Anchored tether technology -- one way, recently explored in renewed detail by Bradley Edwards under a NASA grant, is that of a tether, attached to the ground at the equator, extending through GEO, the centripetal force on the mass of the 24-hour rotating structures part beyond GEO is balancing the weight of the part of the tether below GEO. Payloads are carried to space by vehicles which climb up and down the tether, utilizing additional energy sources such as lasers, electrical conductors, or lifted electrical power sources.
An exciting recent proposal, funded by NASA's NIAC, Bradley Edwards principle investigator, is published in ASCE's Space 2002 March 17-21 2002 Albuquerque NM conference proceedings. This very interesting carbon nanotube matrix-based tether-type space elevator was proposed by Bradley Edwards in detail at ASCE's Space 2002 conference, and advance info can be found at http://www.niac.usra.edu/. This detailed conceptual design, funded by NASA for the past 2 years, is highly developed and ready for the next steps, when money is available.
Equatorially anchored tethered space elevators, supported by the centrifugal force on it by virtue of the Earths 24 hour spin, having slightly more centripetal force on its part which is above GEO, in comparison the portion of its weight below GEO, have been proposed for over 40 years, frequently excitingly "re-invented" by individuals (including this author, in 1970), yet the strength to weight requirements of such immense structures seemed barely in distant sight until recently, with hypothetical diamond fiber material in immense quantities, emplaced to essentially center its weight to each side of GEO, appearing to be a pre-requisite.
Delivering lift energy up such an earth tower is a problem, too, losses in conductors or inefficient laser power conversion and continuous uninterrupted distribution of beam power to multiple vehicles on the structure. Its potential transportation efficiencies are derived from the fact the payloads are climbing up a structure extending up from the ground; for example, a vehicle could just stop and hang on such a tower, without further expending energy, yet a conventional rocket launch vehicle hanging motionless up at same altitude would have to expend fuel energy at a ferocious rate in continuous support of its weight, yet adding no potential energy to its payload thereby. It has an advangtage in that as it extends beyond GEO, it can deliver payloads to a much higher energy level than that of GEO, using the energy of the rotating planet to fling vehicles far out into space. Howevder, it has another disadvantage in that management of lateral transient live loads whiplash effects could be difficult, requiring anti-resonant nodes and conversion of lateral cyclical motion into heat.
As Arthur Clarke pointed out at the end of his novel "Fountains Of Paradise", many people have independently come up with the concept of an anchored tether earth to space elevator. Artsutanov in 1960, J D Isaacs et al in 1966, (myself too but not formally published, in about 1970), Pearson in 1976, as well as Clarke, and no doubt others too who gave it up when finding no material close to being strong enough for the task.
One of the problems with such tether space access is the need to provide expensive and slow earth surface transportation first to the equatorial anchor site, prior to lifting to space. So here is an idea for a variation which could solve that problem. Multiple anchor site tethers would make direct access to space from locations in higher latitudes, such as from anywhere in the continental United States. This would require stronger tether material if built with constant crossection tether techniques, due to the vector stresses. However, anchor sites need not be mirrored about the equatorial plane (as "Mirrored KESTS" would require), not even be of equal latitude above and below the equatorial plane if unequal length ties were used; the requirement being that the mltiple anchor tie point itself lie in the equatorial plane. See sketch below.

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