Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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?

share|improve this question
5  
Making a perfect right angle is harder than making a perfect circle. –  David H Apr 14 '13 at 18:17
    
Really? I always thought that a perfect circle was the most difficult shape to make. –  moray95 Apr 14 '13 at 18:28
    
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? –  David H Apr 14 '13 at 18:28
3  
π is not really a source of imprecision. It can be calculated to any arbitrary procision. A million digits for example. –  SpiderPig Apr 14 '13 at 18:31
    
Related: physics.stackexchange.com/q/32120/2451 –  Qmechanic Apr 14 '13 at 18:31

1 Answer 1

up vote 1 down vote accepted

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.

share|improve this answer
1  
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. –  Steven Walton Apr 14 '13 at 19:42

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.