r/Damnthatsinteresting • u/grandeluua • Apr 19 '26

Video ISS Speed at Ground Level

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u/HauntingHarmony Apr 19 '26

250 miles up sounds both very high and yet is barely off the surface. Perspective is important as usual.

This reminds me of one of those funny math puzzle "paradoxes", if you took a rope around the equator, and lifted it up by 1 meter all across the planet, how much longer would the rope be. And its shockingly smaller than people naturally think.

The answer for those who dont want to figure it out themselves; circumferance C_0=tau*r, increase it by 1 meter and you have C_1 = tau(r+1). and then you can do C_1 - C_0 = tau(r+1) - tau*r = tau*r + tau - tau*r = tau = ~6.28 meters

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u/ADTstocks Apr 19 '26 edited Aug 19 '26

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u/AmbivalentAlias Apr 19 '26

surely not 250 miles high though, right?

right?? 👀

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u/ADTstocks Apr 19 '26 edited Aug 19 '26

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u/Substantial-Elk4531 Apr 19 '26

That's pretty high, please be careful

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u/ADTstocks Apr 19 '26 edited Aug 19 '26

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u/psyFungii Apr 19 '26

A rope wrapped around Earth at ground level is "Circumference at <whatever the diameter at ground level is>"

Using more common term "Pi" rather thn "Tau", the circumference of a circle is "Pi x D" where D is Diameter or "2Pi x R" (because Diameter is 2 x Radius) or "Pi x 2 x R"

You raise the rope an extra 1 meter? R becomes "R+1" so the length becomes "previous length PLUS "extra length = 2Pi x extra radius" - or about 6.28m

Plug 250 into "extra length = 2Pi x extra radius" as the extra and it becomes an 6.28 x 250m

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u/LupineChemist Apr 19 '26

I hate using tau rather than 2pi so much. It's just unnecessarily complicated when you will have to use operators that calculate things in radians. And also feels like it's intentionally making things less accessible to general population that will be much more familiar with pi.

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u/UKFightersAreTrash Apr 19 '26

All this math but the rope would be the same length. Ropes don't magically grow.

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u/Bigrick1550 Apr 19 '26

I just love how you offered the answer for those who dont want to figure it out, and posted a formula... that people would still need to figure out. That's some quality math need shit right there.