[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:20.68,Default,,0000,0000,0000,,{\i1}36C3 preroll music{\i0}
Dialogue: 0,0:00:20.68,0:00:25.93,Default,,0000,0000,0000,,Herald: OK, so the next talk for this\Nevening is on how to get to Mars and all
Dialogue: 0,0:00:25.93,0:00:31.89,Default,,0000,0000,0000,,in very interesting ways. Some of them\Nmight be really, really slow. Our next
Dialogue: 0,0:00:31.89,0:00:36.64,Default,,0000,0000,0000,,speaker has studied physics and has a PhD\Nin maths and is currently working as a
Dialogue: 0,0:00:36.64,0:00:41.18,Default,,0000,0000,0000,,mission planner at the German Space\NOperations Center. Please give a big round
Dialogue: 0,0:00:41.18,0:00:50.14,Default,,0000,0000,0000,,of applause to Sven.\NSven: Thank you.
Dialogue: 0,0:00:50.14,0:00:52.55,Default,,0000,0000,0000,,Hello and welcome to\N"Thrust is not an option: How to get a
Dialogue: 0,0:00:52.55,0:00:56.91,Default,,0000,0000,0000,,Mars really slow". My name is Sven. I'm a\Nmission planner at the German Space
Dialogue: 0,0:00:56.91,0:01:01.38,Default,,0000,0000,0000,,Operations Center, which is a part of the\NDLR, the Deutsches Zentrum für Luft- und
Dialogue: 0,0:01:01.38,0:01:05.19,Default,,0000,0000,0000,,Raumfahrt. And first of all, I have to\Napologize because I kind of cheated a
Dialogue: 0,0:01:05.19,0:01:11.46,Default,,0000,0000,0000,,little bit in the title. The accurate\Ntitle would have been "Reducing thrust: How
Dialogue: 0,0:01:11.46,0:01:16.99,Default,,0000,0000,0000,,to get to Mars or maybe Mercury really\Nslow". The reason for this is that I will
Dialogue: 0,0:01:16.99,0:01:22.75,Default,,0000,0000,0000,,actually use Mercury as an example quite\Na few times. And also we will not be able
Dialogue: 0,0:01:22.75,0:01:29.00,Default,,0000,0000,0000,,to actually get rid of all the maneuvers\Nthat we want to do. So the goal of this
Dialogue: 0,0:01:29.00,0:01:34.55,Default,,0000,0000,0000,,talk is to give you an introduction to\Norbital mechanics to see what we can do.
Dialogue: 0,0:01:34.55,0:01:37.86,Default,,0000,0000,0000,,What are the techniques that you can use\Nto actually get to another planet, to
Dialogue: 0,0:01:37.86,0:01:44.00,Default,,0000,0000,0000,,bring a spacecraft to another planet and\Nalso go a few more, go a bit further into
Dialogue: 0,0:01:44.00,0:01:49.95,Default,,0000,0000,0000,,some more advanced techniques. So we will\Nstart with gravity and the two body
Dialogue: 0,0:01:49.95,0:01:54.90,Default,,0000,0000,0000,,problem. So this is the basics, the\Nunderlying physics that we need. Then we
Dialogue: 0,0:01:54.90,0:01:59.11,Default,,0000,0000,0000,,will talk about the two main techniques\Nmaybe to get to Mars, for example, the
Dialogue: 0,0:01:59.11,0:02:04.53,Default,,0000,0000,0000,,Hohmann-transfer as well as gravity\Nassists. The third point will be an
Dialogue: 0,0:02:04.53,0:02:08.52,Default,,0000,0000,0000,,extension of that that's called a planar\Ncircular restricted three body problem.
Dialogue: 0,0:02:08.52,0:02:14.71,Default,,0000,0000,0000,,Sounds pretty complicated, but we will see\Nin pictures what it is about. And then we
Dialogue: 0,0:02:14.71,0:02:21.92,Default,,0000,0000,0000,,will finally get a taste of certain ways\Nto actually be even better, be even more
Dialogue: 0,0:02:21.92,0:02:26.19,Default,,0000,0000,0000,,efficient by looking at what's called\Nballistic capture and the weak stability
Dialogue: 0,0:02:26.19,0:02:32.77,Default,,0000,0000,0000,,boundary. All right, so let's start. First\Nof all, we have gravity and we need to
Dialogue: 0,0:02:32.77,0:02:36.30,Default,,0000,0000,0000,,talk about a two body problem. So I'm\Nstanding here on the stage and I'm
Dialogue: 0,0:02:36.30,0:02:41.66,Default,,0000,0000,0000,,actually being well accelerated downwards,\Nright? The earth actually attracts me. And
Dialogue: 0,0:02:41.66,0:02:47.54,Default,,0000,0000,0000,,this is the same thing that happens for\Nany two bodies that have mass. OK. So they
Dialogue: 0,0:02:47.54,0:02:51.73,Default,,0000,0000,0000,,attract each other by gravitational force\Nand this force will actually accelerate
Dialogue: 0,0:02:51.73,0:02:56.62,Default,,0000,0000,0000,,the objects towards each other. Notice\Nthat the force actually depends on the
Dialogue: 0,0:02:56.62,0:03:03.72,Default,,0000,0000,0000,,distance. OK. So we don't need\Nto know any details. But in principle, the
Dialogue: 0,0:03:03.72,0:03:11.31,Default,,0000,0000,0000,,force gets stronger the closer the objects\Nare. OK, good. Now, we can't really
Dialogue: 0,0:03:11.31,0:03:17.08,Default,,0000,0000,0000,,analyze this whole thing in every\Ndetail. So we will make a few assumptions.
Dialogue: 0,0:03:17.08,0:03:23.09,Default,,0000,0000,0000,,One of them will be that all our bodies,\Nin particular, the Sun, Earth will
Dialogue: 0,0:03:23.09,0:03:27.47,Default,,0000,0000,0000,,actually be points, OK? So we will just\Nconsider points because anything else is
Dialogue: 0,0:03:27.47,0:03:32.68,Default,,0000,0000,0000,,too complicated for me. Also, all our\Nsatellites will actually be just points.
Dialogue: 0,0:03:32.68,0:03:38.57,Default,,0000,0000,0000,,One of the reasons is that, in principle,\Nyou have to deal with the attitude of the
Dialogue: 0,0:03:38.57,0:03:42.62,Default,,0000,0000,0000,,satellites. For example, a solar panel\Nneeds to actually point towards the sun,
Dialogue: 0,0:03:42.62,0:03:47.30,Default,,0000,0000,0000,,but of course that's complicated. So we\Nwill skip this for this talk. Third point
Dialogue: 0,0:03:47.30,0:03:51.79,Default,,0000,0000,0000,,is that none of our planets will have an\Natmosphere, so there won't be any
Dialogue: 0,0:03:51.79,0:03:58.76,Default,,0000,0000,0000,,friction anywhere in the space. And the\Nfourth point is that we will mostly
Dialogue: 0,0:03:58.76,0:04:03.73,Default,,0000,0000,0000,,restrict to movement within the plane. So\Nwe only have like two dimensions during
Dialogue: 0,0:04:03.73,0:04:11.35,Default,,0000,0000,0000,,this talk. And also, I will kind of forget\Nabout certain planets and other masses
Dialogue: 0,0:04:11.35,0:04:16.07,Default,,0000,0000,0000,,from time to time. Okay. I'm mentioning\Nthis because I do not want you to go home
Dialogue: 0,0:04:16.07,0:04:20.59,Default,,0000,0000,0000,,this evening, start planning your own\Ninterplanetary mission, then maybe
Dialogue: 0,0:04:20.59,0:04:24.72,Default,,0000,0000,0000,,building your spacecraft tomorrow,\Nlaunching in three days and then a week
Dialogue: 0,0:04:24.72,0:04:31.03,Default,,0000,0000,0000,,later I get an e-mail: "Hey, this \Ndidn't work. I mean, what did you tell me?"
Dialogue: 0,0:04:31.03,0:04:35.68,Default,,0000,0000,0000,,OK. So if you actually want to do this at\Nhome, don't try this just now but please
Dialogue: 0,0:04:35.68,0:04:40.54,Default,,0000,0000,0000,,consult your local flight dynamics department, \Nthey will actually supply with the necessary
Dialogue: 0,0:04:40.54,0:04:46.41,Default,,0000,0000,0000,,details. All right. So what's the two body\Nproblem about? So in principle we have
Dialogue: 0,0:04:46.41,0:04:51.23,Default,,0000,0000,0000,,some body - the Sun - and the spacecraft\Nthat is being attracted by the Sun. Now,
Dialogue: 0,0:04:51.23,0:04:55.52,Default,,0000,0000,0000,,the Sun is obviously much heavier than a\Nspacecraft, meaning that we will actually
Dialogue: 0,0:04:55.52,0:05:01.70,Default,,0000,0000,0000,,neglect the force that the spacecraft\Nexerts on the Sun. So instead, the Sun
Dialogue: 0,0:05:01.70,0:05:06.32,Default,,0000,0000,0000,,will be at some place. It \Nmight move in some way, or a
Dialogue: 0,0:05:06.32,0:05:12.31,Default,,0000,0000,0000,,planet. But we only care about a\Nspacecraft, in general. Furthermore,
Dialogue: 0,0:05:12.31,0:05:16.47,Default,,0000,0000,0000,,notice that if you specify the position\Nand the velocity of a spacecraft at some
Dialogue: 0,0:05:16.47,0:05:23.49,Default,,0000,0000,0000,,point, then the gravitational force will\Nactually determine the whole path of the
Dialogue: 0,0:05:23.49,0:05:31.37,Default,,0000,0000,0000,,spacecraft for all time. OK. So this path\Nis called the orbit and this is what we
Dialogue: 0,0:05:31.37,0:05:34.93,Default,,0000,0000,0000,,are talking about. So we want to determine\Norbits. We want to actually find ways how
Dialogue: 0,0:05:34.93,0:05:44.13,Default,,0000,0000,0000,,to efficiently change orbits in order to\Nactually reach Mars, for example. There is
Dialogue: 0,0:05:44.13,0:05:51.38,Default,,0000,0000,0000,,one other thing that you may know from\Nyour day to day life. If you actually take
Dialogue: 0,0:05:51.38,0:05:55.68,Default,,0000,0000,0000,,an object and you put it high up and you\Nlet it fall down, then it will accelerate.
