How do gravitational lenses work? Where would a spacecraft need to be to use the Sun’s gravity as a telescope? What could we learn about exoplanets with this on weird trick? I discuss these questions and more in today’s Ask a Spaceman!

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Episode Transcription (Auto Generated)

We're going to build a telescope, but it's not going to be like any telescope you've ever encountered in your life. It's going to be different. It's going to be strange. It won't even come with a lens, but it will be so powerful that you could take a picture of an alien city sitting on the surface of a planet orbiting another star. Just as a dramatic example, to be clear, I'm not saying that there are any alien cities nearby, but but you get my drift.

And this telescope is going to use the sun itself. But before I get into the construction of this strange, not a telescope, but still a telescope, I want to build up just how powerful it can be. In general, in astronomy, when we go to build a telescope, we care about 3 things. One is the resolution. How sharp our images?

What minute detail can we see in the image? That's our resolution. The second thing is the field of view. How broad of a view do we get? Yo.

You've you've all seen that thing where, like, you, you look at something and your eyeball has this fantastic field of view, and then you hold up your phone camera, and you're like, wait a minute. That's not everything I'm capturing with my eye. That's field of view. And the third is wavelength. What wavelength of light are we going to be observing at?

And when we call a telescope powerful, it means it could be powerful in any or all of these capacities. And for our purposes today, when I say we're we are going to build the world's most powerful telescope, for now, we're going to ignore the wavelength part because it's, you know, just not a major point of this story. So thank you, Wavelength. You're important and useful, but you can go take a break and grab a sandwich or something because you're not needed in this episode. Field of view, just wait for a second outside.

We'll bring you in towards the end. But resolution, sharpness, why don't you join us for a moment and get comfortable? Because we need to talk about you a lot. The entire point of introducing telescopes into astronomy is to make distant things more visible. And to do that, you need high resolution.

You've all taken our phone cameras and started pinching and zooming, and very quickly, the results become rather lackluster. Images start to get all blurry and pixelated because when you zoom all the way in, you reach the resolution limit of your camera. If you had a more powerful camera, you could keep pinching and zooming and still get a clear, not blurry, not pixelated image. Same thing for a TV. If you have, like, an older TV with low resolution and you go up close to it, you can see the individual pixels, and then the image doesn't look as great.

But if you have a newer, a 4 k TV, whatever they're making now, then you can still see a sharp crystal clear picture even nice and up close. In astronomy, we usually measure resolution in terms of things called arc minutes and arc seconds. This is a very old, even ancient method of dividing up the sky. And for once, we have the case where an old ancient tradition in astronomy still makes sense and describes exactly what it's trying to accomplish. You know, check out my episode on bad jargon if you want some counterexamples of which there are, a couple.

Normally, when us non astronomers think of resolution, we think of, like, our phone or computer screen or TV. We think of how many pixels are jammed together on the screen. The more pixels, the higher resolution. The sharper, the crisper, the better your display. This is something called linear resolution.

This is the density of pixels, down a line or or squeezed into an area. But in astronomy, this is less than useful because different objects are at different distances. If you point a telescope at the moon, you can see some features like mountains or or even individual boulders. You have a certain linear resolution when looking at the moon. But when you point your telescope at, say, Jupiter, all you can make out are gigantic cloud bands that are tens of thousands of kilometers across.

Your linear resolution looking at Jupiter is much, much worse because Jupiter is so far away. So to standardize everything, we we measure a different kind of resolution, something we call angular resolution. This makes the resolution a known property of the telescope, something we can calculate, something we can write down. And this is independent of what you're trying to look at so we can judge and compare 1 telescope against the other in a fair way. This is as I introduce the most powerful telescope we could build.

This is how I'm going to measure it. To get to angular resolution, I want you to imagine, you're standing out on a big empty plane in the middle of nowhere, and you can see the horizon all around you. I want you to imagine that horizon is a giant circle surrounding you, and you will divide this circle into 360 degrees. So 360 little chunks on this circle going all around you. Now you divide each of those individual degrees just 1360th of that circle into 60 sections of its own.

