If you placed a rope around the circumference of the earth tautly and then added 3 feet of slack to the length of rope, how far above the surface could the rope now be?
This comes with some caveats and assumptions:
- We know it is not physically possible to do this.
- We're assuming a completely smooth surface.
- The globe is wider at the equator than around the poles. Let's also assume a perfect sphere.
- The longer rope would equally and magically suspend itself above this smooth surface.
- We're using a circumference of 24,900 miles.
- OK, math time.
Circumference (C) rope length = 24,900 miles or 131,472,000 feet
Radius of earth = C/2π = 20,924,418.678 feet
New Rope Length = 131,472,000 + 3 = 131,472,003 feet
Radius that new rope encircles: 131,472,003 / 2π = 20,924,419.156 feet
Distance of New Rope above Earth surface
= radius of new rope - radius of earth = 29,924,419.156 - 29,924,418.678 =
= 0.478 feet = 5.74 inches (145.8 mm)
So if you tie a rope around the earth, then add 3 feet to the length of rope, it could encircle the earth 5.74" above the surface all the way around. That seems amazing that merely adding 3' to the circumference of the earth would make it 5.74 inches higher at the surface.
What if you lengthened the rope by 20 feet? The rope would now be 38 inches above the surface. What about a mile of extra rope? Then the rope would be 10,084 inches or 840 feet above the surface. In fact the length of extra rope is a direct ratio to the height above the surface where the rope would be. That ratio is 6.283:1. For every 6.283 feet (a tall man) you lengthen the rope, it will be long enough to be 1 foot above the entire surface. It doesn't matter if you lengthen the rope by 1 inch or 1 mile.