1 00:00:00,210 --> 00:00:07,260 So you see, we started from the typical velocity of satellites on this circular orbit around Earth, 2 00:00:07,710 --> 00:00:13,440 and then we increase the velocity at this point and give rise to such an elliptical trajectory. 3 00:00:14,310 --> 00:00:19,740 So of course, when we increase not a lot of T here, this radius will get larger and larger. 4 00:00:19,740 --> 00:00:27,480 And now we may encounter the moon or if we go even higher, we will leave the gravitational field of 5 00:00:27,480 --> 00:00:27,930 the Earth. 6 00:00:28,440 --> 00:00:34,260 I mean, we will never really leave it, but it has one of our dependence, so it becomes basically 7 00:00:34,260 --> 00:00:35,280 not negligible. 8 00:00:36,060 --> 00:00:38,820 And this is what we want to analyze next. 9 00:00:39,060 --> 00:00:44,880 The direct earth escape where the spaceship leaves basically hit the Earth. 10 00:00:46,110 --> 00:00:52,530 So I will just copy what we have here and paste it here. 11 00:00:53,010 --> 00:00:57,630 And now we have a look once again at the velocity and I try to bits. 12 00:00:57,780 --> 00:01:06,600 It is already sufficient if we just briefly increase the velocity here and we can go, for example, 13 00:01:06,600 --> 00:01:08,790 to 1.5 feet orbit. 14 00:01:10,170 --> 00:01:16,410 And when they're on it, you see, this is here to position off the Earth. 15 00:01:17,100 --> 00:01:22,410 This is here the moon trajectory and this trajectory of our spaceship. 16 00:01:22,980 --> 00:01:27,660 So we start from Earth and then be straightforwardly leave it. 17 00:01:28,800 --> 00:01:33,900 And what happens then is we will enter the fields of the Sun. 18 00:01:34,260 --> 00:01:36,270 Of course, we are always in the field of the Sun. 19 00:01:36,270 --> 00:01:42,210 But now the effect of the gravity of the sun is larger than the effect of the gravity of the Earth. 20 00:01:42,750 --> 00:01:47,370 So then the motion will be more effected by the Sun than the Earth. 21 00:01:48,240 --> 00:01:51,420 So for this reason, let's re plot this whole thing here. 22 00:01:52,200 --> 00:01:57,000 Let's go ahead and copy this and make a new figure. 23 00:01:58,290 --> 00:02:01,120 And this time we will not subtract here. 24 00:02:01,140 --> 00:02:05,700 The Earth coordinates, so we will not put it in the reference systems. 25 00:02:05,890 --> 00:02:08,880 The system of the Earth bump in the reference system of the Sun. 26 00:02:09,419 --> 00:02:12,030 So we would have to subtract you the coordinates of the Sun. 27 00:02:12,030 --> 00:02:16,050 But since they are basically zero, we don't have to do it. 28 00:02:16,110 --> 00:02:20,850 I mean, we have seen they're not exactly zero, but we can neglect really this effect. 29 00:02:21,690 --> 00:02:28,740 So for the green, we have the moon and then the spaceship, and now I want to remind the Sun and the 30 00:02:28,740 --> 00:02:30,380 Earth from before. 31 00:02:30,390 --> 00:02:37,770 So this would be zero and one and three and four, and the colors were blue and red. 32 00:02:41,250 --> 00:02:47,720 And when I plot this, we see this is now what happens here, the Sun. 33 00:02:48,450 --> 00:02:51,690 And I think actually it was a red and blue. 34 00:02:53,880 --> 00:02:54,180 Yes. 35 00:02:54,510 --> 00:02:55,980 So this is here to sun. 36 00:02:55,980 --> 00:03:02,310 And then we have here the moon and the Earth, and we see the spaceship is moving on a different trajectory. 37 00:03:03,210 --> 00:03:12,000 So of course, now we should increase the simulation time and I will simulate here not one month, but 38 00:03:12,000 --> 00:03:14,790 I will now simulate here for years. 39 00:03:15,420 --> 00:03:20,550 So our first plot, which was with respect to the Earth, changed to this one. 40 00:03:21,090 --> 00:03:26,310 We have here the Earth and also the Moon, which is not really visible anymore, but you have to zoom 41 00:03:26,310 --> 00:03:27,360 in here to see it. 42 00:03:27,840 --> 00:03:35,430 And in this coordinate frame, the satellite will spiral away from the Earth, which is clear it's not 43 00:03:35,430 --> 00:03:37,710 anymore in a circle which is spiral away. 44 00:03:38,850 --> 00:03:42,210 And in the coordinate system of the Sun. 45 00:03:42,720 --> 00:03:43,760 This is what happens. 46 00:03:43,770 --> 00:03:45,780 We see blue and green are here. 47 00:03:45,810 --> 00:03:50,190 Actually, we can only see green, but we know that the moon and the Earth in the very similar trajectory. 48 00:03:50,730 --> 00:03:59,160 So this here to circle with the larger radius and this is here the motion of our spaceship. 49 00:03:59,970 --> 00:04:05,760 And it's pretty interesting that at some point the spaceship will come back to the Earth and to the 50 00:04:05,760 --> 00:04:06,030 Moon. 51 00:04:07,110 --> 00:04:12,420 They don't have to be here at the same time, necessarily, but at least the possibility exists that 52 00:04:12,420 --> 00:04:14,130 they re-enter the orbit. 