So you take that one little degree, and now you you chop that up into 60 little sections. Those little sections are called arc minutes or minutes of arc. And then you can take each one of those individual arc minutes, those each of those 1 60th subdivisions of a degree, and each degree is just 1 360th of the entire circle surrounding you. You can subdivide each arc minute into 60 arc seconds. And if you need even finer divisions than that, which we will, we'll switch to decimals because we quickly get tired of all that divide by 60 nonsense.

And if you're wondering why 360, why 60 arc minutes in a degree, why 60 arc seconds in a minute, you can thank the ancient Babylonians who also gave us 24 hours in a day, 60 minutes in an hour, 60 seconds in a minute. Coincidence? Absolutely not, but that's a different episode. This is angular resolution. This is measuring how finally you can chop up a circle surrounding you.

And it's angular resolution that we use to judge telescopes because the angular resolution is independent of what you're looking at. It's just something you know, how finely you can divide a circle surrounding you. And then from here, you can look at objects at different distances with the same angular resolution and you end up with different linear resolution. So if you have very, very fine angular resolution and you look at something up close, you can see tiny, tiny little details. And then if you look at something far away, you can't see those tiny details, but the angular resolution tells you how well you're going to do when looking at all these different objects.

For example, to give you some perspective, and in a second, you'll realize that for the clever pun that it is, The human eye has an angular resolution of about 1 arc minute. That's pretty impressive that it's if you take a circle surrounding you on the horizon, divide it into 360 little bits, we'll call those bits degrees and then you divide each of that degree into 60 arc minutes. One of those little slices is the angular resolution of the human eye. We can translate this into linear resolution based on the distance of the thing we're observing. So if you're looking at something about 1 kilometer away, you can distinguish 2 points if they're separated by at least about a third of a meter, which is pretty impressive.

But if you hold your finger up nice and close to your eye, you can see the tiny tiny like millimeter level differences in the markings of your fingerprint which is also pretty impressive. You cannot make out a fingerprint sitting a kilometer away, and you can very easily distinguish something, that is separated by a third of a meter if it's in the same room as you. The angular resolution allows us to translate and calculate our linear resolution for whatever distant object we are studying, which is why it's so handy in astronomy. And we need to take a quick break, folks, to mention that this show is sponsored by BetterHelp. You know, it's the season of Halloween, and, you know, there's a lot of scary things out there like zombies, ghosts, black holes, magnetars, the usual.

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Visitbetterhelp.com/ spaceman today to get 10% off your 1st month. That's betterhelphelp.com/spaceman. So let's kick things up a notch and jump right to the James Webb Space Telescope. That instrument's primary mirror is 6.5 meters across, which is so big it couldn't even fit inside of the rocket that we had to fold it up and devise all these clever, origami like schemes to get it to up in space. That gives the telescope an angular resolution around a 10th of an arc second.

So you take the human eye resolution, which is already pretty impressive. You divide that by 60 60 to go from arc minutes to arc seconds, and then you divide by 10 to get a a tenth of an arc second. So right there, the resolution of the James Webb Space Telescope is 600 times better than the human eye. To give some fun examples, the James Webb could see the details of a coin placed 40 kilometers away from it, or it could pick up the pattern of a regulation soccer ball sitting 550 kilometers away from the telescope. It's that's an impressive telescope.

We want to go bigger. We want even bigger telescopes than the James Webb. We want to do this. We'd like them to be in space because observing in space is super easy. We don't have to deal with nasty atmosphere stuff.

But we can all agree that the James Webb was kind of a pain to make. It was like a decade late. It was 1,000,000,000 of dollars over budget. It was expend it was just a mess to get it up there. We like that it's there now, but it wasn't fun in the lead up to it.

So in astronomy, the only way to get higher resolution is to have a bigger dish, but bigger dishes are hard to do. Thankfully, there are some ways to cheat. One way is with a technique called interferometry where you don't have a single large dish. Instead, you have lots of small independent dishes, and then you cleverly connect them together. You correlate them together.

