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Hop's Blog

## Golden Tethers

20 Feb 2013, 18:45 UTC
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Golden TethersĪ¦, also known as the golden ratio, is one of my favorite numbers. It is (sqrt(5) + 1) / 2, approximately 1.618. I've done many paintings and drawings using this number. Here are a couple: Two images from my coloring booksThe number occurs naturally in designs having a 5 fold symmetry but it also turns up in unexpected places. I was happy to find it when I was playing with orbital tethers.Vertical Tethers vs Space ElevatorsGravity gradient stabilized vertical tethers are smaller cousins of a full blown space elevator. Jerome Pearson has developed equations giving a space elevator's dimensions and taper ratio.Some of Pearson's terms:r0 planet's radiusg0 planet's surface gravityrs radius of planet's synchronous orbitFor looking at vertical tethers I use P. K. Aravind's equations which I believe are based on Pearson's work. But I substitute the above terms with rf for r0, gf for g0, and rc for rs.Tether FootThe term rf refers to distance from planet center to tether foot. Imagine a planet the same mass of earth but with a larger radius, rf. Then rf and r0become the same. Same with surface gravity, gravity at the tether foot would be the same as surface gravity of ...