WEBVTT 1 00:00:03.399 --> 00:00:07.719 Welcome to Bedtime Astronomy. Explore the wonders of the cosmos 2 00:00:07.759 --> 00:00:12.279 with our soothing Bedtime Astronomie podcast. Each episode offers a 3 00:00:12.359 --> 00:00:16.320 gentle journey through the stars, planets, and beyond, perfect for 4 00:00:16.399 --> 00:00:20.239 unwinding after a long day. Let's travel through the mysteries 5 00:00:20.239 --> 00:00:22.440 of the universe as you drift off into a peaceful 6 00:00:22.480 --> 00:00:23.800 slumber under the night sky. 7 00:00:26.920 --> 00:00:29.399 You know, it's so easy when you step outside on 8 00:00:29.440 --> 00:00:32.439 a clear night and look up. It is incredibly easy 9 00:00:32.479 --> 00:00:35.920 to fall into this psychological trap of thinking about space 10 00:00:36.520 --> 00:00:40.920 as just this this quiet, echoing void. 11 00:00:40.960 --> 00:00:45.000 Right, Yeah, Like it's just endless emptiness exactly. 12 00:00:44.640 --> 00:00:47.799 Just a massive expanse with a few major planets scattered 13 00:00:47.799 --> 00:00:49.679 around in the dark. But I mean, if you actually 14 00:00:49.759 --> 00:00:53.719 zoom in on our immediate cosmic neighborhood, the physical reality is, 15 00:00:54.320 --> 00:00:58.320 oh no, it's entirely different. It's crowded, it is bustling 16 00:00:58.479 --> 00:01:00.840 right now as we speak. There are there are tens 17 00:01:00.880 --> 00:01:05.400 of thousands of Near Earth objects. Neo's just tumbling through 18 00:01:05.400 --> 00:01:06.480 the dark right in our backyard. 19 00:01:06.560 --> 00:01:08.480 Yeah, and we're talking about miniature worlds here. Some are 20 00:01:08.480 --> 00:01:11.359 the size of a city block, others are the size 21 00:01:11.400 --> 00:01:12.079 of a mountain. 22 00:01:12.239 --> 00:01:14.599 Right, And these aren't just you know, scientific curiosities for 23 00:01:14.680 --> 00:01:16.760 us to map and then forget about for you listening. 24 00:01:16.840 --> 00:01:19.920 Think of these as the most easily accessible resource caches 25 00:01:19.920 --> 00:01:21.159 in the entire Solar system. 26 00:01:21.239 --> 00:01:23.359 Absolutely heavy metals, rare earth. 27 00:01:23.159 --> 00:01:29.000 Elements, volatile compounds, water, ice, for institu resource utilization. They're 28 00:01:29.120 --> 00:01:32.840 practically right next door astronomically speaking. But the catch, and 29 00:01:32.879 --> 00:01:36.159 it's a huge catch to actually reaching them is massive. 30 00:01:36.280 --> 00:01:39.480 It really is, because figuring out the astrodynamics, like how 31 00:01:39.519 --> 00:01:42.040 to mathematically plot path drive up to one of these 32 00:01:42.120 --> 00:01:45.480 rocks and actually park next to it is a notoriously 33 00:01:46.040 --> 00:01:47.840 mind bendingly difficult problem. 34 00:01:47.959 --> 00:01:49.040 Okay, let's unpack this. 35 00:01:49.519 --> 00:01:52.680 Yeah, it remains one of the supreme challenges in aerospace 36 00:01:52.760 --> 00:01:55.840 engineering because the assumption by a lot of people is 37 00:01:55.920 --> 00:01:58.799 often that well, since space is a vacuum devoid of 38 00:01:58.840 --> 00:02:02.480 atmospheric friction, you simply aim your thrust vector at the 39 00:02:02.560 --> 00:02:06.439 target rendezvous coordinates and just let momentum do the rest. 40 00:02:06.519 --> 00:02:08.639 Just point and shoot right like a bullet exactly. 41 00:02:09.000 --> 00:02:12.159 But the reality of astrodynamics is governed by this chaotic 42 00:02:12.199 --> 00:02:17.000 web of n body gravitational interactions. Every planetary mass, every moon, 43 00:02:17.199 --> 00:02:20.400 the Sun, itself. They are all constantly warping the space 44 00:02:20.400 --> 00:02:21.000 time around them. 45 00:02:21.000 --> 00:02:24.240 You're all pulling at once, right, They're exerting these dynamic 46 00:02:24.280 --> 00:02:29.599 gravitational pulls. So calculating a viable fuel efficient path through 47 00:02:29.680 --> 00:02:34.280 that that constantly shifting gravitational topography has historically been one 48 00:02:34.280 --> 00:02:36.240 of the tightest bottlenecks in mission planning. 49 00:02:36.599 --> 00:02:37.800 It sounds like a nightmare. 50 00:02:37.879 --> 00:02:40.800 You are essentially trying to thread a needle, right, but 51 00:02:40.879 --> 00:02:43.599 the needle is moving at tens of thousands of miles 52 00:02:43.639 --> 00:02:46.400 an hour, and the thread is constantly being pulled by 53 00:02:46.400 --> 00:02:48.240 invisible magnets from every direction. 