## Perfect Spheres

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In an odd connection both to yesterday’s post on spherical Buckeyes and TwoPi’s November post on how the official kilogram is losing weight (although by definition, its mass remains the same), it turns out that spheres are being used in a quest to redefine the kilogram. In particular, according to this article, Australian scientists are trying to create a perfect sphere out of a single crystal of silicon. In theory, once they have a perfect sphere they can count the number of atoms, and use that unchanging quantity as a way to define the kilogram.

The perfect sphere is still out of reach: their closest approximation has variations in the diameter that average 35 nanometers (0.000035 of a millimeter). The sphere itself is 9.3 centimeters across: you can see a picture here.

The picture below (created by NASA) is of the second most perfect sphere in front of a poster of Albert Einstein:

This rotor of fused quartz was used in the center of the gyroscope on the Gravity Probe B, the experiment designed by NASA and Stanford University to test predictions of Einstein’s general theory of relativity. (See Stanford’s site or NASA’s site for more information.) The sphere (and its 3 copies) were 1.5 inches in diameter, and differed from a perfect sphere by 40 atomic layers (0.0000003 inches, or about 7.6 nanometers). There are more cool pictures of these spheres here.

Aside #1: I’m not completely sure why the Australian sphere is considered to be more accurate than the Gravity Probe B sphere: the ratio of variation/diameter for the Australian sphere is $(0.0000035 \mbox{ cm})/( 9.3\mbox{ cm}) \approx 3.7 \times 10^{-7},$ while variation/diameter for the sphere on the Gravity Probe B is only $(0.0000003 \mbox{ inches})/(1.5 \mbox{ inches}) = 2 \times 10^{-7}.$ Perhaps it has to do with the difference in materials or differences in ways that the variation was calculated?

Aside #2: The measurements for the Gravity Probe B come from this site on Stanford, which was probably written in 2004 around the time of the data collection. Notice how they are all in inches, even though the whole imperial vs. metric units caused a bit of trouble for NASA back in 1998.