Dialogue: 0,0:05:55.68,0:06:01.88,Default,,0000,0000,0000,,OK. So one way to actually describe this\Nis by looking at the energy. There is a
Dialogue: 0,0:06:01.88,0:06:05.62,Default,,0000,0000,0000,,kinetic energy that's related to movement,\Nto velocity, and there is a potential
Dialogue: 0,0:06:05.62,0:06:10.68,Default,,0000,0000,0000,,energy which is related to this\Ngravitational field. And the sum of those
Dialogue: 0,0:06:10.68,0:06:17.90,Default,,0000,0000,0000,,energies is actually conserved. This means\Nthat when the spacecraft moves, for
Dialogue: 0,0:06:17.90,0:06:23.37,Default,,0000,0000,0000,,example, closer to the Sun, then its\Npotential energy will decrease and thus
Dialogue: 0,0:06:23.37,0:06:28.91,Default,,0000,0000,0000,,the kinetic energy will increase. So it\Nwill actually get faster. So you can see
Dialogue: 0,0:06:28.91,0:06:32.55,Default,,0000,0000,0000,,this, for example, here. We have \Ntwo bodies that rotate around their
Dialogue: 0,0:06:32.55,0:06:37.55,Default,,0000,0000,0000,,center of mass. And if you're careful, if\Nyou're looking careful when they actually
Dialogue: 0,0:06:37.55,0:06:43.23,Default,,0000,0000,0000,,approach each other, then they are quite a\Nbit faster. OK. So it is important to keep
Dialogue: 0,0:06:43.23,0:06:48.25,Default,,0000,0000,0000,,in mind. All right, so how do spacecrafts\Nactually move? So we will now actually
Dialogue: 0,0:06:48.25,0:06:55.21,Default,,0000,0000,0000,,assume that we don't use any kind of\Nengine, no thruster. We just cruise along
Dialogue: 0,0:06:55.21,0:07:00.18,Default,,0000,0000,0000,,the gravitational field. And then there\Nare essentially three types of orbits that
Dialogue: 0,0:07:00.18,0:07:04.36,Default,,0000,0000,0000,,we can have. One of them are hyperbolas.\NSo this case happens if the velocity is
Dialogue: 0,0:07:04.36,0:07:10.76,Default,,0000,0000,0000,,very high, because those are not periodic\Nsolutions. They're not closed. So instead,
Dialogue: 0,0:07:10.76,0:07:15.82,Default,,0000,0000,0000,,our spacecraft kind of approaches the Sun\Nor the planet in the middle and the center
Dialogue: 0,0:07:15.82,0:07:21.21,Default,,0000,0000,0000,,from infinity. It will kind of turn,\Nit will change its direction and then it
Dialogue: 0,0:07:21.21,0:07:27.99,Default,,0000,0000,0000,,will leave again to infinity. Another\Norbit that may happen as a parabola, this
Dialogue: 0,0:07:27.99,0:07:33.18,Default,,0000,0000,0000,,is kind of similar. Actually, we won't\Nencounter parabolas during this talk. So I
Dialogue: 0,0:07:33.18,0:07:38.03,Default,,0000,0000,0000,,will skip this. And the probably most\Ncommon orbit that we all know are
Dialogue: 0,0:07:38.03,0:07:44.51,Default,,0000,0000,0000,,ellipses. In particular circles because,\Nwell, we know that the Earth is actually
Dialogue: 0,0:07:44.51,0:07:49.45,Default,,0000,0000,0000,,moving around the sun approximately in a\Ncircle. OK. So those are periodic
Dialogue: 0,0:07:49.45,0:07:56.87,Default,,0000,0000,0000,,solutions. They are closed. And in\Nparticular, they are such that if a
Dialogue: 0,0:07:56.87,0:08:00.79,Default,,0000,0000,0000,,spacecraft is on one of those orbits and\Nit's not doing anything, then it will
Dialogue: 0,0:08:00.79,0:08:09.12,Default,,0000,0000,0000,,forever stay on that orbit, OK, in the two\Nbody problem. So now the problem is we
Dialogue: 0,0:08:09.12,0:08:13.07,Default,,0000,0000,0000,,actually want to change this. So we need\Nto do something. OK. So we want to change
Dialogue: 0,0:08:13.07,0:08:17.59,Default,,0000,0000,0000,,from one circle around the Sun, which \Ncorresponds to Earth orbit, for example, to
Dialogue: 0,0:08:17.59,0:08:21.51,Default,,0000,0000,0000,,another circle around the Sun, which \Ncorresponds to Mars orbit. And in order to
Dialogue: 0,0:08:21.51,0:08:27.32,Default,,0000,0000,0000,,change this, we need to do some kind of\Nmaneuver. OK. So this is an actual picture
Dialogue: 0,0:08:27.32,0:08:33.36,Default,,0000,0000,0000,,of a spacecraft. And what the spacecraft\Nis doing, it's emitting some kind of
Dialogue: 0,0:08:33.36,0:08:40.50,Default,,0000,0000,0000,,particles in some direction. They have a\Nmass m. Those particles might be gases or
Dialogue: 0,0:08:40.50,0:08:48.10,Default,,0000,0000,0000,,ions, for example. And because these gases\Nor these emissions, they carry some mass,
Dialogue: 0,0:08:48.10,0:08:53.16,Default,,0000,0000,0000,,they actually have some momentum due to\Nconservation of momentum. This means that
Dialogue: 0,0:08:53.16,0:08:58.05,Default,,0000,0000,0000,,the spacecraft actually has to accelerate\Nin the opposite direction. OK. So whenever
Dialogue: 0,0:08:58.05,0:09:03.98,Default,,0000,0000,0000,,we do this, we will actually accelerate\Nthe spacecraft and change the velocity and
Dialogue: 0,0:09:03.98,0:09:12.66,Default,,0000,0000,0000,,this change of velocity as denoted by a\Ndelta v. And delta v is sort of the basic
Dialogue: 0,0:09:12.66,0:09:16.98,Default,,0000,0000,0000,,quantity that we actually want to look at\Nall the time. OK. Because this describes
Dialogue: 0,0:09:16.98,0:09:26.01,Default,,0000,0000,0000,,how much thrust we need to actually fly\Nin order to change our orbit. Now,
Dialogue: 0,0:09:26.01,0:09:32.44,Default,,0000,0000,0000,,unfortunately, it's pretty expensive to,\Nwell, to apply a lot of delta v. This is
Dialogue: 0,0:09:32.44,0:09:37.34,Default,,0000,0000,0000,,due to the costly rocket equation. So the\Nfuel that you need in order to reach or to
Dialogue: 0,0:09:37.34,0:09:45.85,Default,,0000,0000,0000,,change your velocity to some delta v this\Ndepends essentially exponentially on the
Dialogue: 0,0:09:45.85,0:09:52.74,Default,,0000,0000,0000,,target delta v. So this means we really\Nneed to take care that we use as few
Dialogue: 0,0:09:52.74,0:10:00.49,Default,,0000,0000,0000,,delta v as possible in order to reduce the\Nneeded fuel. There's one reason for
Dialogue: 0,0:10:00.49,0:10:04.99,Default,,0000,0000,0000,,that is... we want to maybe reduce\Ncosts because then we need to carry
Dialogue: 0,0:10:04.99,0:10:10.01,Default,,0000,0000,0000,,less fuel. However, we can also actually\Nthink the other way round if we actually
Dialogue: 0,0:10:10.01,0:10:16.77,Default,,0000,0000,0000,,use less fuel than we can\Nbring more stuff for payloads, for
Dialogue: 0,0:10:16.77,0:10:24.17,Default,,0000,0000,0000,,missions, for science experiments. Okay.\NSo that's why in spacecraft mission
Dialogue: 0,0:10:24.17,0:10:28.40,Default,,0000,0000,0000,,design we actually have to take care of\Nreducing the amount of delta v that is
Dialogue: 0,0:10:28.40,0:10:34.27,Default,,0000,0000,0000,,spent during maneuvers. So let's see, what\Ncan we actually do? So one example of a
Dialogue: 0,0:10:34.27,0:10:41.50,Default,,0000,0000,0000,,very basic maneuver is actually to, well,\Nsort of raise the orbit. So imagine you
Dialogue: 0,0:10:41.50,0:10:48.10,Default,,0000,0000,0000,,have a spacecraft on a circular orbit\Naround, for example, Sun here. Then you
Dialogue: 0,0:10:48.10,0:10:52.27,Default,,0000,0000,0000,,might want to raise the orbit\Nin the sense that you make it more
Dialogue: 0,0:10:52.27,0:10:57.41,Default,,0000,0000,0000,,elliptic and reach higher altitudes. For\Nthis you just accelerate in the direction
Dialogue: 0,0:10:57.41,0:11:00.68,Default,,0000,0000,0000,,that you're flying. So you apply some\Ndelta v and this will actually change the
Dialogue: 0,0:11:00.68,0:11:08.03,Default,,0000,0000,0000,,form of the ellipse. OK. So it's a very\Ncommon scenario. Another one is if you
Dialogue: 0,0:11:08.03,0:11:12.37,Default,,0000,0000,0000,,approach a planet from very far away, then\Nyou might have a very high relative
Dialogue: 0,0:11:12.37,0:11:18.57,Default,,0000,0000,0000,,velocity such that with respect to the\Nplanet, you're on a hyperbolic orbit. OK.
Dialogue: 0,0:11:18.57,0:11:22.54,Default,,0000,0000,0000,,So you would actually leave the planet.\NHowever, if this is actually your
Dialogue: 0,0:11:22.54,0:11:26.84,Default,,0000,0000,0000,,target planet that you want to reach, then\Nof course you have to enter orbit. You
Dialogue: 0,0:11:26.84,0:11:31.29,Default,,0000,0000,0000,,have to somehow slow down. So the idea\Nhere is that when you approach
Dialogue: 0,0:11:31.29,0:11:37.45,Default,,0000,0000,0000,,the closest point to the planet,\Nfor example, then you actually slow down.
Dialogue: 0,0:11:37.45,0:11:41.83,Default,,0000,0000,0000,,So you apply delta v in sort of in the\Nopposite direction and change the orbit to
Dialogue: 0,0:11:41.83,0:11:45.71,Default,,0000,0000,0000,,something that you prefer, for example an\Nellipse. Because now you will actually
Dialogue: 0,0:11:45.71,0:11:54.76,Default,,0000,0000,0000,,stay close to the planet forever. Well, if\Nrelative it would a two body problem. OK,
Dialogue: 0,0:11:54.76,0:12:02.23,Default,,0000,0000,0000,,so. Let's continue. Now, we actually want\Nto apply this knowledge to well, getting,
Dialogue: 0,0:12:02.23,0:12:08.83,Default,,0000,0000,0000,,for example, to Mars. Let's start with \NHohmann transfers. Mars and Earth both
Dialogue: 0,0:12:08.83,0:12:16.59,Default,,0000,0000,0000,,revolve around the Sun in pretty much\Ncircular orbits. And our spacecraft starts
Dialogue: 0,0:12:16.59,0:12:21.22,Default,,0000,0000,0000,,at the Earth. So now we want to reach\NMars. How do we do this? Well, we can fly
Dialogue: 0,0:12:21.22,0:12:27.27,Default,,0000,0000,0000,,what we just said. So we accelerate \Nwhen we are at the Earth orbit,
Dialogue: 0,0:12:27.27,0:12:36.81,Default,,0000,0000,0000,,such that our orbit touches the Mars orbit\Non the other side. OK. So this gives us
Dialogue: 0,0:12:36.81,0:12:40.99,Default,,0000,0000,0000,,some amount of delta v we have to apply.\NWe need to calculate this. I'm not going
Dialogue: 0,0:12:40.99,0:12:47.94,Default,,0000,0000,0000,,to do this. Then we actually fly around\Nthis orbit for half an ellipse. And once
Dialogue: 0,0:12:47.94,0:12:53.14,Default,,0000,0000,0000,,we have reached the Mars orbit, then we\Ncan actually accelerate again in order to
Dialogue: 0,0:12:53.14,0:12:59.68,Default,,0000,0000,0000,,raise other side of the Ellipse until that\None reaches the Mars orbit. So with two
Dialogue: 0,0:12:59.68,0:13:04.84,Default,,0000,0000,0000,,maneuvers, two accelerations, we can\Nactually change from one circular orbit to
Dialogue: 0,0:13:04.84,0:13:09.96,Default,,0000,0000,0000,,another one. OK. This is the basic idea of\Nhow you actually fly to Mars. So let's
Dialogue: 0,0:13:09.96,0:13:16.34,Default,,0000,0000,0000,,look at an animation. So this is the orbit\Nof the InSight mission. That's another Mars
Dialogue: 0,0:13:16.34,0:13:25.20,Default,,0000,0000,0000,,mission which launched and landed last\Nyear. The blue circle is the Earth and the
Dialogue: 0,0:13:25.20,0:13:33.13,Default,,0000,0000,0000,,green one is Mars. And the pink is\Nactually the satellite or the probe.
Dialogue: 0,0:13:33.13,0:13:40.38,Default,,0000,0000,0000,,You can see that, well, it's flying in\Nthis sort of half ellipse. However, there
Dialogue: 0,0:13:40.38,0:13:47.34,Default,,0000,0000,0000,,are two... well, there's just one problem,\Nnamely when it actually reaches Mars, Mars
Dialogue: 0,0:13:47.34,0:13:51.78,Default,,0000,0000,0000,,needs to be there. I mean, that sounds\Ntrivial. Yeah. But I mean, imagine you fly
Dialogue: 0,0:13:51.78,0:13:57.45,Default,,0000,0000,0000,,there and then well, Mars is somewhere\Nelse, that's not good. I mean this happens
Dialogue: 0,0:13:57.45,0:14:05.44,Default,,0000,0000,0000,,pretty regularly when you begin playing a\NKerbal Space Program, for example.
Dialogue: 0,0:14:05.44,0:14:11.05,Default,,0000,0000,0000,,So we don't want to like play around\Nwith this the whole time, we actually want
Dialogue: 0,0:14:11.05,0:14:16.76,Default,,0000,0000,0000,,to hit Mars. So we need to take care of\Nthat Mars is at the right position when we
Dialogue: 0,0:14:16.76,0:14:21.78,Default,,0000,0000,0000,,actually launch. Because it will traverse\Nthe whole green line during our transfer.
Dialogue: 0,0:14:21.78,0:14:27.98,Default,,0000,0000,0000,,This means that we can only launch such a\NHohmann transfer at very particular times.
Dialogue: 0,0:14:27.98,0:14:31.58,Default,,0000,0000,0000,,And sort of this time when you can do\Nthis transfer is called the transfer
Dialogue: 0,0:14:31.58,0:14:39.60,Default,,0000,0000,0000,,window. And for Earth-Mars, for example.\NThis is possible every 26 months. So if
Dialogue: 0,0:14:39.60,0:14:44.64,Default,,0000,0000,0000,,you miss something, like, software's not\Nready, whatever, then you have to wait for
Dialogue: 0,0:14:44.64,0:14:53.00,Default,,0000,0000,0000,,another twenty six months. So, the flight\Nitself takes about six months. All right.