54 00:02:48.560 --> 00:02:52.159 Man. That is a great visual which makes the recent 55 00:02:52.199 --> 00:02:57.280 work coming out of Khalifa University so incredibly compelling. Alisandra 56 00:02:57.360 --> 00:02:59.240 Biolci and his co authors, they put this out on 57 00:02:59.360 --> 00:03:04.280 our sleeve. They've effectively rewritten the fundamental mathematical road maps 58 00:03:04.280 --> 00:03:05.960 we use to navigate deep space. 59 00:03:06.039 --> 00:03:07.120 It's a massive deal. 60 00:03:07.439 --> 00:03:10.000 And just to be clear, this isn't some minor optimization 61 00:03:10.080 --> 00:03:13.800 of existing software. They haven't just like tweaked a fuel 62 00:03:13.840 --> 00:03:16.840 mixture or shaved a few kilograms off a chassis. 63 00:03:17.000 --> 00:03:17.919 No, not at all. 64 00:03:18.120 --> 00:03:21.360 They are proposing a wholesale paradigm shift in the underlying 65 00:03:21.400 --> 00:03:26.960 mathematics of trajectory generation. By integrating modern continuous thrust propulsion 66 00:03:27.000 --> 00:03:32.280 models with highly complex dynamical systems theory, they've unlocked, get this, 67 00:03:32.319 --> 00:03:36.800 over two million new incredibly low energy, highly viable routes 68 00:03:36.840 --> 00:03:38.080 to these asteroids. Yeah. 69 00:03:38.120 --> 00:03:41.599 The magnitude of finding two million viable trajectories, I mean, 70 00:03:41.599 --> 00:03:45.159 it really cannot be overstated. It's staggering because for decades, 71 00:03:45.319 --> 00:03:49.159 orbital mechanics has been heavily constrained by a very rigid 72 00:03:49.280 --> 00:03:53.400 set of mathematical assumptions. And you know, those assumptions were 73 00:03:53.439 --> 00:03:55.680 brilliant for the Apollo era, right, they got us to 74 00:03:55.719 --> 00:03:58.919 the Moon exactly, and they successfully navigated the voyager probes 75 00:03:59.039 --> 00:04:01.879 entirely out of the Solar system, but they were inextricably 76 00:04:01.919 --> 00:04:05.960 tied to the hardware and the computational limitations of the 77 00:04:06.000 --> 00:04:07.000 mid twentieth century. 78 00:04:07.080 --> 00:04:07.719 So it changed. 79 00:04:08.120 --> 00:04:12.240 Well, what Bilchi's team recognized is that our modern hardware, 80 00:04:12.439 --> 00:04:17.839 specifically our propulsion technology, has vastly outpaced those legacy trajectory algorithms. 81 00:04:18.279 --> 00:04:21.000 We have basically been trying to fly twenty first century 82 00:04:21.040 --> 00:04:24.399 ion engines using math that was designed for chemical rockets. 83 00:04:24.639 --> 00:04:26.720 That sounds like running a modern video game on a 84 00:04:26.720 --> 00:04:28.120 computer from the nineteen nineties. 85 00:04:28.279 --> 00:04:31.839 It's exactly like that. And by abandoning those legacy constraints 86 00:04:31.879 --> 00:04:37.879 and developing a less computationally prohibitive way to model multi 87 00:04:37.879 --> 00:04:42.040 body gravity, they've drastically reduced the launch escape energy required 88 00:04:42.079 --> 00:04:43.600 to get these missions off the ground. 89 00:04:44.079 --> 00:04:46.600 Okay, so to really understand why this new math is 90 00:04:46.639 --> 00:04:50.319 so groundbreaking, we first have to understand the flawed kind 91 00:04:50.360 --> 00:04:54.279 of brute force way we've been exploring space for decades, right. 92 00:04:54.199 --> 00:04:55.879 Yeah, the legacy constraints, right. 93 00:04:55.920 --> 00:04:58.199 So the contrast is where the genius of this new 94 00:04:58.240 --> 00:05:02.360 approach really shines. Let's talk about the patched conics method, 95 00:05:02.720 --> 00:05:05.759 because for a long time this was the absolute gold 96 00:05:05.800 --> 00:05:07.759 standard for NASA mission planners. 97 00:05:07.879 --> 00:05:09.639 He was the only way to do it really right. 98 00:05:10.079 --> 00:05:13.199 And the mathematical foundation of this patched conics method relies 99 00:05:13.240 --> 00:05:16.879 heavily on something called the two body problem. It simplifies 100 00:05:16.879 --> 00:05:20.920 that crazy magnetic thread chaos you mentioned earlier by stripping 101 00:05:20.959 --> 00:05:23.839 the universe down to just two interacting masses at any 102 00:05:23.879 --> 00:05:27.639 given time. Usually that's just the Sun and the spacecraft, right. 