Latest / Daniel and Kelly’s Extraordinary Universe / Can you sail on light?

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Can you sail on light? · Daniel and Kelly’s Extraordinary Universe

0:09
Speaker 1: Hey, Daniel, you like the outdoors. You're an outdoorsy kind
0:12
Speaker 1: of person. Are you a fan of sailing? Oh? Man,
0:14
Speaker 1: I love sailing. There's so much to appreciate, the wind,
0:18
Speaker 1: the quiet, But mostly it's because it's about applied physics.
0:22
Speaker 1: That's the part you love the most about it is
0:23
Speaker 1: the physics of sailing. Yeah. You know, you've got the
0:26
Speaker 1: wind coming in one way and the boat is pointing
0:28
Speaker 1: another way, and you have the you know, the keel
0:30
Speaker 1: underneath and the rudder. It's a it's a big complicated calculation,
0:34
Speaker 1: all happening in real time under you. Yeah, and you
0:37
Speaker 1: might die or or get strounded out and see if
0:39
Speaker 1: you if you mess it up, that's right, that's right.
0:41
Speaker 1: So physics can save your life. It's good to understand vectors.
0:45
Speaker 1: But no, yeah, I always find it really confusing. You know.
0:47
Speaker 1: It's like if you want to go one way, you
0:49
Speaker 1: actually have to point the boat the other way. But
0:51
Speaker 1: then you have to move the sail in line with
0:53
Speaker 1: the wind, and so there's like the Bernoulli effect that
0:55
Speaker 1: I just I found it. What we're really confusing? It
0:57
Speaker 1: is confusing basically, Um, you know, all you need to
1:00
Speaker 1: know is if you want to go one way. Make
1:02
Speaker 1: sure you point the boat a different direction, right, That's
1:04
Speaker 1: the only way to get there. Never never point to
1:07
Speaker 1: where you're going. No, that's classic groupie mistake. Him Orgey,
1:26
Speaker 1: I'm a cartoonist and the creator of PhD Comics. Hi,
1:29
Speaker 1: I'm Daniel. I'm a particle physicist and the co author
1:33
Speaker 1: of our book Together We Have No Idea, A Guide
1:36
Speaker 1: to the Unknown Universe. Right now, you're listening to our podcast,
1:39
Speaker 1: Daniel and Jorge Explain the Universe, a production of I
1:42
Speaker 1: Heart Radio, in which we try to find weird, crazy, wacky, interesting,
1:47
Speaker 1: amazing things about the universe that will blow your mind
1:50
Speaker 1: and explain them to you in a way that makes
1:52
Speaker 1: you understand them and also laugh along the way. That's right.
1:55
Speaker 1: We take you to all the corners of the universe
1:57
Speaker 1: in rockets, in spaceships, in warp drives potentially, and also
2:02
Speaker 1: maybe using sailboats. That's right. We want to navigate your
2:06
Speaker 1: brain from here to there and all around, and we're
2:09
Speaker 1: willing to do in any sort of mental capsule that's possible.
2:12
Speaker 1: And so today on the program, we're going to be
2:14
Speaker 1: answering a listener question, who was wondering if there are
2:17
Speaker 1: better ways to travel through space. That's right. You guys
2:21
Speaker 1: might be familiar with the question of how do we
2:23
Speaker 1: get from here to there? Right? And if you want
2:26
Speaker 1: to fly from Earth to Mars, or Earth to Jupiter,
2:29
Speaker 1: or even do another star, you gotta push yourself there,
2:32
Speaker 1: or you gotta get your ship going at a certain speed,
2:35
Speaker 1: and that requires energy. And most of the technologies that
2:38
Speaker 1: we have currently are basically just like a fire spewing
2:41
Speaker 1: out the back, and that requires some sort of fuel.
2:44
Speaker 1: That's right, you need fuel, And unfortunately there are no
2:46
Speaker 1: gas stations between here and Mars, and so that you
2:49
Speaker 1: kind of have to bring it all with you. But
2:50
Speaker 1: there might be Tesla supercharger stations for all we know. Right,
2:53
Speaker 1: isn't that Elon Musk's plan? How does that company doing
2:56
Speaker 1: these days? I haven't really checked my stock portfolio, but
2:59
Speaker 1: you know, the guy thinks big. So probably as SpaceX
3:02
Speaker 1: goes to Mars, he's gonna stop along the way and leave,
3:04
Speaker 1: you know, charging stations. Yeah. So to the end the program,
3:07
Speaker 1: we'll be talking about an interesting idea about traveling to
3:10
Speaker 1: the stars. We'll be talking about solar sales. How do
3:19
Speaker 1: they work? Do you really sale our solar cells on sale. Right,
3:23
Speaker 1: how did what does this thing even mean? That'd be
3:25
Speaker 1: nice if they're on sale, everyone can get one, that's right.
3:28
Speaker 1: That's right, more than just our listeners in Delaware. Remember
3:31
Speaker 1: that podcast when we were going to cover the state
3:33
Speaker 1: of Delaware with solar cells. Oh? Yeah, do we get
3:35
Speaker 1: any feedback from delawareans? Oh? Actually we did. Um. First
3:40
Speaker 1: of all, they commented that we need to also include Maryland.
3:43
Speaker 1: And they weren't defended at all. Actually, they were just
3:45
Speaker 1: glad to have any sort of Delaware shout out. They
3:47
Speaker 1: say that they don't often get mentioned. Never happens. I
3:50
Speaker 1: guess exactly. So we love you, Delaware. Keep listening. Yeah,
3:54
Speaker 1: so it's kind of an interesting idea that you can
3:57
Speaker 1: make a sale to sale all the deep blue blackness
4:02
Speaker 1: of space. Yeah, it's really kind of an awesome idea.
4:04
Speaker 1: I mean, you're we're familiar with the wind, right, and
4:07
Speaker 1: the wind is a wonderful way to use a sailboat
4:09
Speaker 1: because you don't have to bring any fuel with you. Right,
4:12
Speaker 1: you go on a motor boat, you've got to bring
4:14
Speaker 1: all that fuel with you. It makes your boat heavier,
4:16
Speaker 1: it's loud, it's noisy, is obnoxious. Right, One of the
4:19
Speaker 1: things I love about sailing is that it's quiet. Right.