Dialogue: 0,0:14:53.00,0:14:59.40,Default,,0000,0000,0000,,There is another thing that we kind of\Nneglected so far, namely when we start,
Dialogue: 0,0:14:59.40,0:15:04.45,Default,,0000,0000,0000,,when we depart from Earth, then well\Nthere's Earth mainly. And so that's the
Dialogue: 0,0:15:04.45,0:15:11.01,Default,,0000,0000,0000,,main source of gravitational force. For\Nexample, right now I'm standing here on
Dialogue: 0,0:15:11.01,0:15:19.80,Default,,0000,0000,0000,,the stage and I experience the Earth. I\Nalso experience Sun and Mars. But I mean,
Dialogue: 0,0:15:19.80,0:15:24.90,Default,,0000,0000,0000,,that's very weak. I can ignore this. So at\Nthe beginning of our mission to Mars, we
Dialogue: 0,0:15:24.90,0:15:29.41,Default,,0000,0000,0000,,actually have to take care that we\Nare close to Earth. Then during the
Dialogue: 0,0:15:29.41,0:15:34.38,Default,,0000,0000,0000,,flight, the Sun actually dominates the\Ngravitational force. So we will only
Dialogue: 0,0:15:34.38,0:15:38.03,Default,,0000,0000,0000,,consider this. But then when we approach\NMars, we actually have to take care about
Dialogue: 0,0:15:38.03,0:15:44.43,Default,,0000,0000,0000,,Mars. Okay. So we kind of forgot this\Nduring the Hohmann transfer. So what you
Dialogue: 0,0:15:44.43,0:15:49.97,Default,,0000,0000,0000,,actually do is you patch together\Nsolutions of these transfers. Yeah. So in
Dialogue: 0,0:15:49.97,0:15:55.24,Default,,0000,0000,0000,,this case, there are there are essentially\Nthree sources of gravitational force so
Dialogue: 0,0:15:55.24,0:15:59.39,Default,,0000,0000,0000,,Earth, Sun, Mars. So we will have three two\Nbody problems that we need to consider.
Dialogue: 0,0:15:59.39,0:16:04.64,Default,,0000,0000,0000,,Yeah. One for departing, one for the\Nactual Hohmann transfer. And then the third
Dialogue: 0,0:16:04.64,0:16:09.45,Default,,0000,0000,0000,,one when we actually approach Mars. So\Nthis makes this whole thing a bit more
Dialogue: 0,0:16:09.45,0:16:14.65,Default,,0000,0000,0000,,complicated. But it's also nice because\Nactually we need less delta v than we
Dialogue: 0,0:16:14.65,0:16:19.59,Default,,0000,0000,0000,,would for the basic hohmann transfer. One\Nreason for this is that when we look at
Dialogue: 0,0:16:19.59,0:16:25.93,Default,,0000,0000,0000,,Mars. So the green line is now the Mars\Norbit and the red one is again the
Dialogue: 0,0:16:25.93,0:16:31.51,Default,,0000,0000,0000,,spacecraft, it approaches Mars now we can\Nactually look at what happens at Mars by
Dialogue: 0,0:16:31.51,0:16:40.48,Default,,0000,0000,0000,,kind of zooming into the system of Mars.\NOK. So Mars is now standing still. And
Dialogue: 0,0:16:40.48,0:16:46.05,Default,,0000,0000,0000,,then we see that the velocity of the\Nspacecraft is actually very high relative
Dialogue: 0,0:16:46.05,0:16:50.40,Default,,0000,0000,0000,,to Mars. So it will be on the hyperbolic\Norbit and will actually leave Mars again.
Dialogue: 0,0:16:50.40,0:16:55.27,Default,,0000,0000,0000,,You can see this on the left side. Right.\NBecause it's leaving Mars again. So what
Dialogue: 0,0:16:55.27,0:17:00.46,Default,,0000,0000,0000,,you need to do is, in fact, you need to\Nslow down and change your orbit into an
Dialogue: 0,0:17:00.46,0:17:04.77,Default,,0000,0000,0000,,ellipse. Okay. And this delta v, is that\Nyou that you need here for this maneuver
Dialogue: 0,0:17:04.77,0:17:12.22,Default,,0000,0000,0000,,it's actually less than the delta v you\Nwould need to to circularize the orbit to
Dialogue: 0,0:17:12.22,0:17:18.40,Default,,0000,0000,0000,,just fly in the same orbit as Mars. So we\Nneed to slow down. A similar argument
Dialogue: 0,0:17:18.40,0:17:24.64,Default,,0000,0000,0000,,actually at Earth shows that, well, if you\Nactually launch into space, then you do
Dialogue: 0,0:17:24.64,0:17:29.78,Default,,0000,0000,0000,,need quite some speed already to not fall\Ndown back onto Earth. So that's something
Dialogue: 0,0:17:29.78,0:17:33.70,Default,,0000,0000,0000,,like seven kilometers per second or so.\NThis means that you already have some
Dialogue: 0,0:17:33.70,0:17:38.81,Default,,0000,0000,0000,,speed. OK. And if you align your orbit or\Nyour launch correctly, then you already
Dialogue: 0,0:17:38.81,0:17:43.35,Default,,0000,0000,0000,,have some of the delta v that you need for\Nthe Hohmann transfer. So in principle, you
Dialogue: 0,0:17:43.35,0:17:52.08,Default,,0000,0000,0000,,need quite a bit less delta v than than\Nyou might naively think. All right. So
Dialogue: 0,0:17:52.08,0:17:57.28,Default,,0000,0000,0000,,that much about Hohmann transfer. Let's look\Nat Gravity assist. That's another major
Dialogue: 0,0:17:57.28,0:18:03.53,Default,,0000,0000,0000,,technique for interplanetary missions. The\Nidea is that we can actually use planets
Dialogue: 0,0:18:03.53,0:18:10.57,Default,,0000,0000,0000,,to sort of getting pulled along. So this\Nis an animation, on the lower animation
Dialogue: 0,0:18:10.57,0:18:16.30,Default,,0000,0000,0000,,you see kind of the picture when you look\Nat the planet. So the planets standing
Dialogue: 0,0:18:16.30,0:18:21.32,Default,,0000,0000,0000,,still and we assume that the spacecraft's\Nsort of blue object is on a hyperbolic
Dialogue: 0,0:18:21.32,0:18:27.12,Default,,0000,0000,0000,,orbit and it's kind of making a 90 degree\Nturn. OK. And the upper image, you
Dialogue: 0,0:18:27.12,0:18:32.32,Default,,0000,0000,0000,,actually see the picture when\Nyou look from the Sun, so the planet is
Dialogue: 0,0:18:32.32,0:18:38.82,Default,,0000,0000,0000,,actually moving. And if you look very\Ncarefully at the blue object then you can
Dialogue: 0,0:18:38.82,0:18:45.03,Default,,0000,0000,0000,,see that it is faster. So once it has\Npassed, the planet is actually faster.
Dialogue: 0,0:18:45.03,0:18:52.90,Default,,0000,0000,0000,,Well, we can actually look at this problem.\NSo this is, again, the picture. When
Dialogue: 0,0:18:52.90,0:18:56.26,Default,,0000,0000,0000,,Mars is centered, we have some entry\Nvelocity. Then we are in this hyperbolic
Dialogue: 0,0:18:56.26,0:19:03.16,Default,,0000,0000,0000,,orbit. We have an exit velocity. Notice\Nthat the lengths are actually equal. So
Dialogue: 0,0:19:03.16,0:19:08.58,Default,,0000,0000,0000,,it's the same speed. But just a turn\Ndirection of this example. But then we can
Dialogue: 0,0:19:08.58,0:19:13.41,Default,,0000,0000,0000,,look at the whole problem with a moving\NMars. OK, so now Mars has some velocity
Dialogue: 0,0:19:13.41,0:19:19.61,Default,,0000,0000,0000,,v_mars. So the actual velocity that we see\Nis the sum of the entry and the Mars
Dialogue: 0,0:19:19.61,0:19:25.87,Default,,0000,0000,0000,,velocity before and afterwards exit, plus\NMars velocity. And if you look at those
Dialogue: 0,0:19:25.87,0:19:31.91,Default,,0000,0000,0000,,two arrows, then you see immediately that,\Nwell, the lengths are different. Okay. So
Dialogue: 0,0:19:31.91,0:19:37.65,Default,,0000,0000,0000,,this is just the whole phenomenon here. So\Nwe see that by actually passing close to
Dialogue: 0,0:19:37.65,0:19:43.25,Default,,0000,0000,0000,,such a planet or massive body, we\Ncan sort of gain free delta v. Okay, so of
Dialogue: 0,0:19:43.25,0:19:49.08,Default,,0000,0000,0000,,course, it's not. I mean, the energy is\Nstill conserved. Okay. But yeah, let's not
Dialogue: 0,0:19:49.08,0:19:53.55,Default,,0000,0000,0000,,worry about these details here. Now, the\Nnice thing is we can use this technique to
Dialogue: 0,0:19:53.55,0:19:58.97,Default,,0000,0000,0000,,actually alter course. We can speed up. So\Nthis is the example that I'm shown here.
Dialogue: 0,0:19:58.97,0:20:02.79,Default,,0000,0000,0000,,But also, we can use this to slow down.\NOkay. So that's a pretty common
Dialogue: 0,0:20:02.79,0:20:08.16,Default,,0000,0000,0000,,application as well. We can use this to\Nslow down by just changing the arrows,
Dialogue: 0,0:20:08.16,0:20:15.86,Default,,0000,0000,0000,,essentially. So just approaching Mars from\Na different direction, essentially. So
Dialogue: 0,0:20:15.86,0:20:21.96,Default,,0000,0000,0000,,let's look at the example. And this is\NBepicolombo. That's actually the reason
Dialogue: 0,0:20:21.96,0:20:26.24,Default,,0000,0000,0000,,why I kind of changed the title, because\NBepicolombo is actually a mission to
Dialogue: 0,0:20:26.24,0:20:32.66,Default,,0000,0000,0000,,Mercury. So it was launched last year.\NIt's a combined ESA/JAXA mission and it
Dialogue: 0,0:20:32.66,0:20:38.39,Default,,0000,0000,0000,,consists of two probes and one thruster\Ncentrally. So it's a through three stages
Dialogue: 0,0:20:38.39,0:20:43.78,Default,,0000,0000,0000,,that you can see in the picture. Yeah.\NThat's a pretty awesome mission, actually.
Dialogue: 0,0:20:43.78,0:20:49.93,Default,,0000,0000,0000,,It's really nice. But it has in\Nparticular, a very cool orbit. So that's
Dialogue: 0,0:20:49.93,0:20:56.63,Default,,0000,0000,0000,,it. What can we see here? So first of all,\Nthe blue line, that's actually Earth. The
Dialogue: 0,0:20:56.63,0:21:00.18,Default,,0000,0000,0000,,green one, that's Mercury. So that's where\Nwe want to go. And we have this
Dialogue: 0,0:21:00.18,0:21:07.13,Default,,0000,0000,0000,,intermediate turquoise one - that's\NVenus. And well the curve is
Dialogue: 0,0:21:07.13,0:21:10.79,Default,,0000,0000,0000,,Bepicolombo's orbit, so it looks pretty\Ncomplicated. Yeah, it's definitely not the
Dialogue: 0,0:21:10.79,0:21:16.02,Default,,0000,0000,0000,,Hohmann transfer. And in fact, this\Nmission uses nine Gravity assists to reach
Dialogue: 0,0:21:16.02,0:21:21.95,Default,,0000,0000,0000,,Mercury. And if you look at the\Npath so, for example, right now
Dialogue: 0,0:21:21.95,0:21:28.69,Default,,0000,0000,0000,,it actually is very close to Mercury\Nbecause the last five or six Gravity
Dialogue: 0,0:21:28.69,0:21:34.50,Default,,0000,0000,0000,,assists are just around Mercury or just\Nslow down. OK. And this saves a lot of
Dialogue: 0,0:21:34.50,0:21:41.76,Default,,0000,0000,0000,,delta v compared to the standard \NHohmann transfer. All right. But we
Dialogue: 0,0:21:41.76,0:21:45.81,Default,,0000,0000,0000,,want to do even better. OK. So let's now\Nactually make the whole problem more
Dialogue: 0,0:21:45.81,0:21:53.83,Default,,0000,0000,0000,,complicated in order to hope for some kind\Nof nice tricks that we can do. OK, so now
Dialogue: 0,0:21:53.83,0:21:58.55,Default,,0000,0000,0000,,we will talk about a planar circular\Nrestricted three body problem. All right.
