# To use a gravitational lens as a telescope, does the hypothetical user have to do so from a given angle?

This question is about the use of a gravitational lens for example of a distant galaxy or sun. I’m curious to know whether the two outer masses, say galaxies or suns (when to the observers of course) have to be sufficiently far away or used from the right angle for the telescopic effect to work.

I ask the question because like with any lens, one would assume that it can only be used from the correct angle. I also ask the question because I assume that given gravitational lenses yield a far greater effect than do others, and thus I assume that with the right positioning, some lenses would be far more valuable to us than others. If the positioning of the observer complicates the use of the lens, however, this would mean that certain positions in space yield greater or lesser overall observational potential.

To get useful performance from a gravitational lens the bending angle for light rays coming from behind the object must be large enough that the highly distorted "image" of the distant ("background") object is offset far enough from the lensing object that light from the lensing object, or dust clouds within the lensing object, etc., don't obscure the light from the background object. That angle is a complex function of the lensing object's mass, size, and shape (mass distribution), and also of the distances from the observer to the lensing object and from the lensing object to the background object; see the worthwhile article https://en.wikipedia.org/wiki/Einstein_ring. Indeed, the observer, the lensing object, and the lensed object must be very closely aligned along a "geodesic", the nearest thing to a straight line that General Relativity allows. They don't have to be exactly aligned or we'd never see one, but nearly so. And indeed, in general the observer must be far from the lensing object. But if that object has a high mass density, the distance required can be surprisingly small, at least as compared to intragalactic distances.

Most gravitational lenses anyone has heard about involve distant galaxies lensing even more distant galaxies. Almost every form of public media features spectacular example images. Sometimes the lensed light forms an almost-perfect "Einstein-Chwolson ring" (ECR) around the lensing object, when the lensing galaxy's gravity field is nicely symmetrical and the alignment is nearly perfect. Sometimes it is very asymmetric, to go with less perfect alignment or a very asymmetric galaxy. But anything with a gravitational field can act as a gravitational lens, including stars and even planets. Stars and exoplanets are so small, and usually so distant, that the entire lensed image is less than a pixel even in powerful telescopes, so we don't have any images of such lensing — yet. The wikipedia article draws attention to the potential (45% chance) of seeing Alpha Centauri A generate an ECR when it occults a distant red star in early May of 2028. Astronomers have been seeing "microlensing", the lensing effects of small and dark objects on more distant stars, for decades, and are using this effect to search for "rogue" exoplanets, ones that were ejected from orbit around their stars and now wander through the galaxy on their own. They've seen a few! In microlensing the lensing doesn't produce an image in the observing telescope, but instead produces a readily identifiable variation in the intensity of the light we see from the background star, over a period from days up to a year or so. See https://en.wikipedia.org/wiki/Gravitational_microlensing.

"High mass density" objects include stars, which are far more dense than galaxies, and are very nearly spherically symmetrical in most cases. At JPL I worked on a feasibility study of a future mission to send a spacecraft to the minimum distance for a gravitational focus by our sun, at only 550 AU, not light-years! It's an idea that's been around a while but recently (2016) was explored by Geoff Landis at NASA Glenn Research Center; see https://arxiv.org/ftp/arxiv/papers/1604/1604.06351.pdf . At that distance the ECR radius is far enough outside the sun's photosphere to get useful data. Landis's paper also describes how the hugely distorted image in the ECR can be transformed into a "normal" image of the background object.

The trouble lies in that alignment requirement: the observer, lensing object, and background object must all lie along that General Relativistic equivalent of a straight line. This means that if you want to image a certain object, the spacecraft must not only be at least 550 AU from the sun, it must also be in the correct lateral position (right ascension and declination) to put it along that line, very precisely. Imaging only one object is relatively simple: you steer the spacecraft to that position on its way out. But if you want to image a second object, and a third, etc., the only way to steer the "telescope" is to move the spacecraft laterally to get onto a new line. At 550 AU, moving the aim line by only 0.1 degree requires you move laterally by a whole AU. To do that in a reasonable amount of time takes a lot of delta-V: going that lateral distance after imparting a lateral velocity of 1 km/s would take almost 5 years. Steering the focus of galactic gravitational lenses would take lateral motions on galactic scales, so that's far outside our current technological capability.

• I've added some paragraph breaks to make your answer a little easier to read. Just use return twice and it will work. However don't add spaces to try to indent the next paragraph; if you add four, it turns into a code-block object. – uhoh Apr 29 '18 at 8:01
• Thank you for the edits @uhoh. I've spent a long time with space exploration, but I'm new to online text editing. – Tom Spilker Apr 29 '18 at 17:02

This may be more of an astronomy question but it is certainly related to space exploration since it involves placement of a space-based observatory. In any case, absolutely, the lensing object has to be right between the observer and the target.

Unfortunately, my understanding is that "sufficiently far away" for lensing to be useful for telescopic purposes is very far indeed, on the scale of light-years. So gravitational-lens-based astronomy is always opportunistic, where we are lucky enough to have a good gravitational lens right between us and something interesting.

• According to this video found linked here it's 550 AU for the Sun, but somewhat closer to a light-year for the planets. – uhoh Apr 29 '18 at 7:59