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Space is starting to look like the better mining operation
(arstechnica.com)
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this post was submitted on 21 Oct 2023
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You'd want tensile strength rather than compressive. The trick is to anchor a counterweight out beyond your target distance and let it pull the weight of the cable up rather than building a tower. Think of swinging a ball on a string rather than building a skyscraper. Assuming a sufficiently sized counterweight you can support the weight of the anchoring cable plus whatever else you want to hang off of it (space dock, elevator terminus, etc.)