Packing Earth with 1m Extra String - Unexpected Result?

[wimms]

This is simple exercise with unintuitive result, perhaps old as hell, but still surprising.

Suppose we wrap Earth with a string along equator, tightly, so that string is touching ground along its whole path. Assume Earth is perfect sphere. Length of this string would be calculated as circumference of earth.

Now imagine we add 1 meter to the total length of this string.

Question is: by how much would this string lift off ground if distance to the ground is kept uniform along whole length of it?

 

[russ_watters]

The circumference of Earth is about 40,000km. A change of 1m is 1/400,000%. The radius is 6366.2km. A change of 1/400,000% is 16cm.

This could likely also be figured algebraically (spelled horribly wrong) since you can get the same result by plugging 1m into the radius of a circle equation.

 

[wimms]

Of course Russ, but you could let people less advanced discover this.

More general answer is that radius changes by L/2Pi where L is addition to circumference. So, if orbit of Earth around Sun were extended by 1meter, then Earth's distance to Sun would increase by 16cm. If Sun's orbit around galaxy was extended by 1 meter, then its distance to center of it would increase by 16cm..
I wonder if this was intuitively obvious to you?