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A telescope located in the gravitational focus of the Sun can use the Sun as a magnifying lens. The focus begins 550 AU away, but maybe a 700 or 1000 AU distance is needed to get rid of disturbances from the Corona, and the focus extends practically indefinately. Here are some slides by Dr. Maccone who has promoted this idea he calls FOCAL: http://www.spaceroutes.com/astrocon/AstroconVTalks/Maccone-AstroconV.pdf

I intend to ask about the technical design and feasibility of such a project in the Space Exploration SE. Here I rather ask about the scientific value and challenges.

POINTING: The magnification would occur only in the exact direction of the Sun. But since the Sun moves and the background objects magnified move, I suppose that the observed targets would change continuously. Would it even be practically possible to give the telescope a trajectory which keeps it aiming at for example Alpha Centauri? Would there most of the time be nothing in the right direction as the line between the telescope and the Sun sweeps across space, or would there alway be some star or galaxy in sight? Like CMB if nothing else.

GAIN: In the slides linked above, Maccone has calculated the expected gain to 114 dB for infrared wavelengths. How many times "magnification" does this mean? I don't think I understand the units here, I get a ridiculously large number. Can it be explained somewhat intuitively? Would a FOCAL mission be a unique revolution in astronomy, or could similar results be achieved by building an interferometer with interplanetary sized baselines here nearer to the Sun? How does the science value of a gravity lens compare to that of a wide baseline? Are they good for different tasks?

DISTORTIONS: Could the lensed signals be reconstructed thanks to our knowledge of the Sun and measurements of corona activity? If pointed towards a central part of the Milky Way, wouldn't signals come from multiple objects at the same time, some much further away than others? Would the gravity lens of the Sun have bigger problems with distortion than the intergalactic gravity lenses we know of today?

And finally, can any natural strong lensing inside the Milky Way be used today, for example using a globular cluster as a lens?

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I think this is one of the most interesting projects ever proposed, which actually could be realized in our lifetime (or at least this century)! So, why is the interest, even in communities like this, so very low? I've seen it proposed since years in other contexts, by Dr. Maccone and others, and the response has been about zero zilt. Is it just impatience, or is there an unspoken obvious conceptual flaw? –  LocalFluff Apr 7 at 19:33
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The pointing is not a fundamental problem with the suggested design: The suggested trajectory is designed to include a Sun flyby as the last flyby. This ensures an asymptotically radial trajectory away from the sun after the flyby, hence maintaining the pointing relative to the sun. The proper motion of the observed object may be some challenge, but the trajectory could be adjusted appropriately by an additional burn.

114 dB are an amplification of a factor of about $2.51\cdot 10^{11}$. It doesn't refer just to the magnification, but to the intensity of the signal. Therefore interferometry with a long baseline isn't the same; the latter provides a high resolution. Whether those numbers are achievable in practice is a different question; a factor of 1000 for naturally occuring gravitational lenses would mostly be regarded as excellent. Theory allows arbitrary amplification for perfect alignment of observer, lense and observed object.

Most of the distortions can be deconvoluted, revealing the field of gravity of the sun, and the shape of the observed object.

Gravitational lensing is used today, here some lecture notes, and here quasars as an example.

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