Could someone explain gravitational lensing and its relation to dark matter?

Light is affected by gravity.

If you look at a pair of distant stars, you can measure the apparent distance between them (the angle they appear to make as seen from Earth, for example).

If you put a large mass between you and the two stars, placing this mass such that it appears exactly between the two stars, the light paths from the stars will be bent by gravity when they pass close to the massive object, and these stars will appear a little further apart than they really are.

This was tested during total solar eclipses (when it is possible to measure the position of stars that appear very close to the Sun.

As far as objects in the universe, the Sun is a puny thing.

But it is close to us and large.

Imagine a large planet that has no star around it (a rogue planet floating by itself). If it were to pass very close (in apparent direction) to a distant star, it would temporarity distort the position (and maybe the apperance) of that star.

In fact, if such a planet were to pass EXACTLY in front of a distant star, it could curve the star's light in such a way that it would make the star's light visible ALL AROUND the planet at once, making the star appear a lot brighter for a short period of time.

That is one example of gravitational lensing.

The technique was used to see if dark matter could be composed of normal planets, simply floating around in the halo of the Galaxy, by themselves.

Theses possible objects were called Massive Astrophysical Compact Halo Objects (MACHO) as a pun aimed at the proposed "Weakly Interactive Massive Particles" (WIMP) that required a change in the understanding of particle physics.

In the end, the MACHO survey showed that the number of rogue planets was A LOT LESS than expected and, in the meantime, some WIMPS were discovered (neutrinos). This made the search for dark matter a lot more complicated (because WIMPs are difficult to understand and even more difficult to detect).

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The other way gravitational lensing enters the debate for dark matter: Sometimes a whole galaxy acts as the lens (affecting the light from even more distant galaxies). Calculating the amount of gravity needed to cause the measured deviation, we find that the galaxy, based on its size, would normally be too small to cause that much lensing... UNLESS the galaxy contains matter we cannot see but which adds to its gravity. That extra matter is what we call Dark matter (nowadays, the word "dark", in this context, means unknown, because we are not even sure that WIMPs will be enough to explain all of it).

I'm not so sure on gracitational lensing, but I do know a thing or two on dark matter. Dark matter cannot be seen, and has alluded scientists for years, however, dark matter has gravity. In fact, it has enough gravity that it can slighty warp light and cause a distortion. Scientists can then look at that distortion in the light and determine that dark matter is there, even though we can't see it.

Put the wine glass on the spot.