Dialogue: 0,0:21:58.55,0:22:02.59,Default,,0000,0000,0000,,So in general, the three body problem just\Nmeans, hey, well, instead of two bodies,
Dialogue: 0,0:22:02.59,0:22:07.40,Default,,0000,0000,0000,,we have three. OK. They pairwise attract\Neach other and then we can solve this
Dialogue: 0,0:22:07.40,0:22:12.08,Default,,0000,0000,0000,,whole equation of motion. We can ask a\Ncomputer. And this is one animation of
Dialogue: 0,0:22:12.08,0:22:17.49,Default,,0000,0000,0000,,what it could look like. So the three\Nmasses and their orbits are traced and we
Dialogue: 0,0:22:17.49,0:22:24.08,Default,,0000,0000,0000,,see immediately that we don't see anything\Nthat's super complicated. There is no
Dialogue: 0,0:22:24.08,0:22:29.67,Default,,0000,0000,0000,,way we can really... I don't know,\Nformulate a whole solution theory for a
Dialogue: 0,0:22:29.67,0:22:33.65,Default,,0000,0000,0000,,general three body problem. That's\Ncomplicated. Those are definitely not
Dialogue: 0,0:22:33.65,0:22:40.31,Default,,0000,0000,0000,,ellipses. So let's maybe go a step back\Nand make the problem a bit easier. OK. So
Dialogue: 0,0:22:40.31,0:22:44.52,Default,,0000,0000,0000,,we will now talk about a plane or circular\Nrestricted three body problem. There are
Dialogue: 0,0:22:44.52,0:22:49.44,Default,,0000,0000,0000,,three words. So the first one is\Nrestricted. Restricted means that in our
Dialogue: 0,0:22:49.44,0:22:54.35,Default,,0000,0000,0000,,application case, one of the bodies is\Nactually a spacecraft. Spacecrafts are
Dialogue: 0,0:22:54.35,0:22:58.44,Default,,0000,0000,0000,,much lighter than, for example, Sun and\NMars, meaning that we can actually ignore
Dialogue: 0,0:22:58.44,0:23:05.57,Default,,0000,0000,0000,,the force that the spacecraft exerts on\NSun and Mars. Okay. So we will actually
Dialogue: 0,0:23:05.57,0:23:11.74,Default,,0000,0000,0000,,consider Sun and Mars to be independent of\Nthe spacecraft. OK. So in total, we only
Dialogue: 0,0:23:11.74,0:23:18.12,Default,,0000,0000,0000,,have like two gravitational forces now\Nacting on a spacecraft. So we neglect sort
Dialogue: 0,0:23:18.12,0:23:25.61,Default,,0000,0000,0000,,of this other force. Also, we will assume\Nthat the whole problem is what's called
Dialogue: 0,0:23:25.61,0:23:30.80,Default,,0000,0000,0000,,circular. So we assume that Sun and Mars\Nactually rotate in circles around their
Dialogue: 0,0:23:30.80,0:23:37.08,Default,,0000,0000,0000,,center of mass. This assumption is\Nactually pretty okay. We will see a
Dialogue: 0,0:23:37.08,0:23:42.96,Default,,0000,0000,0000,,picture right now. So in this graph, for\Nexample, in this image, you can see that
Dialogue: 0,0:23:42.96,0:23:48.68,Default,,0000,0000,0000,,the black situation. So this might be at\Nsome time, at some point in time. And then
Dialogue: 0,0:23:48.68,0:23:54.52,Default,,0000,0000,0000,,later on, Sun and Mars actually have moved\Nto the red positions and the spacecraft is
Dialogue: 0,0:23:54.52,0:24:00.84,Default,,0000,0000,0000,,at some other place. And now, of course,\Nfeels some other forces. OK. And also we
Dialogue: 0,0:24:00.84,0:24:04.33,Default,,0000,0000,0000,,will assume that this problem is plane,\Nmeaning again that everything takes place
Dialogue: 0,0:24:04.33,0:24:12.38,Default,,0000,0000,0000,,in the plane. OK. So let's look at the\Nvideo. That's a video with a very low
Dialogue: 0,0:24:12.38,0:24:19.61,Default,,0000,0000,0000,,frame rate, something like two images per\Nday. Maybe it's actually Pluto and Charon.
Dialogue: 0,0:24:19.61,0:24:27.25,Default,,0000,0000,0000,,So the larger one, this is the ex-planet\NPluto. It was taken by New Horizons in
Dialogue: 0,0:24:27.25,0:24:34.36,Default,,0000,0000,0000,,2015 and it shows that they actually\Nrotate around the center of mass. Yeah. So
Dialogue: 0,0:24:34.36,0:24:40.27,Default,,0000,0000,0000,,both actually rotate. This also happens,\Nfor example, for Sun and Earth or Sun and
Dialogue: 0,0:24:40.27,0:24:45.25,Default,,0000,0000,0000,,Mars or sun and Jupiter or also Earth and\NMoon. However, in those other cases, the
Dialogue: 0,0:24:45.25,0:24:50.65,Default,,0000,0000,0000,,center of mass is usually contained in the\Nlarger body. And so this means that in the
Dialogue: 0,0:24:50.65,0:24:57.91,Default,,0000,0000,0000,,case of Sun-Earth, for example, the Sun\Nwill just wiggle a little bit. OK. So you
Dialogue: 0,0:24:57.91,0:25:04.41,Default,,0000,0000,0000,,don't really see this extensive rotation.\NOK. Now, this problem is still difficult.
Dialogue: 0,0:25:04.41,0:25:10.14,Default,,0000,0000,0000,,OK. So if you're putting out a mass in\Nthere, then you don't really
Dialogue: 0,0:25:10.14,0:25:15.50,Default,,0000,0000,0000,,know what happens. However, there's a nice\Ntrick to simplify this problem. And
Dialogue: 0,0:25:15.50,0:25:19.73,Default,,0000,0000,0000,,unfortunately, I can't do this here. But\Nmaybe all the viewers at home, they can
Dialogue: 0,0:25:19.73,0:25:25.08,Default,,0000,0000,0000,,try to do this. You can take your laptop.\NPlease don't do this. And you can rotate
Dialogue: 0,0:25:25.08,0:25:34.02,Default,,0000,0000,0000,,your laptop at the same speed as this\Nimage actually rotates. OK. Well, then
Dialogue: 0,0:25:34.02,0:25:39.34,Default,,0000,0000,0000,,what happens? The two masses will actually\Nstand still from your point of view. OK.
Dialogue: 0,0:25:39.34,0:25:45.08,Default,,0000,0000,0000,,If you do it carefully and don't break\Nanything. So we switch to this sort of
Dialogue: 0,0:25:45.08,0:25:50.59,Default,,0000,0000,0000,,rotating point of view. OK, then the two\Nmasses stand still. We still have the two
Dialogue: 0,0:25:50.59,0:25:56.02,Default,,0000,0000,0000,,gravitational forces towards Sun and Mars.\NBut because we kind of look at it from a
Dialogue: 0,0:25:56.02,0:26:00.67,Default,,0000,0000,0000,,rotated or from a moving point of view, we\Nget two new forces, those forces, you
Dialogue: 0,0:26:00.67,0:26:04.89,Default,,0000,0000,0000,,know, the centrifugal forces, of\Ncourse, the one that, for example, you
Dialogue: 0,0:26:04.89,0:26:11.51,Default,,0000,0000,0000,,have when you play with some\Nchildren or so, they want to be pulled in
Dialogue: 0,0:26:11.51,0:26:17.44,Default,,0000,0000,0000,,a circle very quickly and then they start\Nflying and that's pretty cool. But here we
Dialogue: 0,0:26:17.44,0:26:21.73,Default,,0000,0000,0000,,actually have this force acting on the\Nspacecraft. Okay. And also there is the
Dialogue: 0,0:26:21.73,0:26:26.79,Default,,0000,0000,0000,,Coriolis force, which is a bit less known.\NThis depends on the velocity of the
Dialogue: 0,0:26:26.79,0:26:31.66,Default,,0000,0000,0000,,spacecraft. OK. So if there is no velocity\Nin particular, then there will not be any
Dialogue: 0,0:26:31.66,0:26:38.27,Default,,0000,0000,0000,,Coriolis force. So our new problem\Nactually has four forces. OK, but the
Dialogue: 0,0:26:38.27,0:26:43.58,Default,,0000,0000,0000,,advantage is that Sun and Mars actually\Nare standing still. So we don't need to
Dialogue: 0,0:26:43.58,0:26:51.04,Default,,0000,0000,0000,,worry about their movement. OK. So now how\Ndoes this look like? Well, this might be
Dialogue: 0,0:26:51.04,0:26:55.99,Default,,0000,0000,0000,,an example for an orbit. Well, that looks\Nstill pretty complicated. I mean, this is
Dialogue: 0,0:26:55.99,0:27:01.50,Default,,0000,0000,0000,,something that you can't have in a two\Nbody problem. It has these weird wiggles.
Dialogue: 0,0:27:01.50,0:27:06.32,Default,,0000,0000,0000,,I mean, they're not really corners. And it\Nactually kind of switches from Sun to
Dialogue: 0,0:27:06.32,0:27:10.65,Default,,0000,0000,0000,,Mars. Yes. So it stays close to Sun for\Nsome time and it moves somewhere else as
Dialogue: 0,0:27:10.65,0:27:15.65,Default,,0000,0000,0000,,it, it's still pretty complicated. I don't\Nknow. Maybe some of you have have read the
Dialogue: 0,0:27:15.65,0:27:23.49,Default,,0000,0000,0000,,book "The Three-Body Problem". So there,\Nfor example, the two masses might be a
Dialogue: 0,0:27:23.49,0:27:28.76,Default,,0000,0000,0000,,binary star system. OK. And then you have\Na planet that's actually moving along such
Dialogue: 0,0:27:28.76,0:27:35.71,Default,,0000,0000,0000,,an orbit. OK, that looks pretty bad. So in\Nparticular, the seasons might be somewhat
Dialogue: 0,0:27:35.71,0:27:41.96,Default,,0000,0000,0000,,messed up. Yeah. So this problem is, in\Nfact, in a strong mathematical sense,
Dialogue: 0,0:27:41.96,0:27:47.20,Default,,0000,0000,0000,,chaotic. OK. So chaotic means something\Nlike if you start with very close initial
Dialogue: 0,0:27:47.20,0:27:51.61,Default,,0000,0000,0000,,conditions and you just let the system\Nevolve, then the solutions will look very,
Dialogue: 0,0:27:51.61,0:27:58.56,Default,,0000,0000,0000,,very different. OK. And this really\Nhappens here, which is good. All right. So
Dialogue: 0,0:27:58.56,0:28:03.95,Default,,0000,0000,0000,,one thing we can ask is, well, is it\Npossible that if we put a spacecraft into
Dialogue: 0,0:28:03.95,0:28:08.10,Default,,0000,0000,0000,,the system without any velocity, is it\Npossible that all the forces actually
Dialogue: 0,0:28:08.10,0:28:12.45,Default,,0000,0000,0000,,cancel out. And it turns out yes, it is\Npossible. And those points are called
Dialogue: 0,0:28:12.45,0:28:17.95,Default,,0000,0000,0000,,Lagrangian points. So if we have zero\Nvelocity, there is no Coriolis force. So
Dialogue: 0,0:28:17.95,0:28:23.46,Default,,0000,0000,0000,,we have only these three forces. And as\Nyou can see in this little schematics
Dialogue: 0,0:28:23.46,0:28:32.12,Default,,0000,0000,0000,,here, it's possible that all these forces\Nactually cancel out. Now imagine. Yeah. I
Dialogue: 0,0:28:32.12,0:28:36.94,Default,,0000,0000,0000,,give you a homework. Please calculate all\Nthese possible points. Then you can do
Dialogue: 0,0:28:36.94,0:28:42.28,Default,,0000,0000,0000,,this. But we won't do this right here.\NInstead, we just look at the result. So
Dialogue: 0,0:28:42.28,0:28:47.88,Default,,0000,0000,0000,,those are the five Lagrangian points in\Nthis problem. OK, so we have L4 and L5
Dialogue: 0,0:28:47.88,0:28:52.15,Default,,0000,0000,0000,,which are at equilateral triangles with\NSun and Mars. Well, Sun - Mars in this
Dialogue: 0,0:28:52.15,0:28:59.78,Default,,0000,0000,0000,,case. And we have L1, L2 and L3 on the\Nline through Sun and Mars. So if you put
Dialogue: 0,0:28:59.78,0:29:05.25,Default,,0000,0000,0000,,the spacecraft precisely at L1 without any\Nvelocity, then in relation to Sun and Mars
Dialogue: 0,0:29:05.25,0:29:10.15,Default,,0000,0000,0000,,it will actually stay at the same position.\NOkay, that's pretty cool. However,
Dialogue: 0,0:29:10.15,0:29:15.77,Default,,0000,0000,0000,,mathematicians and physicists will\Nimmediately ask well, OK, but what happens
Dialogue: 0,0:29:15.77,0:29:21.92,Default,,0000,0000,0000,,if I actually put a spacecraft close to a\NLagrangian point? OK, so this is
Dialogue: 0,0:29:21.92,0:29:28.20,Default,,0000,0000,0000,,related to what's called stability. And\Nyou can calculate that around L4 and L5.