103 00:05:27.560 --> 00:05:30.560 And it's an incredibly clever workaround for the lack of 104 00:05:30.680 --> 00:05:34.199 raw supercomputing power back in the day. In the two 105 00:05:34.240 --> 00:05:37.279 body problem, you actually have an analytical solution. 106 00:05:37.439 --> 00:05:39.959 Meaning you can solve it cleanly on paper. 107 00:05:39.959 --> 00:05:43.279 Exactly thanks to Johannes Kepler and Isaac Newton. If you 108 00:05:43.360 --> 00:05:46.560 only have two bodies, you can perfectly predict their positions 109 00:05:46.639 --> 00:05:51.199 at any point in the future using relatively simple algebraic equations. 110 00:05:51.639 --> 00:05:54.759 The orbit will always be a perfect conics section, a 111 00:05:54.759 --> 00:05:56.959 circle and ellipse, a parabola, or a. 112 00:05:57.000 --> 00:05:59.920 Hyperbola, hence the name patched conics. Right. 113 00:06:00.600 --> 00:06:03.319 But the moment you introduce a third body, say you 114 00:06:03.360 --> 00:06:06.160 have the Earth, the Sun, and a spacecraft all interacting, 115 00:06:06.480 --> 00:06:10.319 that neat analytical solution just vanishes. You enter the realm 116 00:06:10.319 --> 00:06:11.279 of chaos. 117 00:06:10.920 --> 00:06:13.399 Theory, like on repoint great Proof back in the late 118 00:06:13.480 --> 00:06:14.160 nineteenth century. 119 00:06:14.199 --> 00:06:16.279 Right, Yes, you can no longer solve it with a 120 00:06:16.319 --> 00:06:18.879 neat equation. You have to use numerical integration. You have 121 00:06:18.920 --> 00:06:22.319 to calculate the forces step by step, microsecond by microsecond, 122 00:06:22.360 --> 00:06:24.199 which is computationally exhausting. 123 00:06:24.439 --> 00:06:28.519 Wait, so to avoid that computational nightmare for decades the 124 00:06:28.560 --> 00:06:32.680 space exploration the map basically pretended Jupiter, Mars, and even 125 00:06:32.720 --> 00:06:37.319 Earth didn't exist once we launched. Essentially, yes, That sounds crazy. 126 00:06:37.480 --> 00:06:40.079 That sounds like planning a cross country road trip by 127 00:06:40.560 --> 00:06:43.079 drawing a perfectly straight line on a map and just 128 00:06:43.120 --> 00:06:44.759 assuming there are no mountains in the way. 129 00:06:45.079 --> 00:06:47.360 It's a great analogy, but there's a good reason for it, 130 00:06:47.480 --> 00:06:52.439 computational pragmatism. Calculating multiple gravities at once requires a massive 131 00:06:52.480 --> 00:06:56.319 amount of computational power, So they effectively sliced the Solar 132 00:06:56.360 --> 00:06:58.439 System up into isolated spheres. 133 00:06:58.120 --> 00:07:00.199 Of influence, well place spheres right. 134 00:07:00.079 --> 00:07:03.639 Exactly when a probe launches, the math considers only the 135 00:07:03.680 --> 00:07:07.399 Earth and the spacecraft. The Sun is ignored, Jupiter is ignored. 136 00:07:08.120 --> 00:07:11.519 There Once the probe crosses an invisible mathematical boundary the 137 00:07:11.639 --> 00:07:15.160 edge of Earth's sphere of influence, the software essentially drops 138 00:07:15.199 --> 00:07:18.240 Earth from the equation entirely and switches to a Sun 139 00:07:18.279 --> 00:07:20.000 spacecraft two body problem. 140 00:07:20.360 --> 00:07:23.360 So it treats the complex overlapping gravity wells of the 141 00:07:23.480 --> 00:07:26.959 entire Solar System as just a series of isolated sterile bubbles. 142 00:07:27.240 --> 00:07:29.839 That is the absolute essence of it. You solve the 143 00:07:29.839 --> 00:07:33.360 geocentric hyperbola for the escape, you solve the heliocentric ellipse 144 00:07:33.360 --> 00:07:36.600 for the cruise phase, and you solve the target centric 145 00:07:36.759 --> 00:07:41.600 hyperbola for the arrival. Then you mathematically, quite literally, patch 146 00:07:41.680 --> 00:07:44.000 these conic sections together at the boundaries. 147 00:07:44.160 --> 00:07:46.160 That's wild. It's basically a mathematical fiction. 148 00:07:46.519 --> 00:07:50.040 It is a brilliant mathematical fiction. But the friction between 149 00:07:50.079 --> 00:07:54.439 that fiction and the actual physical reality of the Solar system, well, 150 00:07:54.519 --> 00:07:56.079 that has to be paid for, and it is paid 151 00:07:56.079 --> 00:07:57.079 for in fuel. 152 00:07:56.959 --> 00:07:59.680 Because Earth doesn't actually stop pulling on the spacecraft just 153 00:07:59.680 --> 00:08:02.720 because crossed some imaginary mathematical line. 154 00:08:02.800 --> 00:08:07.639 Exactly, The actual trajectory drifts from the patched conic mathematical prediction. 