You you take their independent measurements, and you stitch together a larger image of that. One of the best examples of this technique is called the event horizon telescope. This is what we've used to observe the ring of material around distant black holes. The resolution of the event horizon telescope, which is made of instruments scattered all across the globe. So it effectively turns the earth into a single astronomical collecting instrument.

There are some downsides because you can only pick up signals where your instrument is. If if light just hits dirt, like ground next to your telescope, you don't get to fold that into the image. So there's this whole complicated business of turning these into images. But at the end of the day, it gives you insanely high resolution. Remember, the James Webb was a tenth of an arc second resolution.

The resolution of the Event Horizon Telescope is 20 micro arc seconds or 2 times 10 to the minus 5 arc seconds. A delightful example given by the Event Horizon Telescope folks is that they could spot an orange sitting on the surface of the moon. That's how high of a resolution they have. Using tricks like this, astronomers have unlocked the wonders of the universe, explored the mysteries of the cosmos, etcetera, etcetera. It's not good enough.

It's not good enough, especially when it comes to searches of exoplanets, of planets outside the solar system. Why? Because if I gave you the opportunity to take a picture, a detailed picture of another world outside the solar system where you could hang a poster in your room or your office or wherever you like posters, a detailed picture of another world with the same level of detail or fidelity that we have of the planets in our own solar system, would you pass that up? What could we learn? What are the limits to what we could learn if we had a detailed portrait of a planet outside our solar system?

Leave alone the rest of astronomy. You know, exploding stars, black holes, distant galaxies, etcetera, etcetera, etcetera. An ultra high resolution telescope would unlock wonders across the universe, but let's just focus now on exoplanets and the hunt for life, the hunt for earth like planets. Yeah. We've developed and are developing a lot of very clever techniques to look at thin slices of data.

You know, very we're not even talking images. We're just talking spectra. Like, we're dealing with literal dots of light from exoplanets and using that to try to understand what's in their atmosphere, whether they might host life. Yeah. We're doing all of this with literal dots of life.

Imagine if we could take a picture of a planet, especially a planet that we suspect might host life. What would we see? Would we see jungles, arid deserts, cities? We're not gonna see cities, but, like, you know, let let's let our imaginations not run wild, but run, you know, free. What would we gain?

Also, that sounds pretty cool. But how could we do that? There are plans for telescopes in the post James Webb era to go even bigger, even badder, larger mirror. Let's let's fold them up. Let's do it.

One of them is called the Habitable World's Observatory. It will be designed to target a few dozen planets orbiting nearby stars and get pictures of them. These pictures of the planets will occupy maybe a couple pixels at best. So the blurriest image possible. Like, it's not a dot of light, but we're talking a telescope that isn't gonna launch for at least another decade.

It's still in the design phase. So, okay, more likely 2 or 3 decades out. It will fly. It will study a few dozen exoplanets, and it's going to give us the next best thing from a dot of light. It's going to be a picture of a planet that's a couple, maybe 3 pixels across, as blurry as blurry can be, as low resolution as low resolution can be.

This isn't gonna work. I mean, we're going to build the thing. It's gonna operate, and we'll get the images. We'll get some cool data out of it, but it's not enough. I want a portrait.

We need to go bigger. How do can we get a bigger telescope? You know, without turning all of Mars into glass or something, we're kinda running into the limits of our technology. Like, we've cleverly figured out how to fold up mirrors and then unfold them in space. That's great, and that's going to enable a lot of science in the future.

But what if a couple pixel picture of a nearby planet isn't good enough? What if we want more? Does it mean we just have to wait a 1000 years before we're sophisticated enough to build a large enough telescope to take a a portrait of a planet? I mean, maybe with enough Patreon support, we can go faster. That's patreon.com/pmsutter where you can go to support this show.

And I can't thank you enough. Patreon.com/pmsutter. I don't know if we can build a super telescope faster with Patreon contributions, but it's worth a shot. No. I don't wanna wait a 1000 years for technology to catch up.

