The dependence on the cube of light frequency, v, tells that, by choosing it well, angular resolution may become from two to four orders of magnitude better than the most accurate instrumentation ever used (e.g., that of the star-mapping Hypparcos satellite launched in 1989). Spatial resolution with a modest 12-m antenna dish positioned at the Sun lens focus could tell details of objects in the Oort Cloud 145 km apart at the frequency of neutral H2 (1,420 MHz), and 9 km apart at the higher emission frequency of water, 22 GHz. The Alpha Centauri star could be resolved at 1,250 and 80 km at the same two frequencies. Note we are talking of telling features 80 km apart on a star some 4.3 light years from Earth!
This nearly unbelievable performance has motivated conceptual planning of missions to the nearest Sun gravitational focus, that is at 542 AU from the Sun. Such is, for instance, the FOCAL mission proposed and described in [Maccone, 2002, Chapter 1).
Much farther away, about half a light year, is the so-called Oort Cloud. Long ago astronomers started to suspect that long-period comets with extremely eccentric orbits spend most of their time at a distance from the Sun between 104 and 105 AU. The Oort Cloud is the farthest known region of the Solar System. It is named after the Dutch astronomer J. Oort, who conjectured that this region of space must contain millions, or even billions of comets (the current estimate is in fact 1011). Its distance from the Sun is between 1,000 AU and 60,000 AU (some push these boundaries to between 20,000 AU and 200,000 AU). In fact, current understanding of the Oort Cloud is that it consists of stably orbiting matter left over from the formation of the Solar System, meaning that the mutual distance between bodies is large and therefore interaction is scarce, thus explaining why it never contributed to planetary formation. Similarly to the Kuiper Belt, the Oort Cloud is interesting because it may contain further and maybe different relics of the formation of our planetary system. However, gravitational interaction with stars during their infrequent approach to the Sun (events occurring every million years or so [Cesarone et al., 1984]) may draw Oort Cloud bodies into very elliptic orbits approaching the Sun. Some become comets (see [Encrenaz et al., 2004, Section 11.2] for an explanation of their formation), others may not form plumes at all (e.g., Sedna, with a 75 AU perihelion).
Comets, according to Carl Sagan's definition, are "dirty snowballs'', their dirt being the original material that the planetesimals are made of. The Rosetta mission planned by ESA should bring back a sample of this "dirt"; its chemical composition will shed light on the mechanism of planetesimal accretion, since the distribution of elements in the Solar System is known [Sciama, 1971]. The type and abundance of elements depends on the supernova explosion that created what astrophysicists call "heavy matter'' or "metals" (i.e., any element heavier than helium) in our Galactic region. In the Kuiper Belt, matter has undergone much more frequent collisions and mixing, unlike what has happened in the Oort Cloud, where the much lower density should ensure finding matter in its pristine state.
As we have already said, not all Oort Cloud matter is cometary. Sedna is a case in point, but many others have been observed (e.g., the recently detected 2006 SQ372, an Oort Cloud body on an elliptic orbit with semiaxes about 1,000 AU and 24 AU [Hecht, 2008] and a period estimated at 22,500 yr). These messengers shuttle back and forth from the outer reaches of the Solar System to the vicinity of the Sun, and are of great interest not only per se, but also as potential scientific platforms: they are true Sun satellites traveling far beyond the heliopause and could record and transmit information from there [Dinerman, 2008], albeit over timescales of many tens of years. Of course, boarding these bodies and installing instrumentation would require unprecedented propulsion systems, but nuclear-powered spacecraft would probably be capable of such performance.
These examples of QI scientific missions are far from involving stellar distances (the distance traveled by FOCAL would be about 5% of a light-year; the Oort Cloud stretches no more than 0.5 light years from Earth). Nevertheless, these destinations are immensely distant compared to what travelled so far; Voyager, the farthest space object manufactured on Earth, is at 93 AU from us, and Pioneer 10 is at 87 AU [The Planetary Report, 2004]. To reach these destinations in times compatible with the lifetimes of crew and mission ground teams, we need propulsion means never developed before.
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