Gary Turner wrote:
Center of gravity (CG) is of doubtful value in thinking about this problem. The object extends over a region in which substantially different gravitational accelerations occur, and is at rest in a reference frame in which there is significant centrifugal force.John Hasler wrote:Pigeon writes:It would be under tension, because the upper station is outside the geosynchronous orbit. So the bit above the break would fly off into space, and the lower bit would fall back.The tension would taper from nominally zero at the base to maximum at the attachment to the counterweight.Actually, maximum tension occurs at the CG, with minimums at the ends. Forces are reversed, maximum at the ends, and minimum (balanced) at the CG. These are tidal forces. A single point counter-weight, as opposed to distributed, will cause a discontinuity in the function, but the function holds true on either side of the break.
The rules of the space elevator game, as I understand them, are 1 a vertical tension member 2 mass at upper end is at higher altitude than geostationary orbit 3 mass at lower end is close to the surface of the Earth4 the whole thing is stationary with respect to the Earth as a reference frame.
5 Adjust unspecified parameters so that it stays put without very large rockets or other cheats.
These conditions imply that maximum tension is at geosychronous orbit altitude. Below that altitude tension is increasing with altitude. Above that altitude tension is decreasing with increase in altitude.
Paul