I wanna do it now. I wanna cheat. Let's use the sun. But, Paul, I hear you saying, the sun is large and made of hot gas. How could it possibly be a telescope?

It's not a mirror. You're right. The sun is not a mirror but it is a lens. And we understand it's a lens through the magic of gravity. Now Einstein when he developed a general relativity, he realized that gravity can bend the path of light.

Okay. Small note here. Light is all the path of light is also bent in Newtonian gravity, but not nearly as much. So just leave that aside. Einstein discovered that gravity really bends light in a big way.

In fact, this was one of the first tests of Einstein's theory of relativity was the Eddington expedition to look at the deflection of starlight. You have you have you have a little star, a little bit of light grazing the sun, and then its path gets bent. And so its position on the sky from our perspective looks different than where it's supposed to be. That was one of the first tests, if not the first test of relativity. Gravity bends light.

Massive objects bend the path of light. Lenses, you know, pieces of curved glass bend the path of light. Coincidence? Yeah. Yeah.

It's a total coincidence, but it does mean that everything we know about optics, about grinding lenses, about bending the light, about focusing light from a distant object onto a focal point to magnify it and increase the resolution, all that, we can take all that language, all that mathematics, and transport it over into gravity. We can create gravitational lenses where the gravity of a massive object, and last time I checked, the sun is a massive object, can bend all the light that comes near it and send it to a focal point where you can just sit and enjoy the magnified image exactly as if there was a giant piece of curved glass right there. This technique already works. We already use gravitational lenses in the distant universe to leapfrog vast distances and see into the early universe where some of the the first galaxies to appear in the universe are simply too far away, too small, and too dim for us to see. But when they happen to coincidentally just randomly sit behind a giant massive cluster of galaxies the gravity of that cluster of galaxies will bend that light focus that light amplify that light, increase the resolution, and we can use an entire cluster of galaxies as a giant lens to see what's behind it and magnify what's behind it and allow us to see some of the most distant galaxies in the universe.

Okay. In the solar system, the most massive object by far is the sun. It's like contains, like, 99% of all the mass in the solar system. It's in the sun. We know that the gravity of the sun bends the path of light around it as if it were a giant lens.

It sends light. Any light that grazes the surface of the sun gets bent and gets sent to a focal point just like light, just like a lens will bend any light that passes through the lens and send it towards a focal point. It's like we have a giant telescope just sitting there in the center of the solar system, and it is by far the most powerful telescope we can conceive of, you know, with reasonable extensions of our current technological limits. Like, yes, you can imagine some super advanced civilization turning an entire galaxy into a giant mirror, and it uses it to peer across the you know, etcetera. It's like, okay.

We can do that. We can talk about that. But with our actual technological capabilities or, like, reasonable extensions of our technological capabilities, like, you know, if we spent a couple $1,000,000,000,000, I bet we could do this kind of stuff. If we limit ourselves to that and we talk about the kind of telescopes we can build, where we could go with them, what materials would we use, how big they could be, This blows it out of the water. The sun has a gravitational lens is the most powerful accessible telescope in history.

We can do the math. We we use Einstein's relativity to calculate what the magnifying power of the solar gravitational lens could be and the its magnification, its angular resolution goes all the way down to 10 to the minus 10 arc seconds. That is a 1000000 times better than the Event Horizon Telescope. And because of the effects of gravitational lensing, you don't just get higher resolution. You also get amplification of brightness because it combines a bunch of light rays and focuses them.

You get brightness amplification up to a factor of 100,000,000,000. To say this is better than any known telescope is an understatement. This is better than any possible telescope that we could possibly build in any possible future for the next few 100 years, and it's just sitting there. What do you get with 10 to the minus 10? That's a 10th of a billionth of an arc second resolution.

A 1000000 times better than our most highest resolution telescope we have right now, the Event Horizon Telescope. What do we get with that? Let me give you an example. We know there is a planet orbiting our nearest neighbor star, Proxima Centauri. We call the planet Proxima b.

