How many poles and lines would be needed to create a zipline around the world?

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Creating a zipline that encircles the Earth involves understanding the geometry of a sphere and the concept of tangent lines. A single zipline cannot be constructed due to the curvature of the Earth; multiple poles would be necessary to maintain a functional design. Each pole would need to be positioned where the tangent line intersects the globe, which complicates the overall structure. The total length of the zipline would depend on the number of poles and the spacing between them, as well as the angle of descent. This hypothetical scenario requires approximations for practical implementation, considering the Earth's circumference and the physics of ziplining.
steadierfooting
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I was trying to figure this out on my own, probably more a trig question then math though. It''s been a few years since I've taken a physics class so forgive me if I'm misusing terminology.

Let's assume I wanted to create a zipline that would take me around the world. You couldn't jus use a x degree angle and use the circumference of the Earth and have one large pole to reach the sky. I'm guessing there would be multiple exsecent lines (poles) where the next pole would be set up where the tangent line reaches the circle (globe). That tangent line probably approaches infinity so I'm looking for approximations, but.

How many 'zip lines' would there need to be disregarding safety, and how long would the total 'lines' be if we were to create a zipline to go around the world?

Thanks for any advice in helping me solve this problem!
 
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errr hypothetical not theoretical
 
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