Dialogue: 0,0:29:28.20,0:29:33.33,Default,,0000,0000,0000,,The spacecraft will actually stay in the\Nvicinity. So it will essentially rotate
Dialogue: 0,0:29:33.33,0:29:38.98,Default,,0000,0000,0000,,around the Lagrangian points. So those are\Ncalled stable, whereas L1, L2 and L3 are
Dialogue: 0,0:29:38.98,0:29:43.99,Default,,0000,0000,0000,,actually unstable. This means that if you\Nput a spacecraft there, then it will
Dialogue: 0,0:29:43.99,0:29:50.60,Default,,0000,0000,0000,,eventually escape. However, this takes a\Ndifferent amount of time depending on the
Dialogue: 0,0:29:50.60,0:29:55.33,Default,,0000,0000,0000,,Lagrangian points. For example, if you're\Nclose to L2, this might take a few months,
Dialogue: 0,0:29:55.33,0:29:58.73,Default,,0000,0000,0000,,but if you're close to L3, this will\Nactually take something like a hundred
Dialogue: 0,0:29:58.73,0:30:08.14,Default,,0000,0000,0000,,years or so. Okay, so those points are\Nstill different. All right. Okay. So
Dialogue: 0,0:30:08.14,0:30:10.95,Default,,0000,0000,0000,,is there actually any evidence that they\Nexist? I mean, maybe I'm just making this
Dialogue: 0,0:30:10.95,0:30:14.69,Default,,0000,0000,0000,,up and, you know, I mean, haven't shown\Nyou any equations. I could just throw
Dialogue: 0,0:30:14.69,0:30:19.95,Default,,0000,0000,0000,,anything. However, we can actually look at\Nthe solar system. So this is the inner
Dialogue: 0,0:30:19.95,0:30:23.57,Default,,0000,0000,0000,,solar system here. In the middle you see,\Nwell, the center you see the Sun, of
Dialogue: 0,0:30:23.57,0:30:28.97,Default,,0000,0000,0000,,course. And to the lower left, there's\NJupiter. Now, if you imagine an
Dialogue: 0,0:30:28.97,0:30:35.25,Default,,0000,0000,0000,,equilateral triangle of Sun and Jupiter,\Nwell, there are two of them. And then you
Dialogue: 0,0:30:35.25,0:30:40.92,Default,,0000,0000,0000,,see all these green dots there. And those\Nare asteroids. Those are the Trojans and
Dialogue: 0,0:30:40.92,0:30:47.77,Default,,0000,0000,0000,,the Greeks. And they accumulate there\Nbecause L4 and L5 are stable. Okay. So we
Dialogue: 0,0:30:47.77,0:30:55.14,Default,,0000,0000,0000,,can really see this dynamics gone on in\Nthe solar system. However, there's also
Dialogue: 0,0:30:55.14,0:30:59.49,Default,,0000,0000,0000,,various other applications of Lagrangian\Npoints. So in particular, you might want
Dialogue: 0,0:30:59.49,0:31:05.71,Default,,0000,0000,0000,,to put a space telescope somewhere in\Nspace, of course, in such a way that the
Dialogue: 0,0:31:05.71,0:31:11.52,Default,,0000,0000,0000,,Sun is not blinding you. Well, there is\NEarth, of course. So if we can put the
Dialogue: 0,0:31:11.52,0:31:18.98,Default,,0000,0000,0000,,spacecraft behind Earth, then we might be\Nin the shadow. And this is the Lagrangian
Dialogue: 0,0:31:18.98,0:31:24.86,Default,,0000,0000,0000,,point L2, which is the reason why this is\Nactually being used for space telescopes
Dialogue: 0,0:31:24.86,0:31:30.47,Default,,0000,0000,0000,,such as, for example, this one. However,\Nit turns out L2 is unstable. So we don't
Dialogue: 0,0:31:30.47,0:31:35.09,Default,,0000,0000,0000,,really want to put the spacecraft just\Nthere. But instead, we put it in an orbit
Dialogue: 0,0:31:35.09,0:31:40.73,Default,,0000,0000,0000,,close... in a close orbit, close to L2.\NAnd this particular example is called the
Dialogue: 0,0:31:40.73,0:31:44.56,Default,,0000,0000,0000,,Halo orbit, and it's actually not\Ncontained in the planes. I'm cheating a
Dialogue: 0,0:31:44.56,0:31:48.03,Default,,0000,0000,0000,,little bit. It's on the right hand side to\Nyou. And in the animation you actually see
Dialogue: 0,0:31:48.03,0:31:54.11,Default,,0000,0000,0000,,the the orbit from the side. So it\Nactually leaves the plane the blue dot is
Dialogue: 0,0:31:54.11,0:32:00.62,Default,,0000,0000,0000,,Earth and the left hand side you see \Nthe actual orbit from the top. So
Dialogue: 0,0:32:00.62,0:32:06.23,Default,,0000,0000,0000,,it's rotating around this place. OK. So\Nthat's the James Webb Space Telescope, by
Dialogue: 0,0:32:06.23,0:32:11.36,Default,,0000,0000,0000,,the way. You can see in the animation it's\Nsupposed to launch in 2018. That didn't
Dialogue: 0,0:32:11.36,0:32:19.53,Default,,0000,0000,0000,,work out, unfortunately, but stay tuned.\NAnother example. That's how it has become
Dialogue: 0,0:32:19.53,0:32:26.20,Default,,0000,0000,0000,,pretty famous recently as the Chinese\NQueqiao relay satellite. This one sits at
Dialogue: 0,0:32:26.20,0:32:31.09,Default,,0000,0000,0000,,the Earth - Moon L2 Lagrange point. And\Nthe reason for this is that the Chinese
Dialogue: 0,0:32:31.09,0:32:37.65,Default,,0000,0000,0000,,wanted to or actually did land the Chang'e 4\NMoon lander on the backside of the Moon.
Dialogue: 0,0:32:37.65,0:32:41.56,Default,,0000,0000,0000,,And in order to stay in contact, radio\Ncontact with the lander, they had to put a
Dialogue: 0,0:32:41.56,0:32:47.64,Default,,0000,0000,0000,,relay satellite behind the Moon, which\Nthey could still see from Earth. And they
Dialogue: 0,0:32:47.64,0:33:00.10,Default,,0000,0000,0000,,chose some similar orbit around L2. OK. So\Nlet's now go to some other more advanced
Dialogue: 0,0:33:00.10,0:33:07.51,Default,,0000,0000,0000,,technique: ballistic capture. Right. Okay.\NSo this whole business sort of started
Dialogue: 0,0:33:07.51,0:33:14.41,Default,,0000,0000,0000,,with a mission from the beginning of the\N1990s, and that's the Hiten mission. So
Dialogue: 0,0:33:14.41,0:33:19.89,Default,,0000,0000,0000,,that was a Japanese well, Moon probe\Nconsisted of a probe which had a small
Dialogue: 0,0:33:19.89,0:33:26.29,Default,,0000,0000,0000,,orbiter site which was separated, and then\Nit was supposed to actually enter orbit
Dialogue: 0,0:33:26.29,0:33:31.61,Default,,0000,0000,0000,,around Moon. Unfortunately, it missed its\Nmaneuver. So it didn't apply enough delta v
Dialogue: 0,0:33:31.61,0:33:37.57,Default,,0000,0000,0000,,so it actually flew off. And the\Nmission was sort of lost at that point
Dialogue: 0,0:33:37.57,0:33:42.43,Default,,0000,0000,0000,,because Hiten itself, so the main probe\Ndid not have enough fuel to reach the
Dialogue: 0,0:33:42.43,0:33:47.70,Default,,0000,0000,0000,,Moon. All right. That's, of course, a\Nproblem. I mean, that's a risk you have to
Dialogue: 0,0:33:47.70,0:33:53.46,Default,,0000,0000,0000,,take. And they were probably pretty\Ndevastated. However, there were two people
Dialogue: 0,0:33:53.46,0:34:00.78,Default,,0000,0000,0000,,from JPL, NASA, who actually heard about\Nthis, Belbruno and Miller, and they were
Dialogue: 0,0:34:00.78,0:34:08.26,Default,,0000,0000,0000,,working on strange orbits, those ballistic\Ncapture orbits. And they actually found
Dialogue: 0,0:34:08.26,0:34:14.61,Default,,0000,0000,0000,,one for the Hiten probe. They sent this to\Nthe Japanese and they actually use that
Dialogue: 0,0:34:14.61,0:34:23.22,Default,,0000,0000,0000,,orbit to get the Hiten probe to the moon.\NAnd it actually arrived in October 1991.
Dialogue: 0,0:34:23.22,0:34:26.45,Default,,0000,0000,0000,,And then it could do some\Nscience, you know, maybe some
Dialogue: 0,0:34:26.45,0:34:31.39,Default,,0000,0000,0000,,different experiments, but it actually\Narrived there. However, the transfer took
Dialogue: 0,0:34:31.39,0:34:37.07,Default,,0000,0000,0000,,quite a bit longer. So a normal Moon\Ntransfer takes like three days or so. But
Dialogue: 0,0:34:37.07,0:34:42.32,Default,,0000,0000,0000,,this one actually took a few months. All\Nright. And the reason for this is that it
Dialogue: 0,0:34:42.32,0:34:48.60,Default,,0000,0000,0000,,looks pretty weird. So this is a\Npicture of the orbiter - schematic picture.
Dialogue: 0,0:34:48.60,0:34:54.26,Default,,0000,0000,0000,,And you can see the Earth. Well, there in\Nthe middle sort of. And the Moon a bit to
Dialogue: 0,0:34:54.26,0:35:01.82,Default,,0000,0000,0000,,the left at the L2 is the Lagrangian point\Nof the Sun - Earth system. OK. So it's
Dialogue: 0,0:35:01.82,0:35:07.43,Default,,0000,0000,0000,,pretty far out. And you can see that the\Norbit sort of consists of two parts.
Dialogue: 0,0:35:07.43,0:35:13.10,Default,,0000,0000,0000,,First, it leaves Earth and it flies far\Nbeyond the Moon. So somewhere completely
Dialogue: 0,0:35:13.10,0:35:18.91,Default,,0000,0000,0000,,different towards some other Lagrangian\Npoint. That's really far away. Then it
Dialogue: 0,0:35:18.91,0:35:24.28,Default,,0000,0000,0000,,does some weird things. And in the upper\Npart of picture there it actually does a
Dialogue: 0,0:35:24.28,0:35:30.24,Default,,0000,0000,0000,,maneuver. So we apply some thrusts there\Nto be to change on a different orbit. And
Dialogue: 0,0:35:30.24,0:35:36.83,Default,,0000,0000,0000,,this orbit led the probe directly to the\Nmoon where it was essentially captured for
Dialogue: 0,0:35:36.83,0:35:42.32,Default,,0000,0000,0000,,free. OK. So it just entered orbit around\Nthe Moon. And this is, of course, not
Dialogue: 0,0:35:42.32,0:35:46.47,Default,,0000,0000,0000,,possible in the two body problem, but we\Nmay find a way for doing this in the three
Dialogue: 0,0:35:46.47,0:35:56.53,Default,,0000,0000,0000,,body problem. OK, so what do we mean by\Ncapture? Now we have to sort of think
Dialogue: 0,0:35:56.53,0:36:02.32,Default,,0000,0000,0000,,a bit more abstractly. The idea is... \Nwe have Sun and Mars and we
Dialogue: 0,0:36:02.32,0:36:08.10,Default,,0000,0000,0000,,have a spacecraft that flies in this three\Nbody problem. So the red orbit is actually
Dialogue: 0,0:36:08.10,0:36:14.96,Default,,0000,0000,0000,,the orbit of the spacecraft. Now, at any\Npoint in time, we may decide to just
Dialogue: 0,0:36:14.96,0:36:20.97,Default,,0000,0000,0000,,forget about the Sun. OK. So instead we\Nconsider the two body problem of Mars and
Dialogue: 0,0:36:20.97,0:36:26.76,Default,,0000,0000,0000,,a spacecraft. OK. Because at this point\Nin time, the spacecraft has a certain
Dialogue: 0,0:36:26.76,0:36:31.24,Default,,0000,0000,0000,,position relative to Mars and a certain\Nvelocity. So this determines its orbit in
Dialogue: 0,0:36:31.24,0:36:36.44,Default,,0000,0000,0000,,the two body problem. Usually it would be\Nvery fast. So it would be on a hyperbolic
Dialogue: 0,0:36:36.44,0:36:43.27,Default,,0000,0000,0000,,orbit, which is denoted by the dashed line\Nhere. OK. Or a dashed curve. So usually
Dialogue: 0,0:36:43.27,0:36:47.24,Default,,0000,0000,0000,,you happen to be in a hyperbolic orbit.\NBut of course, that orbit is only an
Dialogue: 0,0:36:47.24,0:36:50.28,Default,,0000,0000,0000,,approximation because in the three body\Nproblem, the movement is actually
Dialogue: 0,0:36:50.28,0:36:57.49,Default,,0000,0000,0000,,different. But later on, it might happen\Nthat we continue on the orbit. We can do
Dialogue: 0,0:36:57.49,0:37:01.53,Default,,0000,0000,0000,,the same kind of construction, but just\Nlooking... but just ignoring the Sun
Dialogue: 0,0:37:01.53,0:37:09.71,Default,,0000,0000,0000,,essentially, and then we could find that\Nthe spacecraft suddenly is in a elliptical
Dialogue: 0,0:37:09.71,0:37:14.19,Default,,0000,0000,0000,,orbit. This would mean that if you\Nforgot about the Sun, then the spacecraft
Dialogue: 0,0:37:14.19,0:37:19.67,Default,,0000,0000,0000,,would be stable and would be captured by\NMars. It would be there. That would be
Dialogue: 0,0:37:19.67,0:37:27.21,Default,,0000,0000,0000,,pretty nice. So this phenomenon, when this\Nhappens, we call this a temporary capture.