155 00:08:08.240 --> 00:08:10.680 So to fix that drift you have to perform mid 156 00:08:10.680 --> 00:08:15.240 course correction burns. You spend delta V meaning fuel to 157 00:08:15.480 --> 00:08:19.120 force the reality to match your simplified math man. 158 00:08:19.399 --> 00:08:22.000 And that reliance on delta V that perfectly aligns with 159 00:08:22.040 --> 00:08:24.560 the hardware of that era, doesn't it the chemical. 160 00:08:24.279 --> 00:08:29.399 Rocket, oh, perfectly. The patched conics method fundamentally assumes impulsive maneuvers. 161 00:08:29.240 --> 00:08:34.159 Meaning explosive right. It assumes that all velocity changes happen instantaneously, 162 00:08:34.720 --> 00:08:38.480 which from a mathematical perspective, makes total sense. If you 163 00:08:38.519 --> 00:08:42.919 are firing a massive chemical engine, you ignite hydrolocks or 164 00:08:43.159 --> 00:08:47.559 hypergolic propellants. Dump massive thermal energy at the nozzle and 165 00:08:47.679 --> 00:08:51.120 generate thousands of kilinusians of thrust in just a matter 166 00:08:51.120 --> 00:08:51.639 of minutes. 167 00:08:51.960 --> 00:08:55.879 Right, The velocity vector changes so rapidly that for the 168 00:08:55.919 --> 00:08:58.559 sake of the orbital integration math, you can treat the 169 00:08:58.559 --> 00:09:00.000 burn time as effectively zero. 170 00:09:00.320 --> 00:09:02.240 It's an instant note on the path exactly. 171 00:09:02.639 --> 00:09:05.600 The math and the hardware were perfectly symbiotic, but there's 172 00:09:05.600 --> 00:09:09.639 a massive penalty. The Silkovski rocket equation dictates that if 173 00:09:09.639 --> 00:09:12.519 you want to perform these massive impulsive plane changes or 174 00:09:12.679 --> 00:09:15.399 orbital insertions, you need a tremendous amount. 175 00:09:15.120 --> 00:09:17.679 Of chemical propellant, and propellant is heavy, very. 176 00:09:17.519 --> 00:09:20.600 Heavy, and that propellant adds mass to the spacecraft, which 177 00:09:20.600 --> 00:09:23.200 requires an even larger rocket to lift out of Earth's 178 00:09:23.240 --> 00:09:26.840 gravity well, which requires even more propellant. It's the tilent 179 00:09:26.879 --> 00:09:27.600 of mass fraction. 180 00:09:28.120 --> 00:09:31.480 So we were optimizing missions purely to minimize flight time 181 00:09:31.840 --> 00:09:34.960 and limit the number of those impulsive burns, because every 182 00:09:35.000 --> 00:09:38.480 single burn required dragging tons of all chemicals into deep 183 00:09:38.519 --> 00:09:39.480 space exactly. 184 00:09:39.639 --> 00:09:43.879 Chemical rockets are the hair in space travel, fast, explosive, 185 00:09:44.039 --> 00:09:47.120 but they really limit your long term options. The patched 186 00:09:47.159 --> 00:09:51.000 conix method was designed explicitly to string together these explosive 187 00:09:51.159 --> 00:09:52.440 instantaneous nodes. 188 00:09:52.720 --> 00:09:56.159 But the Brude force math that worked for explosive rockets, 189 00:09:56.879 --> 00:09:59.399 it just doesn't compute for the new hardware we have Now. 190 00:10:00.039 --> 00:10:02.000 Mulsion paradigm has completely shifted. 191 00:10:02.120 --> 00:10:05.480 It has We are increasingly moving away from chemical propulsion 192 00:10:05.519 --> 00:10:07.080 for deep space transit. 193 00:10:06.759 --> 00:10:10.639 Right We're moving in favor of solar electric propulsion or SEP, 194 00:10:11.080 --> 00:10:14.840 things like gridded ion thrusters, hall effect thrusters, and SEP 195 00:10:14.919 --> 00:10:17.600 operates on a completely different physical principle. 196 00:10:17.279 --> 00:10:17.879 Totally different. 197 00:10:18.000 --> 00:10:21.399 Instead of chemical combustion, we are using solar arrays to 198 00:10:21.440 --> 00:10:26.000 generate electricity, using that power to ionize an inert gas 199 00:10:26.039 --> 00:10:29.559 like xenon, and then accelerating those ions out the back 200 00:10:29.639 --> 00:10:33.360 through a high voltage grid. And the specific impulse the 201 00:10:33.399 --> 00:10:36.639 efficiency of the engine is an order of magnitude higher 202 00:10:36.639 --> 00:10:37.919 than the best chemical rockets. 