4:22
Speaker 1: First of all, you don't have to fuel up because
4:23
Speaker 1: your fuel is just the wind. And then when you're sailing,
4:26
Speaker 1: there's no obnoxious motor sound to listen to. So the
4:29
Speaker 1: idea of traveling from one planet to another through space
4:33
Speaker 1: using something similar like being propelled without bringing along your
4:37
Speaker 1: own fuel, it's a beautiful idea. Yeah, it's kind of
4:39
Speaker 1: cool to think that you can ride something out in space, right,
4:42
Speaker 1: Like there's something already going there and you can just
4:45
Speaker 1: kind of latch onto it and will push you to
4:47
Speaker 1: where you want to go. That's right. And you might
4:49
Speaker 1: be tempted to say, what's pushing the sail, Like obviously
4:52
Speaker 1: on Earth here it's air, But what's pushing your sail
4:55
Speaker 1: out in space? Because there's no air in space and
4:57
Speaker 1: you're right, right if we're not sailing in that same way.
5:00
Speaker 1: And then you might be tempted to say, what about
5:02
Speaker 1: the solar wind? These guys have told us about all
5:04
Speaker 1: the particles shooting out from the Sun, Is that the
5:07
Speaker 1: solar wind that a solar sale would be riding. But
5:09
Speaker 1: that's not even the case. It's not it's not the
5:12
Speaker 1: solar wind that a solar sale works off of though
5:15
Speaker 1: that would be some sort of poetic you know, beautiful parallel. Wait,
5:18
Speaker 1: so it's not the solar wind that you would sail
5:20
Speaker 1: on in space. No, it seems tempting, right, you'd like
5:24
Speaker 1: to have a solar sail boat using the solar wind
5:27
Speaker 1: for this beautiful analogy for our whiskey fueled adventures on
5:31
Speaker 1: the high seas here. But it's not actually the solar
5:33
Speaker 1: wind that pushes along a solar sail. Oh man. The
5:36
Speaker 1: solar wind does it give you a sunburn and chapped
5:39
Speaker 1: lips at the same time? That's right, It gives you
5:43
Speaker 1: that solar wind touseled hair. Also you have deep fried
5:46
Speaker 1: probably exactly not recommended, folks, not recommended. It's like a
5:51
Speaker 1: Brazilian blowout. But um, Chris here, if you're listening to
5:55
Speaker 1: this podcast on the space station, do not stick your
5:57
Speaker 1: head at the window to get a solar wind tewseled look. Yeah, instead, right,
6:01
Speaker 1: is because that'd be really cool to hear from you,
6:03
Speaker 1: exactly exactly. Yeah, So we'll be talking to me about
6:06
Speaker 1: the solar sales, the idea that you can go between
6:10
Speaker 1: planets or stars or galaxies using a sale to catch
6:14
Speaker 1: something out there in space to take you there. And so,
6:16
Speaker 1: as we mentioned, this question came to us from Derek
6:19
Speaker 1: from Cleveland, and so here is Derek asking his question. Hey,
6:22
Speaker 1: Daniel Jorge, this is Derek from Cleveland, Ohio. My question
6:25
Speaker 1: is how does solar sales work if photons are massless?
6:28
Speaker 1: How can they impart momentum to a satellite? And how
6:31
Speaker 1: is the conservation of momentum upheld? I quickly want to
6:34
Speaker 1: say hi to my brother in law, Tim, who I'm
6:36
Speaker 1: sure we'll listen and discuss your answer with me later.
6:39
Speaker 1: Thanks guys, All right, thank you Derek. That's a pretty
6:41
Speaker 1: interesting question. I mean, it's it's sort of um. It
6:44
Speaker 1: sounds like he's heard of solar sales and he knows
6:46
Speaker 1: they work by catching light, but his question was how
6:50
Speaker 1: does that work if photons have no mass? Yeah, so
6:53
Speaker 1: many good questions here, right, like how does the solar
6:55
Speaker 1: sale work? He seems to understand that it catches light,
6:58
Speaker 1: but it doesn't understand like does light half momentum because
7:01
Speaker 1: he's probably thinking that momentum is mass times velocity, right,
7:06
Speaker 1: which is the case for slow moving massive objects. So
7:09
Speaker 1: he's wondering if the mass term is zero, how can
7:11
Speaker 1: you have any momentum, Like, how do things with no
7:13
Speaker 1: mass have any momentum? And if they have meantum, if
7:16
Speaker 1: they don't have momentum, how can they push along a
7:18
Speaker 1: solar sale? It's a great question, right, I mean, I
7:20
Speaker 1: think it means, like, you know, if light has nothing
7:23
Speaker 1: to it in terms of like mass, how can it
7:25
Speaker 1: push you? Exactly? That's the question. And so I was
7:28
Speaker 1: wondering what people thought about this. So people aware of
7:31
Speaker 1: solar sales do they understand photons and momentum and all
7:34
Speaker 1: this kind of stuff. And so I went around and
7:37
Speaker 1: I asked people, um what they knew about solar sales.
7:40
Speaker 1: And before you listen to these answers, think to yourself,
7:42
Speaker 1: do you know how a solar sale works? Do you
7:45
Speaker 1: understand how light can have momentum if it doesn't have mass.
7:47
Speaker 1: Here's what they had to say. I feel like I've
7:50
Speaker 1: heard of it, but I'm not sure. I mean, I've
7:51
Speaker 1: seen like six once, but I haven't seen I know
7:54
Speaker 1: that they're kind of transitioning like testas doing the roof
7:58
Speaker 1: tiles and stuff that I was sore, but I don't
8:02
Speaker 1: I don't know if I've seen a big pike. I
8:05
Speaker 1: guess kind of like sheet of sunlight. Yes, actually I
8:08
Speaker 1: have a solar sale is basically a really big sale
8:12
Speaker 1: that doesn't get pushed by wind. It gets pushed by
8:15
Speaker 1: energy from the sun. So basically energy has a little
8:18
Speaker 1: bit of movement in it, and that big movement, a
8:22
Speaker 1: little bit of movement can push it because it's not
8:24
Speaker 1: too much movement, but it's a lot of energy in
8:27
Speaker 1: a big area that that will push it. I'm honestly
8:30
Speaker 1: not sure. I couldn't even I couldn't mean guess like
8:33
Speaker 1: maybe the stilted price on solar system or something like that.
