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General template for space elevators

10 Sep 2016, 18:36 UTC
General template for space elevators
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A Family of Conic SectionsBelow is a general vertical space elevator. The conic sections are the paths payloads would follow if released from a point on the tether a distance r from body center. We choose our units so radius of the balance point is 1. The balance point is where centrifugal force matches gravity and that part of the elevator feels zero net acceleration.This family of conic sections are coplanar, coaxial and confocal. Eccentricity is r3-1, setting r = 1 at the circular orbit of the balance point. (See this stack exchange answer for the math). In the yellow region are hyperbolic orbits. In the blue region are are elliptical orbits higher than the circular orbit at the balance point. In the orange region, the tether drops payloads into elliptical orbits lower than the circular orbit at the balance point.A circle of eccentricity zero separates the orange and blue regions, radius of circle = 1.A parabola of eccentricity 1 separates the blue and gold regions, radius of parabola's periapsis = 21/3 Here is the same graphic zoomed in:Here is the graphic as a Scalable Vector Graphic. I am hoping science fiction writers and illustrators will download this resource and ...

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