203 00:10:38.080 --> 00:10:41.519 The efficiency is just staggering. A really good chemical engine 204 00:10:41.600 --> 00:10:44.120 might give you a specific impulse of say four hundred 205 00:10:44.159 --> 00:10:47.360 and fifty seconds. A modern ion thruster can easily push 206 00:10:47.480 --> 00:10:50.279 three thousand to four thousand seconds. Wow, you are getting 207 00:10:50.399 --> 00:10:53.799 vastly more delta V per kilogram of propellant. But the 208 00:10:53.840 --> 00:10:57.399 tradeoff is the raw thrust. The mass of those xenon 209 00:10:57.480 --> 00:11:00.879 ions is so incredibly low that the actual physical force 210 00:11:00.919 --> 00:11:03.759 imparted on the spacecraft at any even moment is minuscule. 211 00:11:03.840 --> 00:11:05.039 Now minuscule, we're talking. 212 00:11:05.120 --> 00:11:07.879 Well, if you activated a standard five kilo ion thruster 213 00:11:08.000 --> 00:11:10.480 right here on Earth, the thrust it produces wouldn't even 214 00:11:10.519 --> 00:11:12.679 be enough to counteract the friction of a rolling coin. 215 00:11:13.039 --> 00:11:16.200 It is roughly equivalent to the downward gravitational force of 216 00:11:16.240 --> 00:11:18.360 a single piece of tinder paper resting in the palm 217 00:11:18.399 --> 00:11:18.919 of your hand. 218 00:11:19.120 --> 00:11:22.200 Wait, okay, here's where it gets really interesting. Let's pause 219 00:11:22.240 --> 00:11:25.559 on that, because the disconnect between the visual of like 220 00:11:25.679 --> 00:11:29.440 a towering Saturn V launch and the reality of deep 221 00:11:29.480 --> 00:11:33.679 space propulsion is vast. You're telling me I could push 222 00:11:33.720 --> 00:11:36.559 a multi ton spaceship with the force of a sticky 223 00:11:36.600 --> 00:11:38.799 note and eventually outraise a chemical rocket. 224 00:11:38.960 --> 00:11:42.559 Yes, because it's continuous. But if you only have that 225 00:11:42.679 --> 00:11:46.159 tiny fraction of a newton of thrust, you can't perform 226 00:11:46.279 --> 00:11:47.840 an impulsive maneuver, right. 227 00:11:47.879 --> 00:11:50.000 You can't just fire the engine for three minutes to 228 00:11:50.120 --> 00:11:51.440 enter an orbit like in the movies. 229 00:11:51.600 --> 00:11:54.679 No, you have to run that ion thruster continuously for 230 00:11:54.799 --> 00:11:59.200 thousands of hours. You're accumulating that tiny acceleration week after week, 231 00:11:59.279 --> 00:12:02.039 month after month. It is the tortoise of space travel. 232 00:12:02.240 --> 00:12:03.759 So how does the old math handle that? 233 00:12:03.960 --> 00:12:07.960 It doesn't. NASA's old code literally couldn't understand or map 234 00:12:08.080 --> 00:12:11.840 routes for slow burn technologies. Like step in a chemical trajectory, 235 00:12:11.879 --> 00:12:15.120 you have long periods of ballistic cursting where Kepler's laws 236 00:12:15.159 --> 00:12:19.720 apply perfectly, punctuated by brief burns. But within sep engine 237 00:12:19.759 --> 00:12:23.480 firing constantly, the spacecraft never actually settles into a clean 238 00:12:23.519 --> 00:12:24.799 cauplearian orbit. 239 00:12:24.679 --> 00:12:27.279 Because the orbital energy is constantly changing. 240 00:12:27.240 --> 00:12:31.519 Exactly this semi major axis is constantly expanding or contracting. 241 00:12:32.120 --> 00:12:35.639 The patched conics method completely collapses when you try to 242 00:12:35.679 --> 00:12:38.960 feed it a continuous thrust profile, because it relies on 243 00:12:39.000 --> 00:12:42.600 the assumption of instantaneous state changes. You can no longer 244 00:12:42.679 --> 00:12:45.840 patch simple curves together. You have to integrate the trajectory 245 00:12:45.919 --> 00:12:47.320 over massive time scales. 246 00:12:47.879 --> 00:12:50.120 And if your engine is only pushing with the force 247 00:12:50.159 --> 00:12:52.960 of a piece of paper, you are completely at the 248 00:12:53.000 --> 00:12:55.799 mercy of the surrounding gravitational environment, aren't you. 249 00:12:56.039 --> 00:12:58.840 Absolutely you can't ignore the Earth and the mood anymore. 250 00:12:58.960 --> 00:13:02.399 It makes me think a chemical rocket is like a speedboat. 251 00:13:02.480 --> 00:13:05.200 Right you point it, hit the throttle, and you can 252 00:13:05.320 --> 00:13:09.240 largely ignore the ocean currents because you're just blasting over them. 253 00:13:09.480 --> 00:13:12.600 But a set powered spacecraft is more like a sailboat. 