We know this planet. We know it's rocky. We know it's earth like. We know it's sitting in the habitable zone of Proxima Centauri, but Proxima Centauri is a red dwarf star like other that's another episode. This telescope called the solar gravitational lens would be able to map the surface of Proxima b to a resolution of 1 kilometer.

That's not one pixel containing the entire planet. That's creating a detailed map of the surface down to 1 kilometer. That's smaller than cities. That's mountain scale. Take a look at the image of an image of the Earth of with a resolution of around a kilometer.

It looks like the Earth. You can see coastlines. You can see hurricanes. You can see jungles. You can trace out rivers.

That's insane. The solar gravitational lens could build a decent map of any exoplanet sitting within roughly 100 light years of us. Compare that to the habitable worlds observatory that might give us a couple pixel images of a couple dozen planets. What could we do with that kind of information? That kind of data?

Okay. Okay. Hype machine down. How do we actually use this? How do we utilize?

Right. The sun is just doing it right now. Like, there you can imagine Proxima b, the light coming from Proxima b going out in all directions. Some of it is aimed towards the sun. Some of it grazes the surface of the sun.

The gravity of the sun is bending that light. It's already happening right now. That's the good news is that the hardest part of the telescope creating this giant lens already exists. We don't have to grind a lens. We don't have to polish a mirror.

We don't have to unfold an instrument. The gravity of the sun is doing all the work. It's taking all these stray bits of light that skim its surface, and it's bending it towards the focal point just happening right now. So all we have to do is put a sensor at the focal point and collect that light and also send that data back to Earth. All we have to do is put a sensor at the focal point and collect the light.

That's the hard part. You can do the Einstein math and figure out where the focal point is, where all the light is concentrating towards with the solar gravitational lens, and its focal point is about 542 astronomical units away from the sun. Okay. Okay. 542 seems like a large, but not impossible number.

Let's put that in context. Let's okay. That's 542 times further than the distance from the sun to the earth. K. That's 13 times the distance to Pluto, and that's, it's over 3 times the distance to Voyager 1, the most distant current spacecraft, which was launched in, in 1977.

I guess it might be a small, tiny challenge to deploy an instrument to that extreme distance, get it to work, collect the data, build an image, and send the results back to Earth. Maybe. Oh, and don't even get me started on pointing the dang thing. Like, we can target one planet, but to even shift where this telescope points by 1 degree, it's not like a telescope that's sitting on a mountain you want to change to a different position. You just you just point it.

Here instead at the solar gravitational lens at this distance of over 500 AU. If you want to point in a different direction, you have to move the entire array here so that you're in a different position in your orbit around the sun. If you want to move if you want to shift and look one degree to the right, it means you have to change your position by 10 astronomical units, which is the distance between the Earth and Jupiter. So that means pointing this thing is essentially impossible. This difficulty in repositioning also means that we may not ever get a full portrait of a planet because this super high resolution image that's coming in, that's bent.

The light is bent around the sun and sent to the focal point. Well, the focal point here is more like the focal area because this image is so high resolution. The actual image is gigantic. It's like a giant, a mosaic image. It's like a giant mural at high resolution.

And so instead of a tiny focal point that you can just, you know, look at with your eye, the image of a distant exoplanet is spread out over tens of kilometers. So if you have a spacecraft just parked in one position, yeah, it will get that one little bit of light, and it will see that little patch of the planet, and that'll be great. But if it wants to build a portrait, it has to scan over tens of kilometers. What this means is that if we want to get anything more than snapshots, we need a mobile spacecraft at that distance where we can't just fling it out and let it stay there. It has to move around so it can scan the image.

And we have to be really, really good at predicting the target that by the time the spacecraft reaches this position, we're looking at Proxima b. We have to know where Proxima b is in its orbit around the star so that all the timing works out. So when this when our our when our in spacecraft carrying all these instruments to collect the image, when it's pointing at Proxima b, it's not just looking at an empty patch of the Proxima system. It's actually looking at where the planet will be. So we have to do all this intricate math.

