Packing of earth

  • Thread starter wimms
  • Start date
  • #1
496
0
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?
 

Answers and Replies

  • #2
russ_watters
Mentor
21,024
7,717
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.
 
  • #3
496
0
Of course Russ, but you could let people less advanced discover this. :smile:

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?
 

Related Threads on Packing of earth

  • Last Post
Replies
3
Views
10K
Replies
1
Views
813
Replies
1
Views
609
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
10K
  • Last Post
2
Replies
29
Views
6K
  • Last Post
Replies
20
Views
4K
  • Last Post
Replies
4
Views
16K
Top