29 Mar '06 17:59

I was looking at the formula for circular orbits, its

P(orbital period in seconds)=SQRT (4 (PI^2)* R^3)/GM

R = distance of orbit from center of earth, and the 4PI^2/GM for the planet earth is just a constant, 9.904 E-14 (to 4 places) so its really easy, R is in meters, which is the radius of the earth in meters added to the altitude of the orbit in meters, so at the geosync orbital height, in miles is 22,414 miles high or 35862400 meters plus 6,378,140 meters so R in this case is 42,240,540 meters.

R^3= 7.536E22, so the whole thing boils down to

P=(9.904E-14 * 7.535E22)^1/2 Which in this case = 86397 seconds, rounding errors take it from exact solution here but my problem is the dudes designing the space elevator, assuming of course it can ever work, want to add an extension of some 100,000 Km as a stabalizing element.

My problem with that is the orbital velocity at geosync is about 3 Km/sec but the velocity at 100,000 Km works out to about 2 ish Km/s.

How can two masses connected by a line ever be stable in such an arrangement?

P(orbital period in seconds)=SQRT (4 (PI^2)* R^3)/GM

R = distance of orbit from center of earth, and the 4PI^2/GM for the planet earth is just a constant, 9.904 E-14 (to 4 places) so its really easy, R is in meters, which is the radius of the earth in meters added to the altitude of the orbit in meters, so at the geosync orbital height, in miles is 22,414 miles high or 35862400 meters plus 6,378,140 meters so R in this case is 42,240,540 meters.

R^3= 7.536E22, so the whole thing boils down to

P=(9.904E-14 * 7.535E22)^1/2 Which in this case = 86397 seconds, rounding errors take it from exact solution here but my problem is the dudes designing the space elevator, assuming of course it can ever work, want to add an extension of some 100,000 Km as a stabalizing element.

My problem with that is the orbital velocity at geosync is about 3 Km/sec but the velocity at 100,000 Km works out to about 2 ish Km/s.

How can two masses connected by a line ever be stable in such an arrangement?