Dialogue: 0,0:37:27.21,0:37:33.81,Default,,0000,0000,0000,,OK. Temporary because it might actually\Nleave that situation again later on. Now,
Dialogue: 0,0:37:33.81,0:37:37.32,Default,,0000,0000,0000,,because the actual movement depends on the\Nthree body problem, which is super
Dialogue: 0,0:37:37.32,0:37:42.15,Default,,0000,0000,0000,,complicated. So it's possible that it\Nactually leaves again. But for that moment
Dialogue: 0,0:37:42.15,0:37:46.30,Default,,0000,0000,0000,,at least, it's captured and we want to\Nfind a way or describe some kind of
Dialogue: 0,0:37:46.30,0:37:54.00,Default,,0000,0000,0000,,algorithm perhaps how we can find\Nthis situation essentially. OK, and in a
Dialogue: 0,0:37:54.00,0:38:01.45,Default,,0000,0000,0000,,reasonable way, and the notion for this is\Nwhat's called, well, n-stability, the idea
Dialogue: 0,0:38:01.45,0:38:08.02,Default,,0000,0000,0000,,is the following: we look at the three\Nbody probleme, we want to go to Mars. So we
Dialogue: 0,0:38:08.02,0:38:13.25,Default,,0000,0000,0000,,pick a line there. And on the line we take\Na point x, which has some distance r to
Dialogue: 0,0:38:13.25,0:38:20.09,Default,,0000,0000,0000,,the Mars and we pick a perpendicular\Nspeed, a perpendicular velocity to the
Dialogue: 0,0:38:20.09,0:38:25.81,Default,,0000,0000,0000,,line such that this corresponds to some\Nkind of elliptic orbit in the two body
Dialogue: 0,0:38:25.81,0:38:30.29,Default,,0000,0000,0000,,problem. Okay. So that's the dashed line.\NBut then we actually look at the problem
Dialogue: 0,0:38:30.29,0:38:37.82,Default,,0000,0000,0000,,in the three body problem and we just\Nevolve the spacecraft. And it's following
Dialogue: 0,0:38:37.82,0:38:46.08,Default,,0000,0000,0000,,the red orbit. It might follow the red\Norbit. And it can happen that after going
Dialogue: 0,0:38:46.08,0:38:54.20,Default,,0000,0000,0000,,around Mars for one time, it hits again\Nthe line. Okay, then we can do the same
Dialogue: 0,0:38:54.20,0:38:59.54,Default,,0000,0000,0000,,construction with forgetting the Sun again\Nand just look at the two body problem. And
Dialogue: 0,0:38:59.54,0:39:04.99,Default,,0000,0000,0000,,it's possible that this point actually\Nstill corresponds to an elliptic orbit.
Dialogue: 0,0:39:04.99,0:39:10.87,Default,,0000,0000,0000,,That's somewhat interesting, right?\NBecause now this means that if we actually
Dialogue: 0,0:39:10.87,0:39:17.12,Default,,0000,0000,0000,,hit the point x, then we can follow the\Norbit and we know that we wrap around
Dialogue: 0,0:39:17.12,0:39:24.03,Default,,0000,0000,0000,,Mars once and are still sort of captured\Nin the corresponding two body problem.
Dialogue: 0,0:39:24.03,0:39:29.23,Default,,0000,0000,0000,,Okay. If we actually are able to wrap\Naround Mars twice, then we would call this
Dialogue: 0,0:39:29.23,0:39:35.98,Default,,0000,0000,0000,,2-stable and, well, for more rotations\Nthat it is n-stable. Okay, so that's good
Dialogue: 0,0:39:35.98,0:39:39.17,Default,,0000,0000,0000,,because such an orbit corresponds to\Nsomething that's usable because we will
Dialogue: 0,0:39:39.17,0:39:45.37,Default,,0000,0000,0000,,wrap around Mars n times. However, it's\Nalso possible that you have an unstable
Dialogue: 0,0:39:45.37,0:39:49.02,Default,,0000,0000,0000,,point, meaning that we again start in\Nsomething that corresponds to an ellipse
Dialogue: 0,0:39:49.02,0:39:54.17,Default,,0000,0000,0000,,around Mars. But if we actually follow the\Norbit in a three body problem, it will,
Dialogue: 0,0:39:54.17,0:39:58.11,Default,,0000,0000,0000,,for example, not come back. It will not\Nwrap around Mars, it will go to the Sun or
Dialogue: 0,0:39:58.11,0:40:03.47,Default,,0000,0000,0000,,somewhere else. OK. So that's that's of\Ncourse, not a nice point. This one's
Dialogue: 0,0:40:03.47,0:40:10.48,Default,,0000,0000,0000,,called unstable. And then there's another\Nthing we can do. That's actually a pretty
Dialogue: 0,0:40:10.48,0:40:18.28,Default,,0000,0000,0000,,common trick in finding orbits, etc. We\Ncan instead of solving the problem in
Dialogue: 0,0:40:18.28,0:40:23.97,Default,,0000,0000,0000,,forward time we actually go back, okay. So\Nessentially in your program you just
Dialogue: 0,0:40:23.97,0:40:28.81,Default,,0000,0000,0000,,replace time by minus time, for example,\Nand then you just solve the thing and you
Dialogue: 0,0:40:28.81,0:40:37.07,Default,,0000,0000,0000,,go back in the past and it's possible \Nthat a point that corresponds to such
Dialogue: 0,0:40:37.07,0:40:41.64,Default,,0000,0000,0000,,an ellipse when you go back into the past\Nand it does not wrap around, but it
Dialogue: 0,0:40:41.64,0:40:47.01,Default,,0000,0000,0000,,actually goes to the Sun, for example, we\Ncall this unstable in the past. Okay. So
Dialogue: 0,0:40:47.01,0:40:56.68,Default,,0000,0000,0000,,that's just some random definition. \NAnd we can use this. The reason for
Dialogue: 0,0:40:56.68,0:41:05.08,Default,,0000,0000,0000,,this is we can actually kind of take these\Nconcepts together and build an orbit from
Dialogue: 0,0:41:05.08,0:41:13.02,Default,,0000,0000,0000,,that. The idea being we pick a point x\Nthat is n-stable. So, for example, it
Dialogue: 0,0:41:13.02,0:41:19.71,Default,,0000,0000,0000,,might wrap around Mars six times, some\Nnumber that we like. This is the blue part
Dialogue: 0,0:41:19.71,0:41:24.13,Default,,0000,0000,0000,,here in the picture. So it wraps around\NMars six times. But the way we go back in
Dialogue: 0,0:41:24.13,0:41:30.56,Default,,0000,0000,0000,,time, it actually leaves Mars or at least\Nit doesn't come back in such a way that
Dialogue: 0,0:41:30.56,0:41:42.07,Default,,0000,0000,0000,,it's again on an ecliptic curve. So this\Nis the red part. Okay. So we can
Dialogue: 0,0:41:42.07,0:41:48.39,Default,,0000,0000,0000,,just follow this and then we pick a point\Ny on that curve. Okay. So this one will be
Dialogue: 0,0:41:48.39,0:41:57.99,Default,,0000,0000,0000,,pretty far away from Mars or we can choose\Nit. And then we sort of use a Hohmann
Dialogue: 0,0:41:57.99,0:42:03.65,Default,,0000,0000,0000,,transfer to get from Earth to that point\Ny. Okay? So our orbit actually consists of
Dialogue: 0,0:42:03.65,0:42:08.52,Default,,0000,0000,0000,,three parts now. Okay. So we have the\NHohmann transfer, but it's not actually
Dialogue: 0,0:42:08.52,0:42:14.39,Default,,0000,0000,0000,,aiming for Mars. It's actually aiming for\Nthe point y. There we do a maneuver
Dialogue: 0,0:42:14.39,0:42:21.47,Default,,0000,0000,0000,,because we want to switch onto this red\Norbit. Okay. And then this one will bring
Dialogue: 0,0:42:21.47,0:42:28.78,Default,,0000,0000,0000,,us to the point x where we know because it\Nwas constructed in this way that the
Dialogue: 0,0:42:28.78,0:42:36.05,Default,,0000,0000,0000,,spacecraft will continue to rotate around\NMars for example six times. Okay. So in
Dialogue: 0,0:42:36.05,0:42:43.62,Default,,0000,0000,0000,,particular at x there is no maneuver\Ntaking place. Okay. So that's a
Dialogue: 0,0:42:43.62,0:42:49.36,Default,,0000,0000,0000,,possible mission scenario. And the way\Nthis is done then usually is you kind of..
Dialogue: 0,0:42:49.36,0:42:54.28,Default,,0000,0000,0000,,you calculate these points x that\Nare suitable for doing this. Okay. So they
Dialogue: 0,0:42:54.28,0:42:58.46,Default,,0000,0000,0000,,have to be stable and unstable in the past\Nat the same time. So we have to find them.
Dialogue: 0,0:42:58.46,0:43:02.50,Default,,0000,0000,0000,,And there's a lot of numerical\Ncomputations involved in that. But once we
Dialogue: 0,0:43:02.50,0:43:07.48,Default,,0000,0000,0000,,have this, you can actually build these\Norbits. OK. So let's look at an actual
Dialogue: 0,0:43:07.48,0:43:16.02,Default,,0000,0000,0000,,example. So this is for Earth - Mars. On\Nthe left, you see, well, that the two
Dialogue: 0,0:43:16.02,0:43:23.38,Default,,0000,0000,0000,,circular orbits of Earth, Mars, and on the\Nright you see the same orbit, but from a
Dialogue: 0,0:43:23.38,0:43:28.37,Default,,0000,0000,0000,,point of view centered around Mars. Okay.\NAnd the colors correspond to each other.
Dialogue: 0,0:43:28.37,0:43:32.50,Default,,0000,0000,0000,,So the mission starts on the left side by\Ndoing a Hohmann transfer. So that's the
Dialogue: 0,0:43:32.50,0:43:35.77,Default,,0000,0000,0000,,black line starting at Earth and then\Nhitting the point, which is called x_c
Dialogue: 0,0:43:35.77,0:43:42.29,Default,,0000,0000,0000,,here. So that's the y that I had on \Nthe other slide. So this point y
Dialogue: 0,0:43:42.29,0:43:47.93,Default,,0000,0000,0000,,or x_c here is pretty far away still from\NMars. There we do a maneuver and we switch
Dialogue: 0,0:43:47.93,0:43:56.73,Default,,0000,0000,0000,,under the red orbit. Which brings us to\Nthe point x closer to Mars, after which we
Dialogue: 0,0:43:56.73,0:44:01.31,Default,,0000,0000,0000,,will actually start rotating round Mars.\NAnd the point x is actually at the top of
Dialogue: 0,0:44:01.31,0:44:08.51,Default,,0000,0000,0000,,this picture. Okay. And then on the right\Nyou can see the orbit and it's looking
Dialogue: 0,0:44:08.51,0:44:13.55,Default,,0000,0000,0000,,pretty strangely. And also the red\Norbit is when we kind of the capture orbit
Dialogue: 0,0:44:13.55,0:44:19.18,Default,,0000,0000,0000,,our way to actually get to Mars. And then\Nif you look very carefully, you can count
Dialogue: 0,0:44:19.18,0:44:26.71,Default,,0000,0000,0000,,we actually rotate around Mars six\Ntimes. Okay. Now, during those six
Dialogue: 0,0:44:26.71,0:44:32.17,Default,,0000,0000,0000,,rotations around Mars, we could do\Nexperiments. So maybe that is enough for
Dialogue: 0,0:44:32.17,0:44:37.00,Default,,0000,0000,0000,,whatever we are trying to do. OK. However,\Nif we want to stay there, we need to
Dialogue: 0,0:44:37.00,0:44:44.80,Default,,0000,0000,0000,,actually execute another maneuver. OK. So\Nto actually stay around Mars. And I mean,
Dialogue: 0,0:44:44.80,0:44:48.06,Default,,0000,0000,0000,,the principle looks nice but of course,\Nyou have to do some calculations. We have
Dialogue: 0,0:44:48.06,0:44:55.64,Default,,0000,0000,0000,,to find some ways to actually quantify how\Ngood this is. And it turns out that there
Dialogue: 0,0:44:55.64,0:45:02.41,Default,,0000,0000,0000,,are few parameters that you can choose, \Nin particular the target point x, this has
Dialogue: 0,0:45:02.41,0:45:07.31,Default,,0000,0000,0000,,a certain distance that you're aiming for\Nat around Mars. And it turns out that this
Dialogue: 0,0:45:07.31,0:45:14.09,Default,,0000,0000,0000,,procedure here, for example, is only very\Ngood if this altitude, this distance r is
Dialogue: 0,0:45:14.09,0:45:17.95,Default,,0000,0000,0000,,actually high enough. If it is high enough\Nthen you can save - in principle - up to
Dialogue: 0,0:45:17.95,0:45:23.72,Default,,0000,0000,0000,,twenty three percent of the delta v, which\Nis enormous. OK. So that would
Dialogue: 0,0:45:23.72,0:45:29.05,Default,,0000,0000,0000,,be really good. However, in reality it's\Nnot as good usually. Yeah. And for a
Dialogue: 0,0:45:29.05,0:45:34.53,Default,,0000,0000,0000,,certain lower distances, for example, you\Ncannot save anything, so there are
Dialogue: 0,0:45:34.53,0:45:40.81,Default,,0000,0000,0000,,certain tradeoffs to make. However, there\Nis another advantage. Remember this point y?