254 00:13:12.879 --> 00:13:14.440 That is a perfect way to look at it. 255 00:13:14.519 --> 00:13:17.039 If you try to fight a strong gravitational tide with 256 00:13:17.080 --> 00:13:20.240 an engine that week, you will simply be overpowered and 257 00:13:20.320 --> 00:13:23.279 dragged way off course. You have to learn how to 258 00:13:23.320 --> 00:13:24.679 read the currents and sail. 259 00:13:24.480 --> 00:13:27.320 With them, and the necessity of reading those currents is 260 00:13:27.360 --> 00:13:30.679 exactly what forced Biulci's team to abandon the two body 261 00:13:30.720 --> 00:13:34.720 patched conics approximation in the vicinity of Earth. If your 262 00:13:34.759 --> 00:13:38.000 thrust is that low, the gravitational perturbations of the Moon 263 00:13:38.039 --> 00:13:40.320 in the Sun are no longer rounding errors you can 264 00:13:40.399 --> 00:13:41.840 just correct later with a fuel burn. 265 00:13:41.919 --> 00:13:44.279 They're dominant forces that dictate your trajectory. 266 00:13:44.360 --> 00:13:48.559 Exactly to accurately model how an SCEP spacecraft navigates the 267 00:13:48.559 --> 00:13:51.679 Earth Moon Sun environment, you have to upgrade the mathematics. 268 00:13:51.879 --> 00:13:54.039 You have to use what's called the circular restricted three 269 00:13:54.039 --> 00:13:57.480 body problem or CR three BP, and the CR three. 270 00:13:57.240 --> 00:14:01.840 BP introduces that gravitational tug of war instead of isolating 271 00:14:01.840 --> 00:14:05.360 the Earth and ignoring the Sun. The math explicitly models 272 00:14:05.360 --> 00:14:09.200 the spacecraft moving through the combined gravitational topography of both 273 00:14:09.279 --> 00:14:11.720 massive bodies simultaneously. 274 00:14:11.080 --> 00:14:14.200 Right, and the physical topology of space changes completely under 275 00:14:14.240 --> 00:14:17.080 the CR three BP well. In a two body system, 276 00:14:17.080 --> 00:14:20.279 the gravity well is just a simple symmetrical funnel leading 277 00:14:20.399 --> 00:14:22.960 straight down to the central mass. But when you have 278 00:14:23.039 --> 00:14:26.240 two massive bodies orbiting their berry center, like the Earth 279 00:14:26.240 --> 00:14:30.200 and the Sun, their intercepting gravitational fields create a highly 280 00:14:30.279 --> 00:14:34.720 complex potential energy surface like it's lumpy, very lumpy. The 281 00:14:34.759 --> 00:14:37.879 centrifugal force of the rotating reference frame combined with the 282 00:14:37.879 --> 00:14:42.279 gravitational pull of the two primary bodies, creates specific regions 283 00:14:42.320 --> 00:14:45.279 where the forces perfectly cancel each other out, and these 284 00:14:45.279 --> 00:14:46.399 are the lagrange. 285 00:14:46.000 --> 00:14:48.759 Points right L one through L five. We frequently hear 286 00:14:48.799 --> 00:14:51.799 about those like the James Web Space Telescope parking out 287 00:14:51.799 --> 00:14:54.600 at L two or the solar observatories at L one. 288 00:14:54.720 --> 00:14:56.600 They are essentially points of equilibrium. 289 00:14:56.639 --> 00:14:59.519 Exactly if you navigate a spacecraft to a lagrange point, 290 00:14:59.600 --> 00:15:02.320 it takes a virtually non existent amount of station keeping 291 00:15:02.360 --> 00:15:06.039 delta V to maintain that position. It's a gravitational balancing act. 292 00:15:06.080 --> 00:15:07.840 So they serve as the perfect staging nodes. 293 00:15:08.120 --> 00:15:10.960 They do, but the lagraage points themselves are just the 294 00:15:11.000 --> 00:15:14.360 anchors for something much more profound in dynamical systems theory. 295 00:15:15.519 --> 00:15:18.759 The mathematics of the CR THREEVP reveals that these equilibrium 296 00:15:18.759 --> 00:15:21.799 points are actually connected by invariant manifolds. 297 00:15:22.080 --> 00:15:24.759 Invariant manifolds, what exactly does that look like? 298 00:15:25.159 --> 00:15:27.679 Well, to visualize this, you have to look at phase space, 299 00:15:27.840 --> 00:15:30.759 which maps not just the position of the spacecraft in 300 00:15:30.799 --> 00:15:33.519 three dimensions, but it's velocity in three dimensions as well. 301 00:15:34.120 --> 00:15:38.000 So within that six dimensional fase space, stable and unstable 302 00:15:38.039 --> 00:15:41.879 manifolds emerge from the lagrange points. They form these topological 303 00:15:41.919 --> 00:15:43.960 tubes that sneak their way through the Solar system. 