Hey Brady, I am Matt Henderson. I like
你好啊Brady 我是马特•亨德森
making mathematical animations and I
我喜欢制作数学动画
wanted to show a few that relate to the
并且想展示一些
patterns of orbits in the solar system.
有关太阳系中行星运动轨迹的图案
The first one is the inner planets; and
首先展示的是近日行星
so this is the approximate pattern that
这是根据近日行星轨迹
the inner planets trace out – obviously
制作出的近似模型
things aren’t to scale. We’ve got the Sun,
显然这些行星的大小不成比例
we’ve got Mercury, Venus, Earth and Mars
这是太阳 这些分别是水星 金星 地球和火星
going around in their approximate orbits
它们在近似轨道上以相对速度
and relative speeds. So they’re spinning
围绕太阳旋转
around, the Sun is at the centre and now
太阳是它们公转的中心
we’re to actually move so we’re
现在我们正式开始绘制图案
following Earth. And we’re interested in,
我们以地球为参照物
what are the patterns that are traced out by
我们对其他行星轨道的
the other planets? From kind of like from
图形很感兴趣
the perspective of Earth we start to see
以地球为中心点
some interesting patterns.
一些有意思的图案开始成形
The pattern from Venus is starting to be
金星的运动轨迹
quite regular.
开始变得有规律可循
We’ll start to see this kind of
我们逐渐发现
five-pointed shape;
轨迹开始接近五边形
you can see we’ve got one of the points
如你所见 这是其中一个角
here, we’ve got two, three, and the next
这里是第二个 第三个
time Venus comes around it completes
以此类推
this five points: 1, 2, 3, 4, 5.
周而复始
And that’s because the ratio of the
这是因为金星和地球
orbits between Venus and Earth are- is in
运动轨迹之间的比例
an 8 to 13 ratio so the difference there
是8比13
is accounting for the five-fold symmetry.
因此这里的差异是因为五重对称
In general it’s just like a pretty pattern.
这些轨迹通常会形成美丽的图案
I think these are called epicycloids,
我认为这些是外摆线
they’re kind of like the spirograph
它们与螺旋形图案
patterns that you get rolling circles
有异曲同工之妙
around circles.
都是围绕圆圈转圈
And those just happen to be the ones
而这些恰好是
that the planets trace out.
行星的运动轨迹
Now let’s look at this asteroid Cruithne,
现在我们来看看
that has been referred to as Earth’s
被称为第二个月球的
second moon, but that’s just a
克鲁特尼小行星
sensationalist kind of thing. It is-
但这种说法只是哗众取宠
what it is is an asteroid that’s in
这只是一颗
orbital resonance with the Earth
轨道与地球共振的小行星
which means- in this case it means that
这说明 在这种情况下
its year is the same as Earth’s year;
它的行星年与地球相同
but it’s not orbiting Earth, it’s also
但它不围绕地球公转
orbiting the Sun but in a more kind of
而是跟地球一样围绕太阳
elliptical orbit. So if we mistakenly
而且轨道的形状更接近椭圆
thought it was orbiting orbiting the
如果我们误以为它围绕地球公转
Earth then what would its orbit look
会得出什么结论呢
like? It wouldn’t be a circle, it’d be
那样它的轨道就不会是圆
some kind of
而是某种
mix of circles and ellipses or something;
圆形和椭圆的结合体
so let’s see.
所以我们来看
So again we start out with the Sun at
我们还是以太阳为中心
the centre;
着手
Earth is orbiting and then this is Cruithne,
地球在围绕太阳公转
this little asteroid that is orbiting
克鲁特尼
with the same year.
