String Girdling Earth Calculator
Solve the famous rope around Earth puzzle - calculate additional string length or resulting gap
Calculate String Girdling Effects
Length of string to be spliced into the original rope
Gap Results
Famous Examples
Classic Problem: Lift 1 meter
Question: If you lift a rope around Earth 1 meter off the ground, how much extra string do you need?
Answer: ΔL = 2π × 1m = 6.283 meters ≈ 6.3 meters
Surprising fact: Earth's radius (6,371 km) doesn't matter!
Reverse Problem: Add 1 meter of string
Question: If you add 1 meter to the rope around Earth, what's the gap?
Answer: d = 1m ÷ (2π) = 0.159 meters ≈ 16 cm
Result: A cat could fit through the gap! 🐱
Earth Reference Data
The formula works for any spherical object, not just Earth!
Key Formulas
Key Insights
The object's size doesn't matter - same result for Earth, a coin, or the sun!
Adding 1 meter creates only a 16cm gap around Earth
The relationship is always linear: gap = length ÷ (2π)
This principle applies to athletics track starting lines
Understanding the String Girdling Earth Problem
The Classic Puzzle
Imagine a string tightly wrapped around Earth's equator. If you lift this string uniformly 1 meter off the ground all around the equator, how much longer would the string need to be? The answer is surprisingly small - only about 6.3 meters!
Why It's Counterintuitive
- •Earth's circumference is ~40,000 km (25,000 miles)
- •Yet adding just 6.3m lifts the entire rope 1 meter
- •The Earth's size doesn't affect the calculation!
Mathematical Explanation
Original circumference: C₁ = 2πR
New circumference: C₂ = 2π(R + d)
Additional length: ΔL = C₂ - C₁
Simplified: ΔL = 2π(R + d) - 2πR = 2πd
Key Insight
The radius R cancels out completely! The additional length depends only on the height increase (d), not the original size of the object.
Real-World Application
Athletics tracks use this principle - outer lanes have staggered starting lines offset by 2π × lane width to ensure equal distances.
Any Sphere Works
This formula applies to any spherical object - a marble, basketball, planet, or star. The size doesn't matter!
Linear Relationship
Double the height, double the required length. The relationship between gap and additional string is perfectly linear.