Like, that's just a bunch of math. We're we're nerds. We're good at that. And there are proposals floating around starting as early as the 19 seventies to make this work. It's not outright impossible.

That's the craziest thing about all this. It's an advanced past Voyager for sure. But it's not crazy outlandish past it. It's not like we have to create brand new schemes for generating energy or we need super large spacecraft. It it's a crazy idea, but it's it's a grounded crazy idea, which is why it's so alluring to me.

One method is to just to chuck a probe out there like a super voyager and hope for the best. Let it fly through this focal point and collect whatever data it can and then send it back to Earth, and then maybe we might get a small portion of a snapshot of one region of of a nearby exoplanet. There have been proposals going back decades to do just that, like take Voyager, but more so, make it faster so it can get to this extreme distance in something less than 4 or 5 decades. But that's not gonna be super satisfying. The most recent proposals is instead of a single large spacecraft that just buzzes its way outside the solar system, and then when it hits this market 540 whatever AU, it collects its data, sends it back to Earth, and we get that one snapshot.

We want to have a spacecraft that can hang out there. We want a spacecraft that can spend some time there. We want a spacecraft that has enough fuel and energy to move around out there so it can scan this giant focal plane and build up an image of an entire planet. The most recent proposals don't involve a single spacecraft, but many very, very small spacecraft. But then you run into challenges of okay.

Let's say I have a small spacecraft. It's just a simple sensor, and then it works together in, like, a swarm and, like, spirals around the focal plane. You know, the the looks at the image, builds this map of a distant exoplanet. The problem with small spacecraft is how do you get them out there? Because you need to load them down with fuel, but then when you add fuel to them, they become heavier.

So you need a bigger rocket, and then you need more fuel, and it it spirals out of control. So the proposals use solar sales. And I know I've poo pooed solar sales before, but that was for interstellar missions. This is much more reasonable. The idea here is to send a swarm of spacecraft, launch them from the earth, let them spiral in towards the sun, then unfurl their solar sails, let the radiation pressure from the sun push them out into the solar system, accelerate them very quickly, get them to this point at 545 AU, Get them to this point at 542 AU in the matter of a couple decades.

Still a long time, but not insane. Then somehow slow them down so that they can stop because once they move past it, it's gonna be a little bit more difficult. Have them start dancing around each other in a pattern where they can all individually start to collect data and then send that data back to Earth. Yeah. The the idea isn't fully fleshed out.

There's been a lot of work in this direction, but there are still still a lot of unknowns. And you know what? It would still require a tremendous amount of technological advancement. We don't have, like, super effective solar sales right now. We don't we don't have, like, swarms of spacecraft that can work together super efficiently.

We yes. All of these proposals are on the edge of the possible, but they're crazy enough. They just might work. It's right there just beyond our current technological capabilities, but not so far out that it's just science fiction and not worth thinking about in a serious, like, technological way. It's entirely possible.

And if we dedicated enough resources to this, we could capture an image, a portrait of an alien planet. We could get to know an alien world the way we know the planets of our own solar system, and we could do it in our lifetime. We just have to cheat a little. Thanks to Jimmy k for the question that led to today's episode, and thank you to all my Patreon supporters. That's patreon.com/pmsutter.

Special thanks to the top contributors this month. Justin g, Chris Elb, Alberto m, Duncan m, Corey d, Stargazer, Robert b, Nyla, Sam r, John s, Joshua, Scott m, Rob h, Scott m, Louis m, John w, Alexis Gilbert m, Rob w, Dennis a, Jules r, Mike g, Jim L, Scott, j, David s, William w, Scott r, Heather, Mike s, Michelle r, Pete H, Seves, Wat Wat Bird, Lisa r Koozie, and Kevin b. Keep those questions coming. That's askaspaceman@gmail.com or the website, askaspaceman.com. Keep the reviews coming on your favorite podcast platform.

There those really help, and please keep sending questions. These episodes are so much fun to do. And I will see you next time for more complete knowledge of time and space.

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