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Does this mean there's a location in space where – on the side of the earth opposite to the sun – the sun's light is focused into a point of extremely high intensity due to the earth's atmosphere acting like a magnifying glass?

If so, that could make for either a very unfortunate surprise (i.e. a spacecraft passing through that point suddenly melting to a crisp) or an interesting source of energy if it could be harnessed.

It's not focused on a point, it's focused on an area, and while it will be hot it won't be unbelievably hot. See this explanation which is far better than I can explain- https://what-if.xkcd.com/145/

I think this what-if has serious issues in its argumentation (though I agree with the conclusion):

The argument about reversibility is kind of a straw man: it answers "why can't you concentrate all light on a single point" while the real question would be "why can't you concentrate light on a smaller surface" (which you can do actually).

Similarly for the conservation of étendue: maybe you can't "swoosh the light rays closer together" but that also doesn't say you can't concentrate beams on a small surface, which might be sufficient to start a fire.

So really it all comes down to the thermodynamic argument, which has its own problem: it only works if you assume that moonlight has the same temperature as the moon. There's nothing in the article that mentions or justifies this assumption. And obviously a mirror can reflect light that is much warmer than itself, so you definitely have to explain why that's not the case with the Moon (e.g. its albedo and heat dissipation are too low).

(However I love the drawing of the encircling sun, it's great to make the point that no matter how much light you concentrate, it won't heat the body warmer than the light's temperature).

It's a great explanation, but a "spherical chickens in a vacuum" textbook explanation. Add in realworld atmospheric effects (diffusion) and non-lens things like the internalized reflections of fiber optics and the infinite reversability of optical systems breaks down. Then look to how easy it is to start a "fire" in some substances and the moonlight-to-fire concept becomes less difficult. Greenhouse effects also throw a wrench at reversability.

That's brilliant, thanks! I never would have guessed. It goes completely against my intuition.

Does that mean you could use light from Mercury to start a fire?

Mercury can get up to 430c, so Maybe yes. But you might as well use the sun

coming soon: rooftop mercurial panels

If a YouTube video I saw whether you can use moonlight to start a fire is to be believed, you cannot achieve higher temperature using lens than the source temperature, so your earth lens will achieve same temperature as 5cm lens from dollar store.

But isn't the actual source the sun (6000K) and not the moon as it is acting only as a mirror?

With a mirror you can also burn things if you focus sunlight, but the surface of the mirror stays cool.

At a guess, the moon is a diffuse rather than a reflective surface, so it's going to be closer to a maximum of the lunar surface temperature than to solar surface temperature.

An atmospheric lens, however, will reach a maximum of somewhat closer to solar surface temperature, though still lower because of scattering and absorption which definitely isn't trivial on this kind of scale.

The moon is pretty dark, reflecting about 12% of the sunlight that falls on it

https://www.universetoday.com/19981/moon-albedo/

If it had an albedo of 0% it would be a black body and be radiating only thermal radiation at its surface temperature; it's not too far away from that but it is reflecting some "black body" radiation from the sun representative of a higher temperature.

a 5cm lens from a dollar store can burn things in the focal point

The author of this paper Prof. Kipping has a good video on the concept. See his YouTube channel Cool Worlds.

To summarise, you put a telescope beyond the orbit of the moon and use the earth's atmosphere as a lens

Video: https://www.youtube.com/watch?v=jgOTZe07eHA

The abstract here says 85% of the distance to the moon. I imagine it would be difficult to maintain an orbit at that distance.

85% is the minimum distance, but lens quality improves the further out you go because the lensing region moves up into the stratosphere so you get less distortion from clouds.

The moon's gravity is in play so the orbit might not be so simple, but there are all sorts of "halo orbits", orbits around the L4 and L5 points, etc.

It seems to me though that the Earth's atmosphere is always going to be "lit up" one way or another by some phenomenon like the Aurora Borealis, scattering and various sorts of skyglow, so there will be some background, but maybe it is not that bad.

Apparently at the distance of the Hill Sphere of the Earth (about 4 times the Moon's orbital distance) the effect would still work.

I think the real challenge here is that you'd need to stay in place while you observed anything. The line from the target object under observation, the lens, and the viewer must remain as close to perfect straight as possible.

For earth or space based telescopes, we just keep the observer and lens rigidly attached and then move the whole apparatus slowly and carefully (computer controlled) to maintain a straight line.

For an earth-atmosphere lens, you don't have the rigid stability between the observer and the lens. You can't move the target or the earth, so you'd need to keep moving the observer to keep it perfectly in place.

That sounds like a lot of delta-V expended for each observation. It's probably easier to just build a 150m telescope on the moon or in space.