8:38
Speaker 1: All right, I love these answers or I feel like
8:41
Speaker 1: they're all correct. Like is it a boat powered by
8:46
Speaker 1: solar power? Yes, technically that would be a solar That
8:50
Speaker 1: would be like a boat with an electric engine on
8:52
Speaker 1: it that's powered by solar cells. That's pretty cool. Yeah, sure, yeah,
8:56
Speaker 1: that's like a solar boat for sure. Or like a discount,
8:59
Speaker 1: I don't think is it? Is it like a discount
9:02
Speaker 1: on solar panel? I think like a solar sale. I
9:04
Speaker 1: think that guy might have thought I was actually trying
9:06
Speaker 1: to sell him solar panels, like he looked kind of wary.
9:09
Speaker 1: He's like, are you another one of those shady solar
9:12
Speaker 1: salesman discounts. They are pretty shady quote unquote, that's right exactly.
9:18
Speaker 1: Their business wouldn't stand up to sunlight. You have to
9:20
Speaker 1: be pretty bright. And there was one folk, one guy
9:23
Speaker 1: who actually had a pretty solid answer. Was this your
9:25
Speaker 1: physics student sale and slash sale instructor? It was not.
9:29
Speaker 1: Actually that was my eleven year old son, who I
9:32
Speaker 1: think overheard me talking about solar sales to somebody else
9:35
Speaker 1: before I asked him, so he had a preview of
9:37
Speaker 1: the answer and just wound wanted to sound smart. You're
9:40
Speaker 1: saying your son cheated, I'm saying I asked him the question,
9:44
Speaker 1: and he knew the answer, and so he answered it.
9:48
Speaker 1: That's right, it's it wasn't a test. Yeah, he had
9:51
Speaker 1: a bit more of a head start than the rest
9:53
Speaker 1: of the other folks that we asked. So, um, it's
9:55
Speaker 1: not something that a lot of people seem to know
9:56
Speaker 1: about or recognize the name of. That's right. It's not
9:59
Speaker 1: a in concept. And that surprised me a little bit
10:01
Speaker 1: because I thought that people had heard more about like
10:05
Speaker 1: how to move through space or the kinds of engines
10:07
Speaker 1: you might use. But I guess not which makes an
10:10
Speaker 1: excellent topic for today's podcast. Yeah. Well, I have to
10:12
Speaker 1: admit my only reference to a solar sale powered spaceship
10:17
Speaker 1: is from Star Wars. Do they do solar sales? And
10:19
Speaker 1: Star Wars? I don't even remember that. I thought they
10:21
Speaker 1: all had ion engines and stuff. Yeah, I know. I mean,
10:24
Speaker 1: if you if you've watched the prequels, which I'm sure
10:27
Speaker 1: we can get into a whole episode about. But count
10:30
Speaker 1: Dooku with that character has rise around in a ship
10:33
Speaker 1: that has solar sales or what looks like what looked
10:36
Speaker 1: like solar sales. Oh my gosh. Why you have like
10:38
Speaker 1: an encyclopedic knowledge of all the ships in every science
10:41
Speaker 1: fiction movie ever. That's that's impressive. And I have an
10:46
Speaker 1: encyclopedic knowledge of all NERD movies. So that's what That's
10:50
Speaker 1: what you do it for In the afternoon when you're
10:52
Speaker 1: not feeling in the mood to do cartooning, it's like
10:54
Speaker 1: turn on some science fiction movie. Yeah, isn't that what
10:57
Speaker 1: everybody does? Yes, yes, that is exactly what everybody does
11:02
Speaker 1: in the middle of the afternoon. Um, no, but you're right,
11:05
Speaker 1: these things are in science fiction. Um. I've read lots
11:08
Speaker 1: of books with solar sale powered chips in them. Uh,
11:11
Speaker 1: it's a pretty common idea in terms of like how
11:13
Speaker 1: to get from here to there. And you know what,
11:15
Speaker 1: we don't have that many ideas for how to get
11:17
Speaker 1: from one planet to another or one star to another,
11:20
Speaker 1: and so it's on a pretty short list. Well, this
11:22
Speaker 1: is how it kind of worked in Star Wars. So
11:24
Speaker 1: count get on this ship. He takes off, he flies
11:27
Speaker 1: up into orbit or space, and then he like unfurls
11:30
Speaker 1: this huge giant sail, this like giant sheet that looks
11:35
Speaker 1: kind of like it's made out of gold, and then
11:37
Speaker 1: then he starts going. So it's like he's it's like
11:40
Speaker 1: he opened a giant umbrella and then that pushed him forward. Yeah,
11:43
Speaker 1: that's basically a solar sales are giant umbrellas. Podcast over,
11:47
Speaker 1: you nailed it Star Wars for the wind. Yeah, let's
11:53
Speaker 1: get into it, Daniel. What is a solar sale? So
11:55
Speaker 1: a solar sale is an enormous flat sheet, just like
11:59
Speaker 1: a sail on a sale boat. Um, and the thing
12:01
Speaker 1: that it captures is not wind like in air, because
12:05
Speaker 1: there is no wind in space and it's not the
12:07
Speaker 1: solar wind because the solar wind member is protons being
12:10
Speaker 1: shot out by the Sun and those could push the sail,
12:13
Speaker 1: but there's just not that much of them. There's just
12:15
Speaker 1: not that many of them. There's not enough of them.
12:17
Speaker 1: What is capturing is light. So the light from the
12:20
Speaker 1: sun is zooming out from the Sun and it's carrying
12:23
Speaker 1: energy with it, and we'll dig into that in a moment.
12:25
Speaker 1: But photons have momentum, and so what happens when they
12:28
Speaker 1: hit the sail is that they give it a little push,
12:31
Speaker 1: and you get enough little pushes and you can actually
12:34
Speaker 1: get going somewhere. So this is a real thing, like
12:36
Speaker 1: people have built these, Like there are functioning solar wind
12:42
Speaker 1: sailboats out there in space. Um, yes, this is a
12:44
Speaker 1: real thing. It's like physics says, there's no reason why
12:47
Speaker 1: I shouldn't work. People have big plans to make huge
12:51
Speaker 1: solar sales that can go all around the Solar System
12:53
Speaker 1: or maybe even to other stars. And somebody has actually
12:57
Speaker 1: built one of these things and made it work. The
12:59
Speaker 1: Japanese they launched one um several years ago and showed
13:03
Speaker 1: that it actually worked. Like the physics isn't just theoretical,
13:05
Speaker 1: Like there is one thing out there that's solar sailing
13:08
Speaker 1: right now, that's pretty cool the Japanese. The Japanese, nice job.