304 00:15:44.080 --> 00:15:46.120 Okay, so these are the invisible highways. Yes. 305 00:15:46.360 --> 00:15:49.279 What's fascinating here is that space is not empty. It 306 00:15:49.360 --> 00:15:52.399 is a topological landscape of peaks and valleys of gravity. 307 00:15:52.720 --> 00:15:55.720 So instead of using a speedboat to blast across the water, 308 00:15:56.039 --> 00:15:59.240 we are suddenly reading the ocean currents. We're parking our 309 00:15:59.320 --> 00:16:02.480 raft and a the lagrange point and then catching a 310 00:16:02.519 --> 00:16:05.879 riptide the invariant manifold to drift exactly where we need 311 00:16:05.879 --> 00:16:07.360 to go for basically free. 312 00:16:07.519 --> 00:16:10.240 Exactly, you expend a tiny bit of fuel to get 313 00:16:10.240 --> 00:16:13.840 into the manifold tube, and the natural gravitational gradient does 314 00:16:13.879 --> 00:16:16.840 all the heavy lifting, carrying you millions of kilometers into 315 00:16:16.840 --> 00:16:21.000 deep space. By mapping the CR THREEVP, we aren't fighting 316 00:16:21.080 --> 00:16:24.399 nature with rocket fuel anymore. We are literally surfing the 317 00:16:24.440 --> 00:16:26.679 Solar System's natural gravity waves. 318 00:16:26.960 --> 00:16:28.600 That is just so elegant. 319 00:16:28.720 --> 00:16:32.159 It is by coupling the continuous, highly efficient thrust of 320 00:16:32.200 --> 00:16:35.840 INCEP engine with the zero cost transit of an invariant manifold, 321 00:16:36.120 --> 00:16:39.159 bi Alce's team solved the massive fuel constraints that played 322 00:16:39.200 --> 00:16:42.080 all those early asteroid missions. You just use a little 323 00:16:42.080 --> 00:16:45.240 ion engine to gently steer between manifolds rather than fighting 324 00:16:45.320 --> 00:16:46.679 gravity to create your own path. 325 00:16:46.759 --> 00:16:49.720 Okay, but navigating the complex currents near Earth is brilliant. 326 00:16:50.159 --> 00:16:53.120 But earlier you mentioned that integrating the CR THREEVP introduces 327 00:16:53.159 --> 00:16:56.879 a computational nightmare. If the three body math is highly 328 00:16:56.960 --> 00:17:00.720 chaotic and incredibly sensitive to initial conditions. You know the 329 00:17:00.720 --> 00:17:04.359 classic butterfly effect where a microscopic rounding error on day 330 00:17:04.359 --> 00:17:07.400 one compounds into a million kilometer or miss by year three. 331 00:17:07.759 --> 00:17:09.960 How do they actually run a simulation for a multi 332 00:17:10.079 --> 00:17:13.200 year asteroid rendezvous without the computers just melting down. 333 00:17:13.440 --> 00:17:16.440 It's a very real problem. The chaotic nature of the 334 00:17:16.480 --> 00:17:20.480 CR three BP means that long duration numerical integration is 335 00:17:20.519 --> 00:17:25.359 intrinsically unstable. There are these things called Lyapunov exponents, which 336 00:17:25.519 --> 00:17:29.680 basically measure how quickly two slightly different trajectories diverge in 337 00:17:29.759 --> 00:17:33.559 a chaotic system, and they guarantee that computing a continuous, 338 00:17:33.720 --> 00:17:37.480 unbroken path from Earth to a deep space NEO and 339 00:17:37.680 --> 00:17:39.920 back is mathematically intractable. 340 00:17:39.960 --> 00:17:43.200 The optimization algorithms will simply fail to converge on a. 341 00:17:43.160 --> 00:17:45.960 Solution every time. So to solve this, the researchers had 342 00:17:45.960 --> 00:17:51.000 to decouple the trajectory. They employ a modular architecture Frankenstein trajectory. Yeah, 343 00:17:51.039 --> 00:17:54.880 Frankenstein trajectory. They break the mission into segments. They use 344 00:17:54.920 --> 00:17:58.119 the complex CR three VP math while the spacecraft is 345 00:17:58.200 --> 00:18:02.400 navigating the Earth's sun lagrange, utilizing those invariant manifolds to 346 00:18:02.480 --> 00:18:06.119 escape the Earth's gravity well efficiently. But once the spacecraft 347 00:18:06.160 --> 00:18:09.039 travels far enough into deep space where the Earth's gravitational 348 00:18:09.079 --> 00:18:13.799 influence drops below a significant perturbation threshold, the software intentionally 349 00:18:13.880 --> 00:18:16.200 drops the three body dynamics. 350 00:18:15.720 --> 00:18:19.720 Oh, it reverts to the traditional two body heliocentric. 351 00:18:19.000 --> 00:18:23.839 Model exactly because at a certain distance, the complex dynamical 352 00:18:23.880 --> 00:18:28.839 topography smooths out, the Sun becomes the overwhelmingly dominant force, 353 00:18:29.279 --> 00:18:33.440 and trying to model the Earth's distant microscopic pull is 354 00:18:33.559 --> 00:18:37.799 just a waste of computational resources that only introduces integration errors. 