1 00:00:00,510 --> 00:00:08,160 So we have varied the starting velocity, and we have seen what can happen if the starting velocity 2 00:00:08,160 --> 00:00:12,810 is just slightly increased from the circular trajectory, we get such an orbital trajectory. 3 00:00:13,380 --> 00:00:22,770 If we increase it by another factor of one point twenty five, approximately then the velocity is so 4 00:00:22,770 --> 00:00:26,700 large that we can even leave the gravitational field of the Earth. 5 00:00:26,790 --> 00:00:31,530 Roughly speaking, of course, it's always in the gravitational field, but then the force or the influence 6 00:00:31,530 --> 00:00:33,960 by the Sun is larger than the influence by the Earth. 7 00:00:35,490 --> 00:00:40,600 So what happens if we set an intermediate velocity where it is oval? 8 00:00:40,600 --> 00:00:47,550 This elliptical trajectory trajectory hits or intersects the trajectory of the Moon. 9 00:00:48,480 --> 00:00:57,690 So then we may get a so-called moon encounter where the object is so close to the moon that the motion 10 00:00:57,690 --> 00:01:02,060 is mostly affected by the Moon, even though the Moon is much lighter than the Earth. 11 00:01:02,070 --> 00:01:09,350 But due to the small distance, it's then strongly affected and there really funky stuff can happen 12 00:01:10,260 --> 00:01:10,860 so. 13 00:01:12,030 --> 00:01:15,600 I have just copied here a few lines of code from our previous examples. 14 00:01:15,960 --> 00:01:19,590 And now I can just change it once again, so I will change here. 15 00:01:19,890 --> 00:01:24,420 The starting velocity and though I will, we have one point twenty five. 16 00:01:24,840 --> 00:01:29,250 We had one point five zero and now I take one point three four. 17 00:01:29,670 --> 00:01:34,860 So here, of course, since this is a very sensitive maneuver, when we want to hit the Moon, it's 18 00:01:34,860 --> 00:01:36,690 very sensitive to this velocity. 19 00:01:36,720 --> 00:01:40,470 So if you changed as a tiny bit, it can give different results, of course. 20 00:01:41,460 --> 00:01:46,560 And I think the time period we can check if this is OK. 21 00:01:46,890 --> 00:01:50,610 And then I also fixed here the X limit and the Y limit as we had before. 22 00:01:51,360 --> 00:01:56,280 So instead of speaking, I just press shift enter and here we see our results. 23 00:01:57,080 --> 00:02:03,810 So we see here the trajectory of the Earth around sorry, the moon around the Earth and the spaceship 24 00:02:03,810 --> 00:02:06,030 around the Earth. 25 00:02:07,080 --> 00:02:11,900 And one thing that we can notice if we zoom in a bit more, if we could, for example, use here year 26 00:02:11,940 --> 00:02:13,770 two to zoom in a bit. 27 00:02:17,080 --> 00:02:22,810 What we can see, then, is that the trajectory is not always on the same oval. 28 00:02:22,900 --> 00:02:27,760 It is a bit shifted, so we see that there was some influence of the Moon already. 29 00:02:28,210 --> 00:02:33,940 So since our spaceship is in the vicinity of the Moon, the trajectory has been shifted a bit. 30 00:02:34,210 --> 00:02:36,190 But this effect is really not so large. 31 00:02:37,150 --> 00:02:41,650 So then let me increase this to a few months. 32 00:02:42,070 --> 00:02:45,790 So I will simulate here to zero point three years. 33 00:02:47,680 --> 00:02:56,020 And you see at the point where we almost hit the moon here, we will have an earth escape, where the 34 00:02:56,020 --> 00:03:01,540 spaceship will leave the Earth and we'll go on a trajectory around the sun. 35 00:03:02,440 --> 00:03:08,860 And the cool thing about this is that we achieved this with a lower velocity compared to the 1.5 that 36 00:03:08,860 --> 00:03:14,020 we had before for the Direct Earth Escape. 37 00:03:14,470 --> 00:03:21,790 So this was here 1.5 B orbits, and now we can get qualitatively the same result. 38 00:03:21,800 --> 00:03:27,310 We leave the sphere of influence by just using a lower starting velocity. 39 00:03:27,820 --> 00:03:32,530 So this is really useful for some maneuvers because you can save a lot of fuel. 40 00:03:32,530 --> 00:03:35,170 You don't have to accelerate to such a high velocity. 41 00:03:35,500 --> 00:03:40,600 You basically get something like a slingshot where you approach the moon. 42 00:03:40,600 --> 00:03:49,180 And since you are so close to this object, you get an additional acceleration and then you get thrown 43 00:03:49,180 --> 00:03:52,030 out of the rotation around the Earth. 44 00:03:53,170 --> 00:04:00,640 So that's a cool trick, and we can use this for leaving, leaving Earth and maybe traveling to Mars 45 00:04:00,640 --> 00:04:01,180 one day. 46 00:04:02,450 --> 00:04:08,540 But what's also really nice is that we are here pretty close to the Moon, we can actually check the 47 00:04:08,540 --> 00:04:09,290 distance here. 48 00:04:09,860 --> 00:04:13,820 This will be the distance spaceship to the Moon. 49 00:04:16,399 --> 00:04:20,810 And so we have to use here nine, 12 and six and nine. 50 00:04:23,100 --> 00:04:29,670 And you see, in the beginning, we are not so far, we always roughly oscillate here, but you see 51 00:04:29,670 --> 00:04:35,820 it's not really a nice oscillation, which means there is also stuff going on in the beginning and we 52 00:04:36,540 --> 00:04:41,730 oscillate approximately twice and then we are here very, very close to zero. 53 00:04:41,730 --> 00:04:45,000 So you see, this is really such a kink where we almost hit the moon. 54 00:04:45,000 --> 00:04:50,970 And since we are so close, we get thrown out of the trajectory and then we leave the moon and we also 55 00:04:50,970 --> 00:04:51,630 leave the Earth. 56 00:04:52,710 --> 00:04:57,960 And now the idea is we approached Moon here pretty closely. 57 00:04:58,590 --> 00:05:01,700 What happens if we break at this point of time? 58 00:05:02,100 --> 00:05:04,080 Can we achieve a moon orbit? 59 00:05:04,890 --> 00:05:06,240 And of course we can. 60 00:05:06,450 --> 00:05:12,570 And of course, this is also how it's done in reality, how you get to the moon orbit and from there, 61 00:05:12,960 --> 00:05:17,130 how you land on the moon by just breaking even more.