13:13
Speaker 1: But the thing about solar sales is that it's gentle, right,
13:17
Speaker 1: It's not really really powerful winds of light out there
13:20
Speaker 1: for you to capture with your sales. So if you
13:22
Speaker 1: have like even a really big sale, like eight hundred
13:26
Speaker 1: meters by eight hundred meters, which is you know, enormous, right,
13:30
Speaker 1: then that only gets five newton's of force, And five
13:33
Speaker 1: newtons is not that much. It's like how much you know,
13:36
Speaker 1: a fourth there isn't like a one pound object on Earth,
13:40
Speaker 1: So like a one pound rock, you know, think about
13:43
Speaker 1: how much that feels in your hand. That's the force
13:45
Speaker 1: of the Earth's gravity on a one pound rock. That's
13:48
Speaker 1: the same amount of force that the Sun would push
13:51
Speaker 1: on a eight hundred meter by eight hundred meters sail
13:55
Speaker 1: about the distance from of the Earth, which is huge, right,
13:58
Speaker 1: I mean it's a several city blocks. Yeah, that is
14:00
Speaker 1: not a small thing to build and to unferral and
14:04
Speaker 1: to keep from getting shredded right by like micro meteorites
14:07
Speaker 1: or whatever. But you're saying if I made a tarp
14:10
Speaker 1: that was about a kilometer on each side over Manhattan,
14:15
Speaker 1: it would get pushed down not just by the weight
14:17
Speaker 1: of it, but also by the sun that's hitting it. Yes, exactly,
14:20
Speaker 1: And every time a photon hits you, you're getting pushed. Like.
14:24
Speaker 1: Photons are actually pushy. They are kind of rude, aren't they.
14:29
Speaker 1: They just like zoom along wherever they want to go.
14:31
Speaker 1: They don't ask questions, they don't take turns, or they
14:33
Speaker 1: just going straight lines wherever they need to know. Photons
14:37
Speaker 1: care momentum, and every time they hit something, they give
14:40
Speaker 1: it a little push. So when you turn, when you
14:42
Speaker 1: flip the switch and turn on the light, you get
14:44
Speaker 1: pushed down a tiny little bit. And you might think, what,
14:47
Speaker 1: I can't feel it, And you're right because it's a
14:50
Speaker 1: small effect, which is why solar sales are very gentle,
14:53
Speaker 1: and you need a huge one to add up to
14:55
Speaker 1: any measurable force. Well, let's step us through a little
14:58
Speaker 1: bit of how this works. I mean, so you're saying,
14:59
Speaker 1: if I take a flashlight and I flash it at you,
15:02
Speaker 1: I am technically kind of pushing you with it. You're
15:05
Speaker 1: basically punching me in the face with light. Yeah. Yeah,
15:09
Speaker 1: that's that's really me because we don't think of light
15:11
Speaker 1: as having substance to it, right, Like you I mean,
15:14
Speaker 1: we know we sort of associated with energy and heat
15:17
Speaker 1: and warmth, but not um force. That's right. We don't
15:20
Speaker 1: think of photons is having mass because they don't, but
15:23
Speaker 1: they do have energy, right, Photons are energies is just
15:26
Speaker 1: pure energy. And if you have energy, that means you
15:30
Speaker 1: have momentum. And it's complicated because we're only used to
15:33
Speaker 1: thinking about things having momentum when they have mass. We
15:36
Speaker 1: think about you give something momentum because it's heavy and
15:39
Speaker 1: it's hard to get going, and once you've pushed it,
15:41
Speaker 1: it keeps going. It has momentum. Right, So something that's
15:44
Speaker 1: like light and fluffy and you know, weighs nothing, it's
15:47
Speaker 1: hard to understand how that can have momentum. Well, I
15:50
Speaker 1: think I think we're all pretty familiar with like if
15:52
Speaker 1: I shine a flashlight on you or a laser, like
15:54
Speaker 1: your body is gonna absorb that energy or you know,
15:58
Speaker 1: warm up a little bit or something. But you're saying
16:00
Speaker 1: that if I have an atom on my skin and
16:02
Speaker 1: you're flashing a flashlight on it, the photons actually sort
16:06
Speaker 1: of hit it and the atom wants to go the
16:07
Speaker 1: other way. Yes, exactly. Think about what happens with a mirror, right,
16:11
Speaker 1: it's a little bit more complicated when the light gets absorbed.
16:13
Speaker 1: So let's think about a mirror where the light gets reflected,
16:16
Speaker 1: the light zooming in one direction, it hits the mirror,
16:18
Speaker 1: and the lights going in the other direction. Right, how
16:21
Speaker 1: does the light change direction? Right? What changes the direction
16:24
Speaker 1: of the light. It's the mirror. Instead of thinking about
16:28
Speaker 1: light in a mirror, think about a ping pong ball
16:30
Speaker 1: and a paddle. Right, if you get hit. If a
16:32
Speaker 1: ping pong paddle gets hit by the ball, then the
16:35
Speaker 1: ball bounces the other direction, but the paddle gets pushed
16:38
Speaker 1: back a little bit. Right, That balances the momentum. Momentum
16:41
Speaker 1: is conserved. So in the same way, when the light
16:44
Speaker 1: hits the mirror, it gives that mirror a little push,
16:46
Speaker 1: and the mirror pushes back, and that's what turns the
16:49
Speaker 1: light the other direction. And so when light reflects off
16:52
Speaker 1: of something, it's giving it a little push. So pure
16:55
Speaker 1: energy can push you basically exactly. It can result in
16:58
Speaker 1: something wanting to move the other way. That's right. And
17:01
Speaker 1: this is one of the cool things in physics when
17:03
Speaker 1: you learn that a concept you thought you had a
17:06
Speaker 1: firm grasp on, like momentum, is actually just a special
17:09
Speaker 1: case of sort of a larger concept. Like we're familiar
17:11
Speaker 1: with momentum is mass times velocity. But that's not it's definition.
17:15
Speaker 1: That's just how you calculated for slow moving things with mass.
17:20
Speaker 1: You can calculate momentum for things that don't have mass,
17:22
Speaker 1: because momentum is a larger concept. It's just it captures
17:26
Speaker 1: like the quantity of motion of something, not just it's
17:29
Speaker 1: mass times velocity. It's just that it's more like the
17:31
Speaker 1: total energy. Yeah, but it's fascinating because energy is just
17:34
Speaker 1: a number. It doesn't have a direction, right, and physics
17:37
Speaker 1: energies is a scaler, not a vector, like it doesn't
17:40
Speaker 1: have a direction, just a magnitude, whereas momentum has a direction.
