A long thin rod, in a 24-hr orbit of the Earth,
viewed looking down from the North Pole.
Despite what often seems like endless problems, the past month or two has seen a substantial advance in a number of programs and projects. The great Chandra X-ray Observatory has been checked out in orbit and recently returned a beautiful image of the Cas A supernova remnant, including as a bonus, the discovery of a unresolved X-ray source near the center which seems likely to be the neutron star (or possibly black hole) remnant of the explosion. Cas A exploded about 1680 (based on the expansion rate of the ring of debris, as seen, for example, in the radio) but was never observed optically at the time. The observatory is now in its final orbit and all the experiments aboard seem to be working well. Then again, Cassini took some nice pictures of Earth and Moon during its flyby on 18 August, and collected science and calibration data from several other instruments as well; by the time you read this it will be near crossing the orbit of Mars on its exit from the inner Solar System.
Lunar Prospector crashed into the Moon on schedule but nothing whatever has been detected so far. It is, I hope, fairly obvious that, despite some negative media comment, this says practically nothing about the presence or absence of ice on the Moon! Further analysis may reveal something, but for now we are simply left with the previous strong evidence from the on-board instrumentation that ice has been detected. Meanwhile, NEAR (Near Earth Asteroid Rendezvous) is easing towards its delayed encounter with 433 Eros, now due in February. In early September it was 426,000 km out, and by the time you read this it will be substantially closer than the Earth/Moon distance. Of course a 40 km object as far away as the Moon is not exactly an awesome sight; but neither is it any longer point in a small telescope. So we are making progress. DS1 had some last-minute problems with its autonomous pointing that caused it to miss the best pictures of 1992 KD (which has lately been renamed "Braille", in honor of the inventor of the system of printing for the blind). Nevertheless, a spectrum was obtained which indicates Braille is likely to be a fragment knocked off of Vesta, one of the largest and most interesting main-belt asteroids. Vesta has been seen to have a large crater, and it is suspected that Braille may have been ejected in the event that created it.
Finally, an exciting JPL shuttle payload is awaiting launch at the Cape. It is curious that the outstanding radar images we have of Venus, with a planet-wide resolution of the order of 100 m, do not exist for Earth. The Shuttle Radar Topography Mission (SRTM), next in line to fly, should remedy this deplorable situation, using the same sort of synthetic aperture radar that gave us our wonderful topographic maps of Venus. The mission has been delayed while the orbiter Endeavour and all the other orbiters in the fleet have the condition of their wiring checked, as a result of a scary situation that arose during the Chandra launch. The two of the computers that control the main engines dropped off-line due to a fault in the wiring, caused by mechanical abrasion to wiring in the orbiter payload bay carry-through. Fortunately each engine has an redundant backup controller, and those took over so there was no actual effect on the flight. However, loss of even one main engine so early in a flight would be an extremely serious situation. To make the situation even more alarming, other independent wiring damage was discovered in follow-up inspections, so the entire fleet is being checked. Troublesome as this may seem (and is), we should count ourselves fortunate to have received such a clear warning of something amiss. From a certain point of view, every anomaly is an opportunity to follow-up and learn about the system without paying the full price, the awful Challenger price, of bitter experience.
Of course nowadays everyone understands that low-altitude satellites orbit quickly, in as short a time as 90 min, while high altitude ones take longer, up to over 27 days for Luna, the Earth's Moon. Thus there must be some altitude at which a satellite orbits in exactly 24 hours, or one day, and thus appears stationary in the sky, eternally fixed over one point on the Equator. Almost the entire space communications industry and much of the global communications network is of course based on these commonplace facts.
One simple way to view the situation is to notice that as the altitude increases, the Earth's gravitational pull drops as 1/R², where R is the distance from the center of the Earth. This is just Newton's Law of Gravitation, informing us that if we increase R by some factor, say 10, then the gravitational force will decrease by that same factor squared (10 × 10 = 100), to 1/100 of its previous value. Furthermore, as gravity decreases, the "centrifugal force" increases with R like R/P² for a given orbital period P. For a circular orbit, these two forces are in balance; and thus P must decrease as R increases.
Now consider a long, thin satellite in geosynchronous orbit (GSO):
The entire rod, being rigid, must orbit in 24 hours, yet the portions inside the GSO circle at 42,242 km are moving too slowly to maintain an independent orbit. Likewise, those portions at the other end outside the GSC circle are moving too quickly. The inner portion will then find itself out of balance between gravity and centrifugal force, with gravity the stronger; it will therefore tend to fall farther in. The outer portion, for which the centrifugal force will exceed gravity, will likewise tend to move further out. The end result will be that the rod as a whole will rotate itself along a radius vector, pointing at the center of the Earth Notice that the entire rod would be in tension due to the excess of centrifugal force at the outer end, and gravitational force at the inner.
Now suppose that instead of a rod, we were to use a long flexible cable. The same argument would apply, and the cable--assuming it did not bcome hopelessly tangled--would also take up a radial orientation, pointing towards the center of the Earth. Finally, imagine that the cable were made very very long, so that the inner end approached the Earth and the outer end moved far out beyond GSO, the whole still maintaining its 24 hr period. Evidently the tension in the cable might be very considerable.
However the really interesting thing is that the inner end, being stationary with respect to the surface, could even reach the atmosphere, and finally touch the ground, where it would appear to be simply hanging out of the sky, stretching up into infinity. Impossible as it may seem at first, one could then seriously consider attaching the hanging end to the Earth, and finally climbing the cable into space, with no expenditure of rocket power at all!
If all this sounds incredible and too good to be true, you are almost right -- almost no real available engineering material is strong enough to withstand the tension needed. A uniform steel cable, with a typical working strength of 100,000 psi (about 700 MPa), could only support its own weight to a length of 90 km or so. To be sure, it is possible to make cables longer than this by tapering them, so that as the weight increases, the cross-sectional area and strength do too. Then the cable grows in area (and mass) exponentially with height; a 1 cm dia steel cable would grow to roughly 1010 km before it reached GSO: hardly promising! Fortunately, there are better materials than steel to consider.
It turns out that the figure-of-merit for a cable material is its tensile strength divided by its density; which is essentially equivalent to the longest length for a uniform cable mentioned above. Richard Smalley, Nobel Prize-winner for the fullerene carbon "buckeyball" discovery, believes carbon nanotubes can be expected to have a strength of the order of 130 GPa, and a density several times less than steel. With such characteristics, the mechanical problems would essentially disappear. Smalley is optimistic that such fibers can be produced in sufficient lengths, although this has not yet been achieved. Finally, according to Dr. Robert L. Forward, the best currently available material is already over 40 times superior to steel in the critical strength/density parameter, (in particular, AlliedSignal Spectra(R) 2000, which he quotes as having 4 GPa tensile strength, density 0.95) and has already been tested in orbit. This is sufficient to bring the GSO cable into the realm of serious possibility. Thus, after decades of living in the realm of unicorns and other fabulous mythical beasts, space cables seem to be poised at the edge of revolutionizing the possibilities for inexpensive space access.