The idea of a space elevator, an elevator compartment that travels up a cable, positioned at the equator and extending 90,000 miles to the Pearson radius (minimum 40,000 miles desired by ISEC.org), is now possible with special graphene (sheets of single-layer carbon) with tensile-strength and momentum tether attributes that may only require 1-1/2 Mega Newtons of tension resistance and no need (as with compressional cable with no momentum tether that will not revolve around the Earth daily, but wrap around Earth to the west) for something to force cable eastward to maintain geosynchronous orbit. Some scientists say you must have a cable strong enough to withstand gravity pulling in one direction, and a centrifugal force pulling in the opposite direction, which is 100 Mega Newtons of tension regardless of what your cable consists of or the shape. This is 22 million pounds, about the weight of a 200 foot high concrete skyscraper, or a sand castle 100 feet cubed. With graphene, it is possible to design a ribbon cable where pressure divided by density is high enough the cable does not break, even if under 100 Mega Newtons of tension, and the diameter of the cable remains the same, but because of hysteresis or history of stress versus strain, there is a debate and need for laboratory come-along study and computer simulation to see how long it will last before potentially breaking. No substance is 100% stiff or elastic, everything is at least a little ductile, like a copper wire that will eventually break if tugged enough times. If a graphene cord enters the Earth’s atmosphere it won’t burn up (melting point is 3,900 degrees Fahrenheit, and re-entry causes temperatures of 3,000 degrees Fahrenheit), so it could potentially take out a continent. The current ISEC model breaks up in legs if re-entry happens. A west Pacific cable will miss the west coast of Chile upon re-entry. For now, graphene is very expensive and it would take a long time to manufacture a 40,000 to 90,000 mile-long cable. Using a Kevlar coaxial cable or hose that will burn up in the atmosphere will prevent the consequences of re-entry, as it has a melting point of 500 degrees Fahrenheit, and is much less expensive because of the material and the fact it has been mass produced by many factories in high volume for many decades.
When you spin a wheel, such that the rate of rotation increases and produces angular acceleration, you produce a force in the perpendicular direction along the axis of the wheel, called torque. In outer space, radiation is so intense you can have two wheels, one to backup the other, that accelerate radially in the proper direction to prevent the cable from breaking when it’s at a maximum distance from the Earth, or the greater of two perigees, given the nature of elliptical or eccentric orbits. Then as you slow down you essentially are decelerating or accelerating in the opposite direction, which is necessary for the cable (with counterweight, or CW, at the radial end) to release CW outward a little to keep orbit stable so the cable does not re-enter the Earth’s atmosphere. Force according to Newton is equal to mass times acceleration, but different calculations are used for rotational dynamics, meaning mass is replaced with moment of inertia. The highest moment of inertia of any rotating body based on its shape is a torus or donut. Think of it as a bicycle wheel, with an easy-to-manufacture outer shell covered with photovoltaic cells. It is possible to use the very low escape velocity of the Moon for Moon mining for space elevator wheel construction and other materials and projects (to fill interior of torus for maximum weight, as torque = force x radius = mass x acceleration x radius, and moment of inertia for a torus = mass x radius ^ 2). There is plenty of silicon oxide to fill the cavities of the torus and even use extraterrestrial stepper to photosynthesize photovoltaic panels, and microprocessor applications. You can easily have two wheels to prevent the cable from breaking. With two wheels on the cable aligned in the perpendicular direction, pointing east and west, you can have angular acceleration to push elevator assembly east to maintain geosynchronous orbit, with a transmission to disengage gears when each wheel is not pushing the elevator assembly to the east. This is designed to overcome Kepler’s Third Law, which dictates the further away you are from the Earth, the longer the period of revolution. The whole cable must always be in geosynchronous orbit, revolving around the Earth once a day. There will a space station at GEO 22.4 thousand miles away.
Because force, mass times acceleration, is time independent regardless of the orbit of your space elevator, where the tension or force on a stiff cable is always 100 MN which a stiff cable must withstand, a non-stiff cable computes energy as the result of “added values of forces from torque” to understand how energy, not force, from solar torque wheels must be high enough to prevent cable from becoming taunt and breaking. It must also move the opposite direction half the time to prevent the cable from returning to Earth. So at any instance, 100 MN is not required, but values much less that can be looked at as integrated forces (eg. F x delta s for arc sector change in orbit) with a perpendicular or radial component that keeps the cable slack but not too slack. It is possible only 2 heavy torque torus wheels are needed, one for backup, as small as 50 meters in radius and 5 meters in torus outer ring diameter, filled with sand or concrete, accelerating tangentially at 10 m/s^2 or about the same as the Earth’s gravity, just to do the job.
The cable I am proposing for the elevator is actually a coaxial cable, or a tube within a tube. Very cheap and easy to manufacture in high-volume, it allows hydrogen and oxygen with a proper ratio, easily extracted from seawater at the equator with electrolysis (see https://en.wikipedia.org/wiki/Electrolysis) starting as H2O, the proper ratio for best force for rocket fuel, to travel at high speed under pressure. With gaseous hydrogen and oxygen pumped to the ends of the space elevator cable, or CW, it can fire exhaust fuel outward in the rare event there might be something wrong with the torque wheels pulling the CW inward. The system must make sure the cable is never too tight, just a little bit of a catenary shape. The same rocket fuel can fuel spacecrafts that go deep into space, but because you are at a Pearson orbit, with a fairly eccentric elliptical path, the smaller of the two perigees moves cable around the earth at a very high tangential speed. You can send satellites and spacecraft deep into space with little-to-no need for rocket fuel. However, the hydrogen and oxygen are useful for water for the astronauts as water cannot always be recycled because of evaporation, and pure oxygen for breathing as well. This means a constant flow of air, water and fuel to ensure the lives of the astronauts come first, as well as the people below, who need not fear cable re-entry, in the very rare event the cable re-enters the Earth’s atmosphere. Because you’re dealing with a Kevlar tube, not graphene, steel, etc., it will burn up in the atmosphere. Because your space elevator will be launched from a ship in middle of the ocean 90 miles away from any islands, Coriolis forces, or human population, there’s little to no need of concern here for safety exceptions.
To avoid the Earth’s eclipsing of the solar panels, the orbit of the CW will be at an angle with respect to the plane of Earth and Sun, or non-coplanar. Slight movement of parabolic dishes on Earth, up and down, is recommended for communicating with space elevator transceivers and crew is easily doable. The estimated cost of this mission, to install the first space elevator, preferably in the West Pacific, will be about 30 billion dollars.