17:44
Speaker 1: Like you know, pointed in one direction is different from
17:46
Speaker 1: pointed in the other direction. Right, Uh, light has momentum.
17:51
Speaker 1: Light has momentum, has energy, and it has momentum and
17:54
Speaker 1: it has no mass. One way that some people like
17:56
Speaker 1: to think about it is you can think about momentum
18:00
Speaker 1: sort of the difference between the energy and the mass.
18:03
Speaker 1: Right because in real and relativity we think of the
18:04
Speaker 1: total energy as the energy store in the mass plus
18:08
Speaker 1: the energy of the momentum. So you can sort of
18:10
Speaker 1: invert that equation and say the momentum is the difference
18:13
Speaker 1: between the total energy and the mass. And in the
18:15
Speaker 1: case of the photon, there is no mass. Momentum just
18:18
Speaker 1: comes from the energy, whereas in the case of another particle, right,
18:21
Speaker 1: it has a bunch of energy. Some of that is
18:23
Speaker 1: in the mass and some of it is in its motion.
18:25
Speaker 1: But for the photon, all the energy is just in
18:27
Speaker 1: its motion, so it just has momentum and no mass.
18:30
Speaker 1: All right. Solar sales are a real thing, and they
18:33
Speaker 1: work by taking the momentum that's in light, absorbing it
18:37
Speaker 1: and then using that to push you along in space.
18:40
Speaker 1: That's right, And it's the light from the Sun that's
18:42
Speaker 1: doing this, not the protons from the solar wind. And
18:45
Speaker 1: everybody actually can see this if you just have seen
18:47
Speaker 1: a comet. You know, comet is just a big ice
18:50
Speaker 1: ball and it falls towards the Sun and as it
18:52
Speaker 1: does so it gets a big tail, right, and that's
18:55
Speaker 1: the tail of it, like the stuff melting and dripping
18:57
Speaker 1: out the back, and the tail points in a specific
19:00
Speaker 1: direction away from the Sun, not in the direction of motion.
19:02
Speaker 1: People think, like, you know, it's like a fuzzy lines
19:05
Speaker 1: behind something that's moving fast. But the commet actually always
19:08
Speaker 1: points away from the Sun, and that's because of this
19:11
Speaker 1: effect of light. That's light pushing the tail of the commet. Really,
19:15
Speaker 1: it's not like a trail of a dust that you
19:17
Speaker 1: leave behind. No, Because as the common is moving towards
19:19
Speaker 1: the Sun, the tail is behind it. But as the
19:21
Speaker 1: comet goes around the Sun and then leaves, the tails
19:24
Speaker 1: in front of it. Wow, so it shouldn't be called
19:27
Speaker 1: the tail once again? Yeah, I guess. Or maybe it's
19:32
Speaker 1: like backing away from the Sun as it leaves. It's
19:34
Speaker 1: like whoa, that was close. All right, let's get into
19:37
Speaker 1: will it work and how how can we make it work?
19:40
Speaker 1: But first let's take a quick break. All right. So
19:55
Speaker 1: that's solar sales Daniel. That's pretty cool. The question now,
19:58
Speaker 1: I think is does it work? If you build it,
20:00
Speaker 1: will it take us to other planets and maybe other galaxies? Yeah,
20:04
Speaker 1: it's it seems like it will. And you know, we
20:05
Speaker 1: know a lot about it. We can do these calculations.
20:08
Speaker 1: We know how much light there is, we can calculate
20:10
Speaker 1: how it will reflect and how much will be absorbed,
20:13
Speaker 1: and we know all the numbers we need. And so
20:15
Speaker 1: people have plugged all this stuff into calculations, and they said,
20:18
Speaker 1: if you build a solar sale that's like a kilometer
20:21
Speaker 1: by a kilometer and you have a really light ship,
20:24
Speaker 1: you know, not too heavy, how long would it take
20:26
Speaker 1: to get to Mars or to get to Jupiter. And
20:29
Speaker 1: the thing you have to understand is that the strength
20:32
Speaker 1: of the light, of course, gets weaker as you get
20:34
Speaker 1: further from the Sun. So the solar sale is very
20:36
Speaker 1: powerful close to the Sun because it's capturing more light,
20:39
Speaker 1: and then as you get further and further away from
20:41
Speaker 1: the Sun, it gets weaker and weaker. So solar sales
20:44
Speaker 1: are great for navigating around the inner parts of a
20:46
Speaker 1: solar system. Well, the question I have is, you know
20:49
Speaker 1: these sales are catch the rays from the Sun, right,
20:52
Speaker 1: they catch the light from the Sun and push it
20:55
Speaker 1: get pushed away from the Sun. But what if you
20:58
Speaker 1: want to travel towards the Sun are perpendicular to the Sun.
21:01
Speaker 1: How would you do that? If you want to move
21:02
Speaker 1: towards the Sun, It's not hard, right, you just need
21:04
Speaker 1: to use gravity. Right, the Sun is going to pull
21:06
Speaker 1: you towards the Sun, so that part is not hard.
21:09
Speaker 1: But the only way you can use the sail to
21:11
Speaker 1: build energies is moving away from the sun. So you
21:14
Speaker 1: can play this game of gravity versus the solar sail
21:18
Speaker 1: depending on which way you want to go. If you're
21:20
Speaker 1: facing the sun, can you go side? What can it
21:22
Speaker 1: push you sideways? Because gravity is pushing me towards the
21:25
Speaker 1: sun and the solar sales pushing me away from the sun.
21:28
Speaker 1: How do how do I gain speed sideways? WHOA, that's
21:32
Speaker 1: a really good question. I haven't even thought about that.
21:34
Speaker 1: How do you steer it? Because the photons are only
21:37
Speaker 1: coming out from the sun, so can you move in
21:40
Speaker 1: a direction that's not out away from the sun. My
21:43
Speaker 1: first thought is, let's think about how a sale works
21:46
Speaker 1: on a sail boat. Right, on a sail boat, you
21:48
Speaker 1: can move in a different direction than the wind if
21:51
Speaker 1: you put the sail across from the wind. But the
21:54
Speaker 1: problem is a sailboat has a keel, right, has something
21:57
Speaker 1: underneath it that keeps it from sliding sideway is and
22:00
Speaker 1: so it can only use the part of the wind
22:02
Speaker 1: that it wants by pointing in the right direction. A
22:05
Speaker 1: solar sale, of course, on a spaceship doesn't have a keel,
22:09
Speaker 1: So I first thought you might think, oh, a solar
22:11
Speaker 1: sale can only take you in the direction the photons
22:14
Speaker 1: are going. Right. Well, let's think about it for a moment.