是与地球有着同样行星年的小行星
Now we’ve shifted to the perspective of
现在我们将注意力转移到地球上
the Earth and the path that Cruithne is
我们发现克鲁特尼运行的轨迹
tracing out is this kind of kidney bean
绘制出来有点像芸豆的形状
shape – again this these aren’t the exact
再强调一下哈
correct orbits but it’s roughly
这些只是大致的运行模型
kind of like what’s going on. So we don’t
并不是完全准确的轨迹
see an elliptical orbit; if we were wrong
因此没有显示出椭圆状
and we thought Earth was the centre of
如果我们错把地球
the solar system then Cruithne would
当作太阳系的中心
be the sort of weird second moon tiny
那克鲁特尼就会成为
asteroid guy that is orbiting us in this
以芸豆的形状围绕我们远转的
kind of kidney bean shape. – (Brady: That would)
像第二个月亮那样奇怪的小行星
(take some explaining if you believe that)
-(布兰迪:“如果谁觉得地球是万物中心”)
(the Earth was at the centre of)
(“那解释起来确实需要费些口舌。”)
(everything!) – Yeah that’s a kind of
是的
complicated behaviour to explain,
这解释起来确实很复杂
but I suppose it’s just built up of a
但我推测这些轨道
circle and an ellipse kind of added
是由圆形和椭圆叠加而成的
together, so maybe as soon as you saw
也许你一看到它的样子
that you might invent that explanation.
就可以描述清楚了
(You put these on Twitter but what have)
(“在把这些发布到推特上之前”)
(you done in the past?) – Yeah I used to run
(“你都研究了些什么?”)
this blog on Tumblr that- where I posted
我之前在汤博乐上发布数学动图
mathematical GIFs and
后来
back then I don’t think they were
我觉得这些不如新的
quite as good as my new ones, I think I’ve
我应该算是
sort of progressed a little bit. So
有点进步吧
for example, you know, this was the new
例如 这是新的克鲁特尼运动动画
Cruithne animation, this is the old one
这是旧的
here. It’s explaining the same
它们生成的形状相同
shape but it takes a little bit longer
但是想要一探究竟
to see exactly what’s happening; possibly
还需要花更多时间
because you don’t have that shift in
可能是因为没有转换视角
perspective, you know where you establish
我们先是以太阳为中心定点
the orbits with the Sun at the centre
建立的轨迹
and then you shift to just following
因为地球的位置固定不变
Earth because Earth is stationary.
我们再将目光转移到地球
You can kind of see what’s going on, right?
这样一切就清晰明朗了 对吧
(The Sun’s stationary too in that one)
(“太阳在这里也是静止的诶”)
Yeah the Sun is stationary as well. So if
对 太阳也是静止的
we look at the new one, the Sun is also
因此如果我们观察这颗新的克鲁特尼
still stationary right, but the fact that
太阳仍然静止不动
the Sun is at the centre of the old one
但其实太阳是旧克鲁特尼的中心
is maybe a bit confusing as well. Here
这听起来好像也有点绕
I’ve just put Earth is the centre to
我在这里把地球作为中心
emphasise that we’re doing a sort of
以强调我们正在做一项
geocentric thing. In both I’ve done the
地心模型研究
trick of having like stars in the
在所有的模型中
background, which are just randomly
我都用随机生成的点
generated points, but the stars that sort
制成了星空背景
of swing around I think helps to show
但是星星忽明忽暗 漂移不定
you’re in a sort of weird reference
它们时刻提醒你处在一个
frame that’s rotating with the Earth.
随着地球旋转的另类参照系里
(And then you’ve got another old one too from there?)
(“所以旧的克鲁特尼也在里面吗?”)
Yeah, related to this ratio of
是的 这跟金星与地球的比例有关
Venus and the Earth: got this one here
金星和地球身在其中
which is, you have Venus going around,
金星和地球
you’ve got Earth going around, and you
都在自转和公转
just draw a line between the two. It’s a
只要将它俩画条线连起来就行了
bit different to tracing the relative
这与追踪它们的相对路径有些不同
path but you get a similar shape, you get
但可以得到一个类似的形状
that five-pointed shape that I pointed
正是之前我们看到的五边形
out before. – (It’s fun stuff all this)
(“行星真奇妙 对吧”)
(planets isn’t it?) – Yeah, and I mean for me
对 于我而言
it’s kind of just a way to talk about
这只是其中一种 解释
the spirograph patterns, epicycloids,
通过圆圈旋转得到的
that you get from circles rotating
螺旋形图样和外摆线 的