oser range; this would be more convenient if it could be done, since 542 AU is already 75 light-hours away from Earth. This means that it would take over six days to send a signal to the telescope and have it send a signal back to Earth, even at the minimum distance.
How much magnification could be achieved? According to this excellent blog post at Centauri Dreams on the same topic, at these sort of distances the light from a lensed object would be magnified by a factor of 100 million. That’s a lot of free magnification for just locating your telescope a few light days further out. Effectively, the object will appear as it if is ten thousand times closer than it actually is. A planet orbiting Alpha Centauri, for instance, would appear as large and bright as it normally would at 27 AU through lensing, even though it is actually 270 000 AU (4.3 light-years) away.
The Hubble Space Telescope, if placed in such a location, could image any planets of Alpha Centauri as well as it currently images Neptune. This would enable very detailed observations, to a degree astronomers and scientists can only dream about today. Space telescopes of far higher resolution than Hubble could be engineered even today (indeed, the soon-to-be-launched James Webb Space Telescope will have higher resolution), and would be trivial to build for any civilization that can manufacture mirrors and telescope assemblies in space, which will include any spacefaring near-future human civilization.
A 2017 article in Air & Space Magazine estimates that near-future space telescope technology ( detailed by NASA at their website , an interesting read by itself) could, using gravitational lensing from the sun, image a planet 100 light-years away at 10 kilometers per pixel. This would yield a (roughly) 1300×1300 pixel picture of an Earth-sized planet. This opens up the mind-boggling possibility of future scientists studying and children gazing in wonder at galleries of pictures of an alien solar system 100 light-years away that are of comparable quality to the ones taken by our probes in our own solar system. Consider that there are 4088 stars located within 100 light-years of Earth, implying that there could very easily be tens of thousands of planets that could be imaged at such high resolutions.
Toward a Telescope Cloud
The impact of such a powerful observational tool on our knowledge of alien solar systems would be nothing short of revolutionary. There is only one serious obstacle to obtaining this bounty: such a telescope can only observe one target at a time, because the telescope, the sun, and the target have to all be in a line. To observe another target, it must change its position so that it is aligned with the sun and the other target. To observe a target on the opposite end of the sky, the telescope will have to travel to the opposite end of the solar system, which since it needs 542 AU or more of distance from the sun, requires a trip of at least 1100 AU, or six light-days.
This distance would take months for even the most advanced near-future propulsion technology (nuclear pulse) to traverse. Instead of accepting months of downtime, it would be far more efficient to have multiple telescopes stationed at different ends of the solar system, perhaps starting with a pair at opposite ends of the sun and filling in different slices of the sky from there. In this way the maximum travel distance could be cut to hundreds of AU, then down into tens of AU, which as outlined in my post on colonizing the Oort cloud is a manageable distance with nuclear pulse propulsion. At 1g of constant acceleration 20 AU can be traversed in twelve days; the required maximum speed of 1.8% of light is easily attained by nuclear pulse. Keep in mind that this would be the maximum travel distance; most repositionings would, when the sphere of space telescopes at >542 AU is fully built out, take only from a few hours to a few days to complete.
Repeated and long-term observations of distant targets are possible and would surely be done extensively when this infrastructure is created. In