Dialogue: 0,0:45:40.81,0:45:45.99,Default,,0000,0000,0000,,We chose this along this capture orbit\Nalong the red orbit. And the thing is, we
Dialogue: 0,0:45:45.99,0:45:51.38,Default,,0000,0000,0000,,can actually choose this freely. This\Nmeans that our Hohmann transfer doesn't
Dialogue: 0,0:45:51.38,0:45:55.00,Default,,0000,0000,0000,,need to hit Mars directly when it's there.\NSo it doesn't need to aim for that
Dialogue: 0,0:45:55.00,0:46:02.97,Default,,0000,0000,0000,,particular point. It can actually aim for\Nany point on that capture orbit. This
Dialogue: 0,0:46:02.97,0:46:06.31,Default,,0000,0000,0000,,means that we have many more Hohmann\Ntransfers available that we can actually
Dialogue: 0,0:46:06.31,0:46:12.50,Default,,0000,0000,0000,,use to get there. This means that we have\Na far larger transfer window. OK. So we
Dialogue: 0,0:46:12.50,0:46:17.73,Default,,0000,0000,0000,,cannot just start every 26 months. But now\Nwe, with this technique, we could actually
Dialogue: 0,0:46:17.73,0:46:24.46,Default,,0000,0000,0000,,launch. Well, quite often. However,\Nthere's a little problem. If you looked at
Dialogue: 0,0:46:24.46,0:46:33.95,Default,,0000,0000,0000,,the graph carefully, then you may have\Nseen that the red orbit actually took like
Dialogue: 0,0:46:33.95,0:46:39.35,Default,,0000,0000,0000,,three quarters of the rotation of Mars.\NThis corresponds to roughly something like
Dialogue: 0,0:46:39.35,0:46:43.75,Default,,0000,0000,0000,,400 days. OK. So this takes a long time.\NSo you probably don't want to use this
Dialogue: 0,0:46:43.75,0:46:49.06,Default,,0000,0000,0000,,with humans on board because they have to\Nactually wait for a long time. But in
Dialogue: 0,0:46:49.06,0:46:52.89,Default,,0000,0000,0000,,principle, there are ways to make this\Nshorter. So you can try to actually
Dialogue: 0,0:46:52.89,0:46:58.45,Default,,0000,0000,0000,,improve on this, but in general, it takes\Na long time. So let's look at a real
Dialogue: 0,0:46:58.45,0:47:04.61,Default,,0000,0000,0000,,example for this. Again, that's\NBepicolombo. The green dot is now Mercury.
Dialogue: 0,0:47:04.61,0:47:09.87,Default,,0000,0000,0000,,So this is kind of a zoom of the other\Nanimation and the purple line is the
Dialogue: 0,0:47:09.87,0:47:20.64,Default,,0000,0000,0000,,orbit. And yeah, it looks strange. So the\Nfirst few movements around Mercury,
Dialogue: 0,0:47:20.64,0:47:28.30,Default,,0000,0000,0000,,they are actually the last gravity assists\Nfor slowing down. And then it actually
Dialogue: 0,0:47:28.30,0:47:36.78,Default,,0000,0000,0000,,starts on the capture orbit. So now it\Nactually approaches Mercury. So this is
Dialogue: 0,0:47:36.78,0:47:41.01,Default,,0000,0000,0000,,the part that's sort of difficult to find,\Nbut which you can do with this stability.
Dialogue: 0,0:47:41.01,0:47:45.61,Default,,0000,0000,0000,,And once the animation actually ends,\Nthis is when it actually reaches the point
Dialogue: 0,0:47:45.61,0:47:52.24,Default,,0000,0000,0000,,when it's temporarily captured. So in this\Ncase, this is at an altitude of 180,000
Dialogue: 0,0:47:52.24,0:47:58.09,Default,,0000,0000,0000,,kilometers. So it is pretty high up above\NMercury, but it's enough for the mission.
Dialogue: 0,0:47:58.09,0:48:03.27,Default,,0000,0000,0000,,OK. And of course, then they do some\Nother maneuver to actually stay around
Dialogue: 0,0:48:03.27,0:48:12.23,Default,,0000,0000,0000,,Mercury. Okay, so in the last few minutes,\Nlet's have a look. Let's have a brief look
Dialogue: 0,0:48:12.23,0:48:18.100,Default,,0000,0000,0000,,at how we can actually extend this. So I\Nwill be very brief here, because while we
Dialogue: 0,0:48:18.100,0:48:23.60,Default,,0000,0000,0000,,can try to actually make this more general\Nto improve on this, this concept is then
Dialogue: 0,0:48:23.60,0:48:29.04,Default,,0000,0000,0000,,called the interplanetary transport\Nnetwork. And it looks a bit similar to
Dialogue: 0,0:48:29.04,0:48:36.29,Default,,0000,0000,0000,,what we just saw. The idea is that, in\Nfact, this capture orbit is part of a
Dialogue: 0,0:48:36.29,0:48:42.95,Default,,0000,0000,0000,,larger well, a set of orbits that have\Nthese kinds of properties that wrap around
Dialogue: 0,0:48:42.95,0:48:48.52,Default,,0000,0000,0000,,Mars and then kind of leave Mars. And \Nthey are very closely related to the
Dialogue: 0,0:48:48.52,0:48:53.28,Default,,0000,0000,0000,,dynamics of particular Lagrangian points,\Nin this case L1. So that was the one
Dialogue: 0,0:48:53.28,0:49:00.33,Default,,0000,0000,0000,,between the two masses. And if you\Ninvestigate this Lagrangian point a bit
Dialogue: 0,0:49:00.33,0:49:05.53,Default,,0000,0000,0000,,closer, you can see, well, you can see\Ndifferent orbits of all kinds of
Dialogue: 0,0:49:05.53,0:49:10.65,Default,,0000,0000,0000,,behaviors. And if you understand this,\Nthen you can actually try to do the same
Dialogue: 0,0:49:10.65,0:49:16.88,Default,,0000,0000,0000,,thing on the other side of the Lagrangian\Npoint. OK. So we just kind of switch from
Dialogue: 0,0:49:16.88,0:49:21.44,Default,,0000,0000,0000,,Mars to the Sun and we do a similar thing\Nthere. Now we expect to actually find
Dialogue: 0,0:49:21.44,0:49:24.92,Default,,0000,0000,0000,,similar orbits that are wrapping around\Nthe Sun and then going towards this
Dialogue: 0,0:49:24.92,0:49:31.86,Default,,0000,0000,0000,,Lagrangian point in a similar way. Well,\Nthen we already have some orbits that are
Dialogue: 0,0:49:31.86,0:49:39.27,Default,,0000,0000,0000,,well, kind of meeting at L1. So we might\Nbe able to actually connect them somehow,
Dialogue: 0,0:49:39.27,0:49:45.07,Default,,0000,0000,0000,,for example by maneuver. And then we only\Nneed to reach the orbit around Earth or
Dialogue: 0,0:49:45.07,0:49:50.13,Default,,0000,0000,0000,,around Sun from Earth. OK. If you find a\Nway to do this, you can get rid of the
Dialogue: 0,0:49:50.13,0:49:55.27,Default,,0000,0000,0000,,Hohmann transfer. And this way you reduce\Nyour delta v even further. The problem is
Dialogue: 0,0:49:55.27,0:50:00.69,Default,,0000,0000,0000,,that this is hard to find because these\Norbits they are pretty rare. And of
Dialogue: 0,0:50:00.69,0:50:07.32,Default,,0000,0000,0000,,course, you have to connect those orbits.\NSo they you approach the Lagrangian point
Dialogue: 0,0:50:07.32,0:50:14.33,Default,,0000,0000,0000,,from L1 from two sides, but you don't\Nreally want to wait forever until they...
Dialogue: 0,0:50:14.33,0:50:19.63,Default,,0000,0000,0000,,it's very easy to switch or so, so instead\Nyou apply some delta v, OK, in order to
Dialogue: 0,0:50:19.63,0:50:24.49,Default,,0000,0000,0000,,not wait that long. So here's a picture \Nof how this might look like. Again
Dialogue: 0,0:50:24.49,0:50:28.96,Default,,0000,0000,0000,,very schematic. So we have Sun, we\Nhave Mars and in between there is the
Dialogue: 0,0:50:28.96,0:50:35.24,Default,,0000,0000,0000,,Lagrangian point L1. The red orbit is sort\Nof an extension of one of those capture
Dialogue: 0,0:50:35.24,0:50:38.23,Default,,0000,0000,0000,,orbits that we have seen. OK, so that\Nwraps around Mars a certain number of
Dialogue: 0,0:50:38.23,0:50:45.35,Default,,0000,0000,0000,,times. And while in the past, for example,\Nit actually goes to Lagrangian point. I
Dialogue: 0,0:50:45.35,0:50:50.78,Default,,0000,0000,0000,,didn't explain this, but in fact, there\Nare many more orbits around L1, closed
Dialogue: 0,0:50:50.78,0:50:55.46,Default,,0000,0000,0000,,orbits, but they're all unstable. And\Nthese orbits that are used in this
Dialogue: 0,0:50:55.46,0:51:05.03,Default,,0000,0000,0000,,interplanetary transport network they\Nactually approach those orbits around L1
Dialogue: 0,0:51:05.03,0:51:10.57,Default,,0000,0000,0000,,and we do the same thing on the other side\Nof the Sun now and then the idea is, OK,
Dialogue: 0,0:51:10.57,0:51:15.59,Default,,0000,0000,0000,,we take these orbits, we connect\Nthem. And when we are in the black orbit
Dialogue: 0,0:51:15.59,0:51:19.07,Default,,0000,0000,0000,,around L1, we actually apply some\Nmaneuver, we apply some delta v to
Dialogue: 0,0:51:19.07,0:51:22.45,Default,,0000,0000,0000,,actually switch from one to the other. And\Nthen we have sort of a connection of how
Dialogue: 0,0:51:22.45,0:51:28.50,Default,,0000,0000,0000,,to get from Sun to Mars. So we just need\Nto do a similar thing again from for Earth
Dialogue: 0,0:51:28.50,0:51:35.12,Default,,0000,0000,0000,,to this particular blue orbit around the\NSun. OK. So that's the general procedure.
Dialogue: 0,0:51:35.12,0:51:38.05,Default,,0000,0000,0000,,But of course, it's difficult. And in the\Nend, you have to do a lot of numerics
Dialogue: 0,0:51:38.05,0:51:44.84,Default,,0000,0000,0000,,because as I said at the beginning, this\Nis just a brief overview. It's not all the
Dialogue: 0,0:51:44.84,0:51:50.90,Default,,0000,0000,0000,,details. Please don't launch your \Nown mission tomorrow. OK. So with
Dialogue: 0,0:51:50.90,0:51:54.96,Default,,0000,0000,0000,,this, I want to thank you. \NAnd I'm open to questions.
Dialogue: 0,0:51:54.96,0:52:05.64,Default,,0000,0000,0000,,{\i1}Applause{\i0}
Dialogue: 0,0:52:05.64,0:52:08.21,Default,,0000,0000,0000,,Herald: So thank you Sven for an\Ninteresting talk. We have a few minutes
Dialogue: 0,0:52:08.21,0:52:11.16,Default,,0000,0000,0000,,for questions, if you have any questions\Nlined up next to the microphones, we'll
Dialogue: 0,0:52:11.16,0:52:18.40,Default,,0000,0000,0000,,start with microphone number one.\NMic1: Hello. So what are the problems
Dialogue: 0,0:52:18.40,0:52:22.68,Default,,0000,0000,0000,,associated? So you showed in the end is\Ngoing around to Lagrange Point L1?
Dialogue: 0,0:52:22.68,0:52:26.71,Default,,0000,0000,0000,,Although this is also possible for
Dialogue: 0,0:52:26.71,0:52:30.14,Default,,0000,0000,0000,,other Lagrange points. Could you do this\Nwith L2?
