1
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So you see, when we take our standards, starting values for the radius and for the velocity we get

2
00:00:07,770 --> 00:00:08,940
are a stationary orbit.

3
00:00:09,120 --> 00:00:14,910
This is what a satellite is supposed to move on, but we can, of course, try out different starting

4
00:00:14,910 --> 00:00:15,390
values.

5
00:00:15,990 --> 00:00:22,200
So, for example, we could think what happens if our spaceship just accelerates here very quickly and

6
00:00:22,200 --> 00:00:24,360
changes to velocity to a certain value.

7
00:00:24,720 --> 00:00:31,050
What will happen to the trajectory, and I don't know, don't know if you are aware of this, but what

8
00:00:31,050 --> 00:00:34,200
will happen is we will go to an oval trajectory.

9
00:00:34,470 --> 00:00:40,440
And first of all, I want to show you this elliptical orbit and then you see here the other four cases

10
00:00:40,440 --> 00:00:43,110
that we will analyze thereafter.

11
00:00:44,250 --> 00:00:50,130
So I copy here from our previous cell just what we had written down.

12
00:00:50,790 --> 00:00:55,860
And we do not need to redefine starting conditions for the Sun, the Earth and the Moon, of course,

13
00:00:55,860 --> 00:00:57,060
but just for the spaceship.

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00:00:57,600 --> 00:01:00,960
And then this is really everything that we had before as well.

15
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So the first thing that I want to try out here is the elliptical orbit.

16
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And for this, I will just increase the velocity.

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00:01:11,820 --> 00:01:15,390
So, for example, one point twenty five times we orbit.

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And then I will use this plot here instead.

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So let me copy this and plot it instead of this one.

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And now we can run it.

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So, OK, now it takes already maybe three seconds.

22
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And you see, this is the solution.

23
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So we have propagated this for a single year and this is what happens.

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So the Moon is still moving on the rather circular trajectory and it is not really affected by the spaceship,

25
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of course.

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It's not, not at all the fact that because we disregarded this interaction and the spacious space Soviet

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00:01:57,300 --> 00:02:03,660
spaceship itself moves on the elliptical trajectory around the Earth, which is positioned here.

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So you see, it can be pretty close and it can be pretty far from the Earth and it gets closer to the

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00:02:11,460 --> 00:02:12,750
moon at points.

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But still, I do not really see much of an influence of the Moon to the spaceship.

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But this will come sooner or later.

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00:02:21,270 --> 00:02:28,590
So the next thing I want to analyze is something we did before, so let me scroll up and let me copy,

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00:02:28,590 --> 00:02:33,330
for example, this one where we analyzed the distance from the Sun to the Earth over time.

34
00:02:34,230 --> 00:02:41,310
And you guessed it already, I want to do the same thing now for our overall trajectory to see how oval

35
00:02:41,310 --> 00:02:42,150
it actually is.

36
00:02:43,020 --> 00:02:49,830
So our right systems space ship to Earth.

37
00:02:53,780 --> 00:02:57,380
Earth and then this is the time we can leave it as it is.

38
00:02:57,830 --> 00:03:03,230
And here we have to use to spaceship.

39
00:03:04,900 --> 00:03:10,300
So the order here doesn't matter that this is the Earth, so is supposed to be the spaceship, this

40
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is nine to 12.

41
00:03:14,380 --> 00:03:19,210
And we give it the color purple like like we used for the spaceship previously.

42
00:03:20,230 --> 00:03:24,010
And you see, this is how the distance changes over time.

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So you see the the the period of this oscillation is very small.

44
00:03:29,680 --> 00:03:31,710
There are many amount of these oscillations.

45
00:03:31,710 --> 00:03:35,440
So maybe like we decrease the time to one month.

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So I divide by 12.

47
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And now you see how it goes.

48
00:03:42,570 --> 00:03:50,490
So in a month, we have one two three four five six seven eight and almost nine constellations.

49
00:03:50,760 --> 00:03:55,170
So one of these oscillations or one of these periods, takes maybe three or four days.

50
00:03:56,310 --> 00:03:59,930
And you see that the distance changes pretty much.

51
00:03:59,940 --> 00:04:02,790
So here we have meters 10 to the power of eight.

52
00:04:03,540 --> 00:04:07,620
So this would be 10 to the power of five kilometers.

53
00:04:07,980 --> 00:04:19,750
So we go from from 40k to 140 K and the radius and of course, our starting radius.

54
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We find up here this one we had.

55
00:04:26,490 --> 00:04:34,980
So this was yeah, this was 4.2 times 10 to the power of two.

56
00:04:35,430 --> 00:04:38,160
So this was forty two thousand kilometers.

57
00:04:39,390 --> 00:04:43,140
OK, so that's probably the minimum point here.

58
00:04:43,800 --> 00:04:46,860
And that corresponds to this point on the trajectory.

59
00:04:48,060 --> 00:04:52,350
OK, so now we have analyzed the motion of the spaceship around the Earth.

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00:04:52,710 --> 00:04:57,480
We could, of course, do the same thing with respect to the Moon.

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But what we can also do is we can analyze the velocity.

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So velocity

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00:05:09,580 --> 00:05:11,620
of the spaceship.

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With respect to the Earth

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in meters per second, I hope it's not too long.

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Let's see.

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And we have to plot now here just the velocities.

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00:05:29,020 --> 00:05:32,260
So we basically have to add here 12 of these indices.

69
00:05:33,220 --> 00:05:36,010
So plus 12, 12, 12, 12, 12.

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And this is the velocity.

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00:05:39,790 --> 00:05:51,130
So when the spaceship is closest to the Earth, 42000 kilometers, then the velocity is actually the

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largest.

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00:05:51,670 --> 00:05:55,420
It's almost four K, so four kilometers per second.

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00:05:56,230 --> 00:06:03,100
And then when the spaceship goes far away from the Earth, when it is in this point here, then the

75
00:06:03,100 --> 00:06:04,600
velocity is the smallest.

76
00:06:04,600 --> 00:06:12,400
It's only 1000 meters per second, which is, of course, still extremely fast, but not so fast.

77
00:06:12,410 --> 00:06:15,670
It's a factor of four decrease here for the velocity.

78
00:06:16,150 --> 00:06:21,760
So it moves very fast here and very slowly here, and this is really what happens also in reality.

79
00:06:23,050 --> 00:06:30,370
OK, so now we have analyzed this elliptical motion and we have analyzed the trajectory and the trend

80
00:06:30,400 --> 00:06:34,210
of the coordinate and the velocities.

81
00:06:34,330 --> 00:06:38,610
And next, we will go ahead and further tune the starting velocity.

82
00:06:38,620 --> 00:06:40,120
We will further increase it.

83
00:06:40,510 --> 00:06:43,720
And then we will see what happens when we increase it here.

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00:06:43,720 --> 00:06:49,210
And the the overall, the elliptical trajectory will get larger and larger, and at some point we may

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00:06:49,210 --> 00:06:55,360
encounter the Moon and let's see what happens when we see when we get an encounter with the moon or

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00:06:55,360 --> 00:06:56,050
even higher.

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00:06:56,290 --> 00:06:58,690
We get a direct earth escape.