Imagine you have a very long piece of string. It's long enough to stretch all the way around the earth. Since the circumference of the Earth is about 40,074 kilometres, that's how much string you would need.Imagine that you lay out this string along the ground and on top of the oceans, all the way round the Earth. That's one long piece of string! Now pull it tight, so it lays flat. The string makes a big circle that is 40,074 kilometres, or Then you realize that you have an extra metre of string in your pocket, and you want to add it to the string laying on the ground all the way around the earth ...
You'll have to cut the circle of string somewhere, as it passes in front of you on the ground. Then you'll add exactly one metre more string. Now you want to spread out this extra bit of string around the Earth, supporting it somehow, so that the string forms a circle off the ground, all 40,074 kilometres (plus one metre) around the world.This may take a while! But eventually, you've smoothed the string out into a perfect circle, all the way around the Earth, and slightly off the ground because of the extra 100 cm you added. Here's the question we want to ask ... How high off the ground would the string be?You would probably say that the string will hardly be off the ground at all. After all, you only added 100 cm, and the string's length was 4,007,400,000 cm to start with. Most people guess something like 0.00005 cm. The very surprising answer is that the string will be 15.9 cm off the ground, all the way around the Earth!If you think about it, this is a very large distance for so little change to the total length of the string!Another way to look at the problem may make the answer seem more reasonable. The height of 15.9 cm is in addition to the radius of the Earth. Since the Earth's radius is about 637,800,000 cm, the change in height is in fact very tiny.But wait, there's more ... The size of the object you're wrapping the string around is completely irrelevant to the problem!
Whether the ball is the Earth, or a basketball, or a marble, adding one metre of string to the circumference will make the string form a loop 15.9 cm above the surface, regardless of the size of the sphere the string is wrapped around!
These surprising results may be more believable once you see the answers worked out. On page two, we'll show you the calculations which prove that the height of the string above the Earth, a basketball, or any sphere, will always be 15.9 cm when you add one metre to the string.
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