You're certainly right about the need to move the observer, but I suspect you're wrong about how hard it is relative to building a 150m optical telescope (the largest to-date is ~10m).

Orbital mechanics is a pretty well understood thing, so figuring out how the earth will move over the next 20 hours isn't that tough.

The rest is just making sure you're able to position the 1m receiver very precisely and move it around in a very controlled way. I'm no expert, but I suspect we've demonstrated both in one or more NASA missions already.

Probably super-expensive, but less of a technical challenge than building a proper 150m optical telescope.

The math is easy, the delta-V is hard.

There is a precise point the craft would need to stay at relative to the earth and the target. There aren't any stable orbits that keep a craft at precisely that position, which means you are firing engines for 20 hours straight.

Remember, you don't stay in space unless you are either in a stable orbit, moving at many km/s, or you're firing engines to resist gravity's pull.

A spacecraft to stay at this point for 20 hours would be massive, and 99.9% fuel tanks.

Could you get anywhere by taking the image over multiple passes?

Even though the first image wouldn't be ready for a long time, if you have a lot of targets then you could increase efficiency to something like a tolerable level.

A LaGrange point would do, and Professor Kipping suggested putting a telescope near the JWST at L2.

At that distance you would be sampling light that has passed through the Earth's atmosphere at an altitude of 14km. About 8% of the light would be lost, but at that altitude there's little weather to disturb the image.

They wouldn't though.

The Lagrange points are stable positions relative to two bodies, like the earth and the moon or the earth and the sun. But those things are moving, orbiting. The points move with them. The line from the earth to any Lagrange point won't stay stably pointing at any star in the sky.

And even then, the focal point of this atmospheric lens is at a specific distance that is not, afaik, the distance to any Lagrange point.

Forget Earth gravitational lenses, let's use the sun:

https://www.youtube.com/watch?v=NQFqDKRAROI

(The whole video is great.)

This setup could resolve the surfaces of exoplanets with its ~100 billion magnification.

JPL is investigating.

Great video, amazing science. This is the sort of project where you wish humanity could put aside its differences and collaborate to get it done, given its potential to fundamentally change the course of civilisation.

Maybe we can put ChatGPT in charge...? :P

Hmm, could you go one step further and use the Sun’s gravitational lens to image distant objects? How far out is the focal point?

Yes! Unfortunately the focal point is around 542 AU out (75 light hours), and Voyager is only 149 AU out, for perspective.

https://en.m.wikipedia.org/wiki/Solar_gravitational_lens

Warning: spoilers

IIRC this is actually one of the plot points in the Three Body Problem, where they used the sun to send out a signal and make first contact with an alien civilization.

Not quite, if I understand it correctly.

This is like chapter ~one of book one (if you skip over the tangential Chinese politics stuff that I didn't understand on my second read either), so not really a spoiler. In the book it's some magic amplification that happens inside the sun, not based on a physical effect we've actually observed in real life as far as I know.

In this case, it's about gravitational lensing (when using the sun) and additionally atmospheric refraction (when using the earth; terrascope).

I'm also not sure we could use this, as in 3BP, to send anything. What this does is collect light rays coming in essentially parallel and focus it on a line along which we can place a detector. If we emit from somewhere along that line, it would be scattered as a ring the size of the lens (the earth or sun, in the examples, plus whatever altitude we use to avoid clouds or corona) because the rays are basically parallel from there. At least, that's my guess. I didn't understand even what my high school teacher tried to explain about lenses so this is speculation based on a drawing I saw in the terrascope video linked elsewhere in the thread (https://www.youtube.com/watch?v=jgOTZe07eHA).

This has actually been proposed before. It’ll be exciting when it’s eventually used.

Unfortunately, the focal point is in interstellar space, far past the orbit of Pluto.

So even if we'll live to see this project funded, started and launched, there's pretty much no way we'll still be alive once the sensor probe reaches it's duty station.

Also, the telescope will be pretty much purpose build to look at one thing. Swiveling the telescope to look at something different or to track a moving object involves moving the sensor probe millions of kilometers across space.

It seems like an attainable ambition for a scaled down

https://en.wikipedia.org/wiki/Breakthrough_Starshot

and if you built some kind of "gun" that can shoot those things you could should numerous ones out in different directions to observe different targets and definitely have results in years if not weeks instead of decades.

Does this require superimposing many images to get a single computed image? Or will a single shot per image suffice?

Need many images to superimpose them into a single computed image. David Kipping has a great video on it https://www.youtube.com/watch?v=jgOTZe07eHA&t=82s

We would need a train of probes being sent in a row because there is a limited amount of time they will pass through the focal area.

There's also non-imaging astronomical applications, consider a stream of extremely high quality spectrographs.