53 00:04:14,970 --> 00:04:21,570 And it turns out that this happens already after two of these oscillations here or two of these rotations 54 00:04:21,570 --> 00:04:23,100 around the Sun rather to see. 55 00:04:24,030 --> 00:04:30,660 So we can find this out by increasing the simulation time even more. 56 00:04:31,440 --> 00:04:39,120 And I will simulated here for 16 years, which is four times the time that we had before. 57 00:04:41,190 --> 00:04:45,270 And of course, now it takes a bit longer. 58 00:04:45,960 --> 00:04:49,810 And you see, this is here to plot in the coordinate system of the Earth. 59 00:04:49,830 --> 00:04:55,740 It's no bit confusing, to be honest, because here is the Earth and the moon in the center, and then 60 00:04:56,070 --> 00:05:02,880 the satellite starts basically leaving this trajectory and then coming back, it seems. 61 00:05:03,480 --> 00:05:06,210 And it's, of course, much better to see on this trajectory. 62 00:05:06,750 --> 00:05:12,660 We go in this circle and then we on the larger circle and then eventually we come back to this point. 63 00:05:12,660 --> 00:05:21,000 So here on this whole path, there always is the possibility that the spaceship re-enters to orbit around 64 00:05:21,000 --> 00:05:25,680 the Earth and to figure out if this is happening or not. 65 00:05:26,130 --> 00:05:38,430 We will now use a different plot and I will basically take this plot here and I will just fix here to 66 00:05:38,430 --> 00:05:43,530 plot range to this area so that we can really see what's going on in the vicinity of the Earth. 67 00:05:47,070 --> 00:05:52,020 So I would right, Pulte thoughts. 68 00:05:52,230 --> 00:05:53,680 Excellent, excellent. 69 00:05:55,560 --> 00:06:02,100 And I will use three times the radius of Earth and Moon. 70 00:06:06,480 --> 00:06:09,090 So in positive and a negative direction. 71 00:06:09,630 --> 00:06:12,420 And of course, I will use the same for the wide range. 72 00:06:13,380 --> 00:06:15,330 So plotted out why Lim? 73 00:06:17,130 --> 00:06:19,320 And now we can see what's going on here. 74 00:06:19,830 --> 00:06:26,970 So at first we start from the Earth or very close to the Earth, and then we have so high velocity that 75 00:06:26,970 --> 00:06:34,530 we basically leave the Earth and the Moon and we move on this trajectory and then we move around the 76 00:06:34,530 --> 00:06:38,730 sun once and twice, maybe and even more times, we don't know. 77 00:06:39,150 --> 00:06:44,040 And eventually we come back very, very close to the Earth and we will almost hit it. 78 00:06:44,520 --> 00:06:45,990 And then we will leave it again. 79 00:06:46,650 --> 00:06:54,930 So at this point, it would in principle be possible to break or basically to use a booster and boost 80 00:06:54,930 --> 00:06:59,060 along the opposite direction and decrease the velocity so that we re-enter here. 81 00:06:59,100 --> 00:07:05,160 The orbits of coasters would cost an enormous amount of energy, but in principle it's possible to do. 82 00:07:07,140 --> 00:07:12,750 So the last thing that I want to analyze is, of course, to time dependence here. 83 00:07:13,170 --> 00:07:18,870 So I will plot the distance of our spaceship with respect to the Earth. 84 00:07:19,890 --> 00:07:25,920 And I think we have done this already here, so I can just copy this. 85 00:07:26,940 --> 00:07:29,850 Go to the bottom and look at it. 86 00:07:30,840 --> 00:07:33,700 And we see we have simulated for 16 years. 87 00:07:34,110 --> 00:07:39,030 Of course, I have tested this before, so I know that it is a good time range to simulate and we see 88 00:07:39,030 --> 00:07:43,290 that the distance increases with some additional fluctuations. 89 00:07:43,770 --> 00:07:52,640 And then we are here for the furthest apart and we get closer and we get once again further apart. 90 00:07:52,650 --> 00:07:55,580 And then we are here almost at zero. 91 00:07:55,590 --> 00:07:57,810 This is where we almost hit the Earth. 92 00:07:58,230 --> 00:08:00,120 So this is this point that we see here. 93 00:08:01,320 --> 00:08:08,340 So I think this is really an interesting discussion because just by increasing the starting velocity, 94 00:08:08,340 --> 00:08:11,850 we get such an interesting physics and such a very different behavior. 95 00:08:12,360 --> 00:08:18,870 So instead of having this oval trajectory, which is always the same around the Earth, we instantly 96 00:08:18,870 --> 00:08:25,410 leave the Earth and then we basically circle around the sun on a different trajectory. 97 00:08:25,950 --> 00:08:33,690 But then eventually, after two rotations after 16 years, we reenter here and we almost hit the Earth. 98 00:08:33,990 --> 00:08:36,659 So that's pretty, pretty nice. 99 00:08:36,780 --> 00:08:38,250 Physics are pretty interesting. 100 00:08:39,280 --> 00:08:46,360 OK, so the next thing I want to analyze is the surface cable, like we just did, we escaped the orbit, 101 00:08:46,690 --> 00:08:51,490 but I want to show you that it's even possible with the lower velocity by using a trick, by using the 102 00:08:51,490 --> 00:08:53,200 so-called moon and copter.