for the diameter, or circumference, one simplifies and gives the number for an averaged circle. The radius is pretty much at least 3 orders of magnitudes larger than any bumps you may encounter on a trip around the equator, so smoothing things out wouldn’t change much.

I meant diameter.

Sea level is not a very precise measurement. Sea Level, the earth’s circumference and diameter are all approximations.

Centrifugal force.

Gesundheit.

Not only that, but the Avogadro project sphere doesn’t even hold the record. That belongs to the gyroscopes made for the satellite Gravity Probe B. They were designed to measure an effect called “frame-dragging”, which is essentially the effect that the Earth’s rotation has on the local properties of spacetime. To do this, they needed some very precisely machined spheres to set into rotation.

Roughly speaking, Earth is out of round by about 1 part in 300 (comparing polar to equatorial radius), and its extreme surface roughness is about 1 part in 1600 (based on the height of Mt Everest).

Perfectly ordinary ball bearings improve on these tolerances by a factor of 10 to 20.

I’ve always heard that we exaggerate the oblate-ness, and that the earth does fit within cue ball tolerance guidelines.

Here is a useful site

Some stats from wikipedia

Given that 71% of the earths surface is water, leveling all continents to fill underwater trenches would raise the sea level by about 758 feet. So absolutely negligible relative to the overall diameter.

Am I missing something? I thought the new kilogram standard was based on Plank’s constant and not on a physical artifact. Is this a metrological in-joke that went over my head?

Coordinate systems such as WGS84 define a “reference ellipsoid”. It’s not supposed to be exactly at sea level AFAIK, which we can see since mean sea level varies from place to place and is defined in that model by a bumpy “geoid”; the diameter to sea level would depend on exactly where you took the measurement.

https://www.nist.gov/si-redefinition/kilogram-silicon-spheres-and-international-avogadro-project

Those are nice, smooth spheres, but why would I want one in my lab? Seems like a pain to use in an analytical balance; it would keep trying to roll away…

This only tangential related to the OP’s question but it is an interesting read none the less:
What would a bowling ball look like if it were blown up to the size of the Earth?
(The first half does discuss how smooth the Earth is compared to a bowling ball.)
https://what-if.xkcd.com/46/

Thanks. Looks to me like that project is making hella-smooth one kilogram spheres but they are not the new standard kilogram.

Then I don’t understand your question 2 at all. “The diameter” of an approximate circle is of course an average of sort. What kind of smoothing of the Earth were you imagining that would change things?