Dialogue: 0,0:52:30.14,0:52:38.18,Default,,0000,0000,0000,,Sven: Yes, you can. Yeah. So in principle,\NI didn't show the whole picture, but
Dialogue: 0,0:52:38.18,0:52:43.11,Default,,0000,0000,0000,,these kind of orbits, they exist at L1,\Nbut they also exist at L2. And in
Dialogue: 0,0:52:43.11,0:52:49.08,Default,,0000,0000,0000,,principle you can this way sort of leave\Nthis two body problem by finding similar
Dialogue: 0,0:52:49.08,0:52:53.65,Default,,0000,0000,0000,,orbits. But of course the the details are\Ndifferent. So you cannot really take your
Dialogue: 0,0:52:53.65,0:52:58.64,Default,,0000,0000,0000,,knowledge or your calculations from L1\Nand just taking over to L2, you actually
Dialogue: 0,0:52:58.64,0:53:03.19,Default,,0000,0000,0000,,have to do the same thing again. You have\Nto calculate everything in detail.
Dialogue: 0,0:53:03.19,0:53:06.65,Default,,0000,0000,0000,,Herald: To a question from the Internet.\NSignal Angel: Is it possible to use these
Dialogue: 0,0:53:06.65,0:53:11.35,Default,,0000,0000,0000,,kinds of transfers in Kerbal Space\NProgram?
Dialogue: 0,0:53:11.35,0:53:23.50,Default,,0000,0000,0000,,Sven: So Hohmann transfers, of course,\Nthe gravity assists as well, but not the
Dialogue: 0,0:53:23.50,0:53:28.90,Default,,0000,0000,0000,,restricted three body problem because the\Nway Kerbal Space Program at least the
Dialogue: 0,0:53:28.90,0:53:33.45,Default,,0000,0000,0000,,default installation so without any mods\Nworks is that it actually switches the
Dialogue: 0,0:53:33.45,0:53:40.27,Default,,0000,0000,0000,,gravitational force. So the thing that I\Ndescribed as a patch solution where we
Dialogue: 0,0:53:40.27,0:53:46.22,Default,,0000,0000,0000,,kind of switch our picture, which\Ngravitational force we consider for our
Dialogue: 0,0:53:46.22,0:53:50.62,Default,,0000,0000,0000,,two body problem. This is actually the way\Nthe physics is implemented in Kerbal space
Dialogue: 0,0:53:50.62,0:53:55.40,Default,,0000,0000,0000,,program. So we can't really do the\Ninterplanetary transport network there.
Dialogue: 0,0:53:55.40,0:54:00.09,Default,,0000,0000,0000,,However, I think there's a mod that allows\Nthis, but your computer might be too slow
Dialogue: 0,0:54:00.09,0:54:04.35,Default,,0000,0000,0000,,for this, I don't know.\NHerald: If you're leaving please do so
Dialogue: 0,0:54:04.35,0:54:07.44,Default,,0000,0000,0000,,quietly. Small question and question from\Nmicrophone number four.
Dialogue: 0,0:54:07.44,0:54:12.62,Default,,0000,0000,0000,,Mic4: Hello. I have actually two\Nquestions. I hope that's okay. First
Dialogue: 0,0:54:12.62,0:54:18.29,Default,,0000,0000,0000,,question is, I wonder how you do that in\Nlike your practical calculations. Like you
Dialogue: 0,0:54:18.29,0:54:22.95,Default,,0000,0000,0000,,said, there's a two body problem and \Nthere are solutions that you can
Dialogue: 0,0:54:22.95,0:54:27.44,Default,,0000,0000,0000,,calculate with a two body problem. And\Nthen there's a three body problem. And I
Dialogue: 0,0:54:27.44,0:54:32.05,Default,,0000,0000,0000,,imagine there's an n-body problem all the\Ntime you do things. So how does it look
Dialogue: 0,0:54:32.05,0:54:37.89,Default,,0000,0000,0000,,when you do that? And the second\Nquestion is: you said that reducing delta v
Dialogue: 0,0:54:37.89,0:54:47.77,Default,,0000,0000,0000,,about 15% is enormous. And I wonder what\Neffect does this have on the payload?
Dialogue: 0,0:54:47.77,0:54:57.55,Default,,0000,0000,0000,,Sven: Okay. So regarding the first\Nquestion. So in principle, I mean, you
Dialogue: 0,0:54:57.55,0:55:05.21,Default,,0000,0000,0000,,make a plan for a mission. So you have to\Nyou calculate those things in these
Dialogue: 0,0:55:05.21,0:55:08.91,Default,,0000,0000,0000,,simplified models. Okay. You kind of you\Npatch together an idea of what you want to
Dialogue: 0,0:55:08.91,0:55:14.91,Default,,0000,0000,0000,,do. But of course, in the end, you're\Nright, there are actually many massive
Dialogue: 0,0:55:14.91,0:55:19.25,Default,,0000,0000,0000,,bodies in the solar system. And because we\Nwant to be precise, we actually have to
Dialogue: 0,0:55:19.25,0:55:25.28,Default,,0000,0000,0000,,incorporate all of them. So in the end,\Nyou have to do an actual numerical search
Dialogue: 0,0:55:25.28,0:55:32.01,Default,,0000,0000,0000,,in a much more complicated n-body problem.\NSo with, I don't know, 100 bodies or so
Dialogue: 0,0:55:32.01,0:55:37.80,Default,,0000,0000,0000,,and you have to incorporate other effects.\NFor example, the solar radiation might
Dialogue: 0,0:55:37.80,0:55:43.23,Default,,0000,0000,0000,,actually have a little influence on your\Norbit. Okay. And there are many effects of
Dialogue: 0,0:55:43.23,0:55:48.04,Default,,0000,0000,0000,,this kind. So once you have a rough idea\Nof what you want to do, you need to take
Dialogue: 0,0:55:48.04,0:55:53.26,Default,,0000,0000,0000,,your very good physics simulator for the\Nn-body problem, which actually has all
Dialogue: 0,0:55:53.26,0:55:57.05,Default,,0000,0000,0000,,these other effects as well. And then you\Nneed to do a numerical search over this.
Dialogue: 0,0:55:57.05,0:56:01.41,Default,,0000,0000,0000,,Kind of, you know, where to start with\Nthese ideas, where to look for solutions.
Dialogue: 0,0:56:01.41,0:56:06.68,Default,,0000,0000,0000,,But then you actually have to just try it\Nand figure out some algorithm to actually
Dialogue: 0,0:56:06.68,0:56:12.01,Default,,0000,0000,0000,,approach a solution that has to behaviors\Nthat you want. But it's a lot of numerics.
Dialogue: 0,0:56:12.01,0:56:16.50,Default,,0000,0000,0000,,Right. And the second question, can you\Nremind me again? Sorry.
Dialogue: 0,0:56:16.50,0:56:23.55,Default,,0000,0000,0000,,Mic4: Well, the second question was in\Nreducing delta v about 15%. What is the
Dialogue: 0,0:56:23.55,0:56:28.89,Default,,0000,0000,0000,,effect on the payload?\NSven: Right. So, I mean, if you need
Dialogue: 0,0:56:28.89,0:56:35.75,Default,,0000,0000,0000,,15% less fuel, then of course you can use\N15% more weight for more mass for the
Dialogue: 0,0:56:35.75,0:56:40.45,Default,,0000,0000,0000,,payload. Right. So you could put maybe\Nanother instrument on there. Another thing
Dialogue: 0,0:56:40.45,0:56:46.12,Default,,0000,0000,0000,,you could do is actually keep the fuel but\Nactually use it for station keeping. So,
Dialogue: 0,0:56:46.12,0:56:52.55,Default,,0000,0000,0000,,for example, in the James Webb telescope\Nexample, the James Webb telescope flies
Dialogue: 0,0:56:52.55,0:56:58.84,Default,,0000,0000,0000,,around this Halo orbit around L2, but the\Norbit itself is unstable. So the James
Dialogue: 0,0:56:58.84,0:57:03.98,Default,,0000,0000,0000,,Webb Space Telescope will actually escape\Nfrom that orbit. So they have to do a few
Dialogue: 0,0:57:03.98,0:57:08.14,Default,,0000,0000,0000,,maneuvers every year to actually stay\Nthere. And they have only a finite amount
Dialogue: 0,0:57:08.14,0:57:13.43,Default,,0000,0000,0000,,of fuels at some point. This won't be\Npossible anymore. So reducing delta v
Dialogue: 0,0:57:13.43,0:57:20.61,Default,,0000,0000,0000,,requirements might actually have increased\Nthe mission lifetime by quite a bit.
Dialogue: 0,0:57:20.61,0:57:25.16,Default,,0000,0000,0000,,Herald: Number three.\NMic3: Hey. When you do such a
Dialogue: 0,0:57:25.16,0:57:29.87,Default,,0000,0000,0000,,mission, I guess you have to adjust the\Ntrajectory of your satellite quite often
Dialogue: 0,0:57:29.87,0:57:34.19,Default,,0000,0000,0000,,because nothing goes exactly as you\Ncalculated it. Right. And the question is,
Dialogue: 0,0:57:34.19,0:57:38.93,Default,,0000,0000,0000,,how precise can you measure the orbit?\NSorry, the position and the speed of a
Dialogue: 0,0:57:38.93,0:57:43.59,Default,,0000,0000,0000,,spacecraft at, let's say, Mars. What's the\Nresolution?
Dialogue: 0,0:57:43.59,0:57:48.30,Default,,0000,0000,0000,,Sven: Right. So from Mars, I'm not\Ncompletely sure how precise it is. But for
Dialogue: 0,0:57:48.30,0:57:52.30,Default,,0000,0000,0000,,example, if you have an Earth observation\Nmission, so something that's flying around
Dialogue: 0,0:57:52.30,0:57:58.50,Default,,0000,0000,0000,,Earth, then you can have a rather precise\Norbit that's good enough for taking
Dialogue: 0,0:57:58.50,0:58:04.22,Default,,0000,0000,0000,,pictures on Earth, for example, for\Nsomething like two weeks or so. So
Dialogue: 0,0:58:04.22,0:58:12.08,Default,,0000,0000,0000,,you can measure the orbit well enough and\Ncalculate the future something like two
Dialogue: 0,0:58:12.08,0:58:21.14,Default,,0000,0000,0000,,weeks in the future. OK. So that's good\Nenough. However. Yeah. The... I can't
Dialogue: 0,0:58:21.14,0:58:25.97,Default,,0000,0000,0000,,really give you good numbers on what the\Naccuracy is, but depending on the
Dialogue: 0,0:58:25.97,0:58:30.62,Default,,0000,0000,0000,,situation, you know, it can get pretty\Nwell for Mars I guess that's pretty
Dialogue: 0,0:58:30.62,0:58:35.44,Default,,0000,0000,0000,,far, I guess that will be a bit less.\NHerald: A very short question for
Dialogue: 0,0:58:35.44,0:58:38.78,Default,,0000,0000,0000,,microphone number one, please.\NMic1: Thank you. Thank you for the talk.
Dialogue: 0,0:58:38.78,0:58:44.54,Default,,0000,0000,0000,,I have a small question. As you said, you\Nroughly plan the trip using the three
Dialogue: 0,0:58:44.54,0:58:50.54,Default,,0000,0000,0000,,body and two body problems. And are there\Nany stable points like Lagrangian points
Dialogue: 0,0:58:50.54,0:58:54.06,Default,,0000,0000,0000,,in there, for example, four body problem?\NAnd can you use them to... during the
Dialogue: 0,0:58:54.06,0:58:59.53,Default,,0000,0000,0000,,roughly planning stage of...\NSven: Oh, yeah. I actually wondered
Dialogue: 0,0:58:59.53,0:59:03.83,Default,,0000,0000,0000,,about this very recently as well. And I\Ndon't know the answer. I'm not sure. So
Dialogue: 0,0:59:03.83,0:59:07.18,Default,,0000,0000,0000,,the three body problem is already\Ncomplicated enough from a mathematical
Dialogue: 0,0:59:07.18,0:59:12.27,Default,,0000,0000,0000,,point of view. So I have never actually\Nreally looked at a four body problem.
Dialogue: 0,0:59:12.27,0:59:18.10,Default,,0000,0000,0000,,However with those many bodies, there\Nare at least very symmetrical solutions.
Dialogue: 0,0:59:18.10,0:59:22.21,Default,,0000,0000,0000,,So you can find some, but it's a different\Nthing than Lagrangian points, right.
Dialogue: 0,0:59:22.21,0:59:26.44,Default,,0000,0000,0000,,Herald: So unfortunately we're almost out\Nof time for this talk. If you have more
Dialogue: 0,0:59:26.44,0:59:29.91,Default,,0000,0000,0000,,questions, I'm sure Sven will be happy to\Ntake them afterwards to talk. So please
Dialogue: 0,0:59:29.91,0:59:33.19,Default,,0000,0000,0000,,approach him after. And again, a big\Nround of applause for the topic.
Dialogue: 0,0:59:33.19,0:59:33.97,Default,,0000,0000,0000,,Sven: Thank you.
Dialogue: 0,0:59:33.97,0:59:39.66,Default,,0000,0000,0000,,{\i1}Applause{\i0}
Dialogue: 0,0:59:39.66,0:59:48.85,Default,,0000,0000,0000,,{\i1}36C3 postroll music{\i0}
Dialogue: 0,0:59:48.85,1:00:06.00,Default,,0000,0000,0000,,Subtitles created by c3subtitles.de\Nin the year 2020. Join, and help us!