It is a simple matter to solve numerically for the minimum mass of such a structure given the force on the ground and the used strength (ultimate strength divided by a safety factor) of the cable. It can also be, and has been, solved in closed form. That is, you can derive either a table of numbers or an equation for the mass. <br /><br />In its most mass efficient form, the tower has a long tail that extends way beyond geosynchronous. Look at it this way. The cable starts thin at the bottom and grows fatter as it climbs and the force increases.<br /><br />At geosynch, there is a huge force that needs to be applied. One can imagine a mass just beyond geosynch, but the force per unit mass is minuscule, so you need an enormous mass. <br /><br />If you double the distance above geosynch, you roughly double the pull per unit mass, so you just about cut the required mass in half. In addition, the mass of the cable between geosynch and the end mass helps pull the tower up a little bit, so that the force required is less. Go farther out, there is more "supra-geosynch" cable mass pulling harder, and the mass decreases some more. Eventually, the most mass efficient system has a huge tail and almost no balance mass.<br /><br />There are obvious compromises. Since the system will have the most tension at geosynch, and the cable is sized for that tension, the cable could be extended without getting thinner. At some point, there would be almost enough mass in just the cable to balance the system.<br /><br />This is a good point for a "far-point station". There would be some "artificial gravity" pointing AWAY from the center of the Earth. Items let go from here would fly to higher orbits. At some point, this "higher orbit" would go to the moon, or beyond, out or in to the orbits other planets. Not having looked at the numbers in a few decades, (yes, decades) I don't recall just how fast would be "reasonable".<br />