355 00:18:38.000 --> 00:18:39.359 That makes total sense, But the. 356 00:18:39.319 --> 00:18:41.680 Real breakthrough in the decoupling is how they handle the 357 00:18:41.720 --> 00:18:45.319 return trip. They don't run a forward integration from launch 358 00:18:45.400 --> 00:18:48.480 to return as one long math problem. They calculate the 359 00:18:48.519 --> 00:18:53.079 outbound leg from Earth to the asteroid, then completely independently, 360 00:18:53.440 --> 00:18:56.599 they calculate the inbound leg from the asteroid back to Earth. 361 00:18:56.759 --> 00:18:59.680 Wait. Wait, so we're effectively running two completely different software 362 00:18:59.680 --> 00:19:03.079 program and just duct taping the results together when we 363 00:19:03.119 --> 00:19:06.319 reach the asteroid. Why does separating the trip home from 364 00:19:06.359 --> 00:19:07.680 the trip there matters so much? 365 00:19:07.759 --> 00:19:10.720 Because of that computational chaos we talked about. If you 366 00:19:10.759 --> 00:19:14.359 calculate a round trip as one continuous equation, a tiny 367 00:19:14.480 --> 00:19:17.759 variable change on day one completely ruins the math for 368 00:19:17.880 --> 00:19:20.759 year three. By cutting the trip in half and stitching 369 00:19:20.799 --> 00:19:23.519 it together at the destination, you save massive amounts of 370 00:19:23.559 --> 00:19:24.599 computational power. 371 00:19:24.920 --> 00:19:28.039 But if you calculate the outbound trip and the inbound 372 00:19:28.039 --> 00:19:32.079 trip as two completely isolated mathematical events, how do you 373 00:19:32.119 --> 00:19:36.200 reconcile them at the asteroid? The spacecraft is physically one 374 00:19:36.279 --> 00:19:39.160 continuous object. You can't just arrive at an asteroid with 375 00:19:39.200 --> 00:19:42.119 one velocity and instantly swap to a different coordinate system 376 00:19:42.200 --> 00:19:45.640 and a different velocity for the trip home without violating 377 00:19:45.640 --> 00:19:46.519 the laws of physics. 378 00:19:46.599 --> 00:19:48.759 Right, there has to be a physical bridge, and that 379 00:19:48.839 --> 00:19:52.880 bridge is established through highly advanced boundary value optimization. 380 00:19:53.240 --> 00:19:54.640 How does that work well? 381 00:19:55.000 --> 00:19:57.880 When the outbound trajectory arrives at the near Earth object, 382 00:19:58.079 --> 00:20:03.079 it has a specific state vector, a precise position, velocity, mass, 383 00:20:03.119 --> 00:20:07.680 and time epoch. Now, the independently calculated return trajectory requires 384 00:20:07.720 --> 00:20:11.279 a very specific starting state vector to successfully ride the 385 00:20:11.359 --> 00:20:14.480 manifolds back to Earth. The gap between those two state 386 00:20:14.559 --> 00:20:17.680 vectors that is the optimization problem I see. The algorithm 387 00:20:17.759 --> 00:20:21.559 uses nonlinear programming to iteratively adjust the launch parameters, the 388 00:20:21.559 --> 00:20:25.039 manifold insertion points, and the SEP thrust profiles until the 389 00:20:25.079 --> 00:20:27.799 state vector at the end of the outbound leg perfectly 390 00:20:27.839 --> 00:20:30.279 matches the state vector required for the inbound leg. 391 00:20:30.599 --> 00:20:33.920 So they're effectively working the problem from both ends toward 392 00:20:33.960 --> 00:20:36.880 the middle, just tweaking the variables on both sides until 393 00:20:36.880 --> 00:20:39.960 the math perfectly aligns at the asteroid, allowing for a 394 00:20:39.960 --> 00:20:41.279 seamless transition. 395 00:20:41.319 --> 00:20:45.000 Duct tape, high tech mathematical duct tape. Yes, they enforce 396 00:20:45.039 --> 00:20:49.359 continuity constraints. They ensure that mass, time, position, and velocity 397 00:20:49.440 --> 00:20:52.799 match perfectly at the boundary, and by doing this they 398 00:20:52.839 --> 00:20:58.279 completely bypass the chaotic instability of a single continuous integration. 399 00:20:58.519 --> 00:21:02.640 Okay, so the researchers built this brilliant, computationally efficient, slow 400 00:21:02.640 --> 00:21:07.319 burn friendly gravity surfing mathematical model. What happened when they 401 00:21:07.319 --> 00:21:08.119