22:17
Speaker 1: What happens if you tilt the sale so that it's
22:21
Speaker 1: not pointing um flat away from the sun right, if
22:24
Speaker 1: it's at an angle with respect to the photons. You
22:27
Speaker 1: might think, well, it doesn't really matter because the photons
22:31
Speaker 1: hit it and bounce off, and they're giving a push
22:33
Speaker 1: the direction they were going. Right. It's actually a tiny
22:36
Speaker 1: bit more complicated. If the photons hit it at an angle,
22:41
Speaker 1: then they also bounce off at an angle right. So
22:45
Speaker 1: if the photons are coming directly out from the sun
22:47
Speaker 1: and they hit flat on the solar sail, then they
22:49
Speaker 1: bounced back the opposite direction, and the momentum they have
22:52
Speaker 1: given is in the direction they were going. But if
22:55
Speaker 1: they come out from the sun and they hit the
22:57
Speaker 1: solar cell at an angle right, then they were flecked off.
23:00
Speaker 1: Think about light hitting a mirror right. It doesn't come
23:03
Speaker 1: back the way it was going. It reflects off at
23:04
Speaker 1: an angle, and so the push that it gives is
23:07
Speaker 1: actually in the direction that the solar sale was facing.
23:11
Speaker 1: So I think that means that you can steer a
23:15
Speaker 1: solar sale you just turn it through the way it
23:17
Speaker 1: wants to go, and it will catch that part of
23:20
Speaker 1: the photons momentum that pushes it in the direction it's facing.
23:24
Speaker 1: You can't just point in that direction and drive the
23:26
Speaker 1: way you came with your car. You have to take
23:28
Speaker 1: an account all these limitations. But you can do it,
23:30
Speaker 1: and you can take a pretty heavy load, you know,
23:32
Speaker 1: a few tons to mercury, and it just takes a
23:35
Speaker 1: few years. If you want to go to Venus, it
23:37
Speaker 1: takes you know, about a year. If you want to
23:39
Speaker 1: go the other direction, it starts taking longer because the
23:43
Speaker 1: radiation from the Sun drops, right, So if you want
23:45
Speaker 1: to go to Mars, it takes like a year and
23:47
Speaker 1: a half maybe two. Takes like two years to get
23:50
Speaker 1: to Jupiter, three to get to Saturn, and then like
23:52
Speaker 1: six years and nine years to get out to the
23:55
Speaker 1: outer planets. It's a lot of whiskey drinking on board.
23:59
Speaker 1: That's your fuel, after all, right, there's no there's no
24:02
Speaker 1: solar whiskey, and you'd be using it up. You could
24:06
Speaker 1: have burned it to evade that asteroid, but no, you
24:09
Speaker 1: had to drink it. Yeah, well, you know, it depends
24:11
Speaker 1: on how well you get along with your crewmates, depending
24:13
Speaker 1: that determines how much whiskey you have to drink. Can
24:15
Speaker 1: you imagine being stuck in a spaceship with your physics
24:18
Speaker 1: student for nine years? Tan? No, but I also can't
24:20
Speaker 1: imagine being a spaceship by myself for nine years, right, Like,
24:24
Speaker 1: what do you think would be easier to handle total
24:26
Speaker 1: isolation or being stuck with one person in a tin
24:29
Speaker 1: can for nine years? Oh? For me, would definitely be
24:32
Speaker 1: by myself. Yeah, you and a big stack of science
24:35
Speaker 1: fiction movies, right all you need and a cartooning pad, obviously,
24:40
Speaker 1: so I can document my descent into madness, your further
24:43
Speaker 1: descent into madness, you ment, surely, that's thank you for
24:47
Speaker 1: reminding me. But yes, but what about beyond the Solar system?
24:52
Speaker 1: Could you use the solar sale to leave the Solar system?
24:55
Speaker 1: You could a little bit. I mean what you can
24:57
Speaker 1: do is try One strategy is to just try to
25:00
Speaker 1: get going as fast as you can using solar sales
25:03
Speaker 1: and gravity, and then zoom off in the direction of
25:05
Speaker 1: another star. So you're like you sling shot around the
25:08
Speaker 1: Sun to get some speed up, and then as you're
25:11
Speaker 1: leaving the Sun, you unfurl your sails and it pushes
25:14
Speaker 1: you away from the sun is as hard as you can.
25:16
Speaker 1: But then once you leave the solar system, it's really
25:18
Speaker 1: going to stop pushing you very much, and so your
25:20
Speaker 1: speed doesn't pick up anymore. But you know, if you
25:23
Speaker 1: do it right and you have a light enough object,
25:24
Speaker 1: you could get up to a reasonable speed UM and
25:27
Speaker 1: head off in that direction. Yeah. I mean, at some
25:29
Speaker 1: point when you leave the solar system, it's like the
25:32
Speaker 1: there's no wind. It's like being on a sailboat with
25:34
Speaker 1: no wind. There's nothing to push you anywhere. Yeah, and
25:37
Speaker 1: you know there is radiation out there, and there are particles,
25:40
Speaker 1: but it's very low density. It's not enough to really
25:42
Speaker 1: really boost you. UM. One idea people have, and I
25:45
Speaker 1: love this idea because it's so crazy plus ambitious, which
25:48
Speaker 1: is my favorite combination, is to basically beam light at
25:53
Speaker 1: these things. Like if you're in a solar sailboat and
25:55
Speaker 1: you're leaving the solar system, maybe we could like build
25:58
Speaker 1: a huge laser and beam the energy at your solar
26:02
Speaker 1: sale to give you a push. What if you punch
26:04
Speaker 1: a hole through the sale with their laser? Yeah, exactly.
26:07
Speaker 1: It can't be too intense. UM. But you know these
26:10
Speaker 1: lass these sales will be very reflective, right. They are
26:14
Speaker 1: essentially the big sheets of aluminum or maybe plastic that's
26:17
Speaker 1: covered with aluminum so that they're super reflective. So if
26:21
Speaker 1: it's reflective enough, then even a really really powerful laser
26:23
Speaker 1: won't punch a hole, right, because punching a hole means
26:27
Speaker 1: the energy gets absorbed and so like melts and destroys
26:30
Speaker 1: the sail. If it's reflective enough, then you should be
26:32
Speaker 1: able to shoot even a really powerful laser and have
26:34
Speaker 1: all the energy to be transferred into the momentum of
26:37
Speaker 1: the sail. It's like blowing on a little sailboat. Yeah, exactly.
