In this video, the woman says that a sphere is a pretty simple object. What intrigues me is the use of a sphere for such a calculation. First of all, the sphere wouldn't be perfect as a perfect sphere doesn't exist in nature (first source of imprecision). Second, one will have to use π for calculating the volume. As π is irrational, one will have to use an approximation for it (second source imprecision). So why not using a simple cube? The shape would be closer to a cube due it's harder to make a sphere and it's volume would be calculated more precisely. Why they choose to do this calculation using a sphere?
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5$\begingroup$ Making a perfect right angle is harder than making a perfect circle. $\endgroup$– David HApr 14, 2013 at 18:17
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$\begingroup$ Really? I always thought that a perfect circle was the most difficult shape to make. $\endgroup$– moray95Apr 14, 2013 at 18:28
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$\begingroup$ Also, you're right that truly perfect spheres don't exist in nature. But, what's a greater source of error/imprecision in measurements of the figure of the Earth: using an approximation of Pi accurate only to 40 significant figures, or modeling the Earth as a simple cube? $\endgroup$– David HApr 14, 2013 at 18:28
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3$\begingroup$ π is not really a source of imprecision. It can be calculated to any arbitrary procision. A million digits for example. $\endgroup$– SpiderPigApr 14, 2013 at 18:31
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$\begingroup$ Related: physics.stackexchange.com/q/32120/2451 $\endgroup$– Qmechanic ♦Apr 14, 2013 at 18:31
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1 Answer
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Because spheres are easy to make, easy to polish and they haven't got any edges, which is very much important to create an object of such a high accuracy. In fact, no one said that this is a perfect sphere. It is polished to around a few nanometers away from being perfect. And, there is no macroscopic object that is ideal to a cent percent perfection. So, the first point isn't good...
I suspect that the reason for your confusion is regarding the volume difference between both the case. The volume of a cube is very easy to determine. But, making it to such a high precision is a very big problem (as I've mentioned at first) because of its edges. As David says, right angles are very difficult.
You're right that $\pi$ can only be approximated. Still, we can use the maximum approximations as possible and we would - because, it's gonna be defined under the SI.
answered Apr 14, 2013 at 18:30
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1$\begingroup$ Its more about it being mathematically simple. If you shrunk the earth down to the size of a pool ball then it'd more of a perfect sphere than anything we've created. There's a joke in physics, but it only works for a spherical cow in a vacuum. $\endgroup$ Apr 14, 2013 at 19:42