# Has any satellite proved the hypothesis that the Sun could be used as a gravitational lens?

Has any satellite proved the statement that the Sun's gravity could be used as a magnifying lens, focussing electromagnetic waves of distant galaxies or other celestial objects?

Or, is this idea, for the time being, only hypothetical?

• <comments removed> Please do not use comments to answer these questions. Not only does it discourage others from posting a proper answer, but it encourages others to do the same, and we've seen that it causes the site to start operating more like the old discussion forums Stack Exchange was designed to avoid. – Robert Cartaino Aug 26 '13 at 15:27

Hubble and various others have proven this (although this was already proven from ground observatories)

There are some excellent pictures of lensed objects online, such as this galaxy arc on Hubblesite - this one was found in 2011:

That was lensed from another stellar object, but there should be no difference between the sun and other stars etc.

• This answer is problematic. The sun is not a proper "lens" despite the unfortunate term "gravitational lensing". For imaging systems deflection increases with distance from the axis, but for gravity the effect is exactly the opposite, it of course decreases with distance. While there is deflection, it is not image-forming but only 1-D concentrating. See this answer for example. Also the figures on page 5 in NASA Scientist Geoffrey Landis' preprint arxiv.org/abs/1604.06351 – uhoh Nov 12 '17 at 12:45
• A single gravitational body with a $1/r$ potential will make an Einstein ring, but not act as a magnifying glass. There are unusual cases of extended complex mass distributions that can generate magnified and distorted, but recognizable images, but these are special cases where you are looking through a small area of an extended distribution, not looking around a single central source. – uhoh Nov 12 '17 at 12:49

There kind of is a problem for doing that within the solar system.

We can imagine the sun's gravitational field to be a lens, but this is an imperfect model. The main issue with the analogy is that the deflection angle increases as you get closer. This isn't a big issue, provided that we recognize that we're talking about the creation of an Einstein ring, and not literally focusing something in the same way we would for a telescope. For the ring, the same relationship between angle of deflection and focal length holds.

All spherically symmetric bodies have the same gravitational field around them. This is true in both classical mechanics and general relativity, and the idea holds right up until you get to the surface of the body. Now here's the problem:

If you calculate it, the radius that gets you the right angle of deflection to form an Einstein ring (of a far-away object) with the sun will be below the radius of the sun. This obviously isn't useful because the light will not pass through the interior (defined by the photosphere) of the sun. To walk through the logic a little bit more, imagine these steps:

• Pick some radius from the center of the sun
• With that radius and the mass of the sun, we can calculate an angle of deflection
• That angle of deflection will correlate to some focal length - this is where you would want to put the probe according to the proposal at hand

For the minimal requirements to do such a mission, we will start out requiring that the radius at which the deflection takes place will be greater than the sun's radius itself. That will give a relatively low angle of deflection. That will then give a long focal length - certainly more than 1 AU, which is kind of the assumption implicit in the question.

Could Voyager possibly see an Einstein ring produced of a distant star when looking at the sun? I haven't done the calculation, but yes, that would be possible if the math checks out. So my is that yes you can do this, but only at a huge distance, certainly not from the inner solar system where we reside.

• 550 AU is the magic number, but you are on the right track. centauri-dreams.org/?p=785 – PearsonArtPhoto Aug 22 '13 at 16:02
• @PearsonArtPhoto I'm so pleased with myself when I completely guess a number within an order of magnitude of a calculation so comically obtuse. One time on physics.SE I guessed the Hawking radiation horizon distance for 1 g of acceleration as 1 parsec. Then I was corrected no, it's 1/3 parsec. Maybe I'm the only one that sees that hilarity, but it had me dying. Hitting in within a factor of 5 here was just about as lucky... – AlanSE Aug 22 '13 at 16:54