26:41
Speaker 1: Or I'm sure I've seen some science fiction movie where
26:43
Speaker 1: somebody like reflects a laser blaster with a mirror. Right, Oh,
26:47
Speaker 1: you just have like a pure mirror shoot at it
26:49
Speaker 1: and then that pushes you forward. Yeah, if somebody shoots
26:51
Speaker 1: you with a laser blaster and you have a mirror,
26:54
Speaker 1: you can just reflect their you know, energy pulse or
26:56
Speaker 1: whatever back at them. All Right, Well, let's let's get
26:59
Speaker 1: into how you actually build a solar sale, even if
27:02
Speaker 1: it wasn't on sale. But first let's take a quick break.
27:18
Speaker 1: That would be a pretty awesome idea for merch like
27:21
Speaker 1: solar sale. Daniel and Jorge solar sale explore the universe
27:24
Speaker 1: instead of explain the universe. That'd be pretty cool. What
27:27
Speaker 1: do you mean, what will we sail sale sell? We'd
27:32
Speaker 1: sell the solar sale like you are. We have a
27:35
Speaker 1: shop where we sell t shirts and coffee mugs with
27:38
Speaker 1: you know, Daniel and Jorge is playing the universe on it.
27:40
Speaker 1: We should add to our Internet merch account a solar
27:44
Speaker 1: sale that you can buy. Okay, cool, done, let's do it.
27:48
Speaker 1: And then you just get a sheet of aluminum foil?
27:50
Speaker 1: Is that the idea? That one kilometer by one kilometers
27:54
Speaker 1: wherever loominum foil with your picture on it. There you go,
27:58
Speaker 1: and you can sail way into bankruptcy, right, and you
28:02
Speaker 1: can shoot a laser at that picture from Earth dual
28:05
Speaker 1: purpose aluminum foil. You can wrap your leftovers and go
28:08
Speaker 1: into space exactly. But that's basically what a solar sailing is. Right.
28:13
Speaker 1: You wanted to be really really big, but you also
28:15
Speaker 1: wanted to be really really light. You want your solar
28:17
Speaker 1: sailboat to be as light as possible so that all
28:19
Speaker 1: that momentum gets turned into speed um. The more massive
28:23
Speaker 1: your sailboat, the slower it's going to go for the
28:25
Speaker 1: same amount of momentum as you want it really big
28:28
Speaker 1: and really thin. I mean, does it matter in the
28:29
Speaker 1: long run how much here solar sail ways? Sure it does. Yeah.
28:33
Speaker 1: I mean you want to get up to like half
28:35
Speaker 1: the speed of light or a quarter of the speed
28:36
Speaker 1: of light or something, it's gonna take a lot longer.
28:38
Speaker 1: And if you don't have a laser push, then you
28:41
Speaker 1: have a limited amount of time to get energy from
28:43
Speaker 1: the sun as you want to get up to as
28:45
Speaker 1: high as speed as possible. Oh, I mean, but that's
28:47
Speaker 1: just in general the same for any acceleration, right, Absolutely,
28:51
Speaker 1: the lighter you are, the faster it is to go faster. Yeah, exactly.
28:54
Speaker 1: And that's like why people who you know, climb mountains
28:58
Speaker 1: on their bicycles or move every tiny little thing that's
29:02
Speaker 1: not necessary because they don't want to carry that mass
29:04
Speaker 1: up the mountain. You know, I met a guy who's
29:06
Speaker 1: climbing Matu Picchu and he like sawt his toothbrush in
29:09
Speaker 1: half because he didn't need the bottom half of it.
29:11
Speaker 1: And you didn't want to carry that thing up the mountain.
29:13
Speaker 1: So yeah, you wanted these your spaceship to be as
29:15
Speaker 1: light as possible so you can translate all of that
29:18
Speaker 1: momentum into speed. So basically that's all you need is
29:21
Speaker 1: just a thin aluminum foil. But usually they showed them,
29:25
Speaker 1: show them in movies and and pictures. Is gold It
29:28
Speaker 1: looks like gold foil. Does that give you a better
29:31
Speaker 1: advantage if it's gold or golden? No? Um, you can't
29:34
Speaker 1: just have aluminum foil because aluminium is too brittle. Like
29:36
Speaker 1: you try to make a huge sheet of aluminum foil,
29:38
Speaker 1: I mean, I can't even get like a one foot
29:40
Speaker 1: square of aluminum foil to stay together without tearing. And
29:43
Speaker 1: so you try to like fold and then unferral a
29:46
Speaker 1: one kilometer square of aluminum foil, It's not gonna work.
29:49
Speaker 1: So usually what they do is they have some sort
29:51
Speaker 1: of plastic and they spray aluminium coating on it. Um
29:55
Speaker 1: And so sometimes that plastic is gold. But I don't
29:57
Speaker 1: think there's a reason why that's gold. I think that's
29:59
Speaker 1: just to look cool. Right. Well, where are we at then,
30:01
Speaker 1: in terms of projects that are trying to use solar
30:05
Speaker 1: sales to get us out there? Yeah, So the best
30:08
Speaker 1: solar sale ever so far is the Icarus project. Launched
30:11
Speaker 1: in by Japan and they had a fourteen by fourteen
30:15
Speaker 1: meter solar sale and that sounds small compared to what
30:17
Speaker 1: we're talking about like eight eight hundred, but fourteen meters
30:21
Speaker 1: is not small, and that's like, you know, the size
30:23
Speaker 1: of an apartment. Can I just comment on their choice
30:25
Speaker 1: of names, like have they read the whole story of Icarus?
30:30
Speaker 1: Do they know how that story ends? I don't know.
30:33
Speaker 1: I love I love the hubris in choosing the name
30:36
Speaker 1: Icarus for a solar sale project. Right, it's they chose
30:40
Speaker 1: a story about Hubris and they did it kind of hubristically.
30:43
Speaker 1: They're like thumbing their nose in history. I love it.
30:46
Speaker 1: That's not going to happen to us. We're gonna fly
30:49
Speaker 1: really close to the sun and nothing bad is going
30:51
Speaker 1: to happen to Maybe they're trying to regain the name Acharis.
30:53
Speaker 1: They're claiming it back, you know the way some people
30:56
Speaker 1: claim back bad words. That we're going to turn this
30:59
Speaker 1: new a positive stereotype. Now, they want to redeem Icarus himself.
31:03
Speaker 1: That's it exactly. Maybe they're like the descendants of Acharis himself. Yeah,
31:10
Speaker 1: so they they're building it. They build it. They're going
31:13
Speaker 1: to build it, they built it, they launched it. It worked.
31:16
Speaker 1: It's solar sailing. It's zooming around the sun right now. Really,
31:19
Speaker 1: it's out there. It's out there, sailing away. It's sipping
31:23
Speaker 1: whiskey and looking down on us. And that's the most
31:25
Speaker 1: successful solar sale so far. But it's not like a ship,
31:28
Speaker 1: right It's like a satellite or a little vessel. Yeah,
31:31
Speaker 1: it's it's a little vessel. It's basically just two experiments
31:34
Speaker 1: that can we do this thing. Let's see if it
31:36
Speaker 1: actually works. Because you know, sometimes in physics, you do
31:38
Speaker 1: the calculations, they sound great, and then you know it
31:41
Speaker 1: doesn't actually work the way you expected because you forgot
31:44
Speaker 1: to account for something. But in this case, it's pretty
31:46
Speaker 1: much worked as they expected. And that's a huge boost
31:49
Speaker 1: for all the solar sale enthusiasts. I didn't know that
31:51
Speaker 1: was such a thing. I'm a solar sale enthusiast. I'm
31:54
Speaker 1: a big fan. First of all, I love sailing, but
31:57
Speaker 1: I'm a big fan of anything that's going to take
31:59
Speaker 1: us to other planets or take us to other stars
32:02
Speaker 1: and it isn't going to require a huge ridiculous amount
32:04
Speaker 1: of fuel cool Well, uh, and then you were telling
32:06
Speaker 1: me there's another cool project called the Breakthrough star Shot project. Yeah,
32:11
Speaker 1: they have this awesome idea. They say, let's not send
32:14
Speaker 1: one big solar sale, let's build a hundred of like
32:17
Speaker 1: a thousand nano sales. So there would be a bunch
32:20
Speaker 1: of really small ones and they would push them along
32:23
Speaker 1: with lasers between here and Alpha Centauri. The problem with
32:26
Speaker 1: building a laser that pushes a big solar sales you
32:30
Speaker 1: need a big laser. So they were like, okay, well,
32:32
Speaker 1: let's just have a small solar sale that can be
32:34
Speaker 1: pushed by a small laser and then just have like
32:36
Speaker 1: a tiny little craft. And so they imagine that that
32:40
Speaker 1: it would take twenty years to get to Alpha Centauri
32:43
Speaker 1: with these little nano sailors, And so they would have
32:45
Speaker 1: a giant laser gun on Earth shooting at these things,
32:49
Speaker 1: pushing them along, a thousand laser guns pushing on them. Oh,
32:52
Speaker 1: each one has their own little laser gun. Yeah, exactly,
32:54
Speaker 1: each one needs its own little boost. But the cool
32:57
Speaker 1: thing about solar sailing is that you know it's a
32:59
Speaker 1: small effect, but it just adds up, and if you're
33:01
Speaker 1: traveling for a long time, it's just like more and
33:03
Speaker 1: more acceleration. Eventually these things can get up to a
33:06
Speaker 1: respectable fraction of the speed of light, you know, so
33:09
Speaker 1: they can cross the distances between stars, and then they
33:11
Speaker 1: would communicate back what they find. But they can't come back,
33:14
Speaker 1: can they. They cannot come back. No, because there's no
33:17
Speaker 1: laser system over there for to shoot them back. I
33:20
Speaker 1: mean that we're aware of. Maybe they'll get there and
33:22
Speaker 1: find Elon Musk has built some you know station over
33:25
Speaker 1: there for recharging your solar your solar lasers or something.
33:29
Speaker 1: But but no, they it's just a it's a one
33:31
Speaker 1: way trip. Well, that's cool. It's like instead of building
33:34
Speaker 1: a giant boat, you build a whole bunch of little
33:37
Speaker 1: rubber duckies into the river. Kind of exactly. That's gonna be.
33:42
Speaker 1: Humanity's first contact with an alien species is the equivalent
33:46
Speaker 1: of a rubber ducky. Hi, look at us, We're so impressive.
33:49
Speaker 1: This is a little squeezed toy. And then the aliens
33:51
Speaker 1: are like, this is a sign of war. That's sorry.
33:55
Speaker 1: Maybe the rubber ducky is like holy to them and
33:57
Speaker 1: it's offensive that we like through on in their face.
34:00
Speaker 1: Plus we probably all of our lasers will be like
34:02
Speaker 1: burning their eyeballs down for a twenty years while the
34:05
Speaker 1: while the natocrafts are getting there. But if we fill
34:07
Speaker 1: them up with whiskey, maybe they'll they'll like it. They'll
34:12
Speaker 1: either love it or hate it. They'd be like, what
34:14
Speaker 1: Scottish whiskey? I only drink irish? This needs war. Wars
34:19
Speaker 1: have been fought over less, I'm sure. All right. So
34:21
Speaker 1: that answers Derek's question, who wanted to know how do
34:24
Speaker 1: sol of our sales work? And hopefully you guys enjoyed
34:27
Speaker 1: that and are inspired to maybe think about taking off sailing.
34:33
Speaker 1: That's right, and you know, maybe someday we'll go out
34:35
Speaker 1: there and we'll sail among the stars. I think it's
34:38
Speaker 1: really beautiful and poetic to imagine using the life from
34:40
Speaker 1: the stars themselves to push ourselves from one to the other.
34:43
Speaker 1: I really wish that could happen. All right, Thanks for listening, guys,
34:46
Speaker 1: see you next time. If you still have a question
34:56
Speaker 1: after listening to all these explanations, please drop us a line.
34:59
Speaker 1: We'd love to hear from you. You can find us
35:01
Speaker 1: at Facebook, Twitter, and Instagram at Daniel and Jorge that's
35:05
Speaker 1: one word, or email us at Feedback at Daniel and
35:09
Speaker 1: Jorge dot com. Thanks for listening and remember that. Daniel
35:12
Speaker 1: and Jorge Explain the Universe is a production of I
35:15
Speaker 1: heart Radio. For more podcast from my heart Radio, visit
35:18
Speaker 1: the i heart Radio app, Apple Podcasts, or wherever you
35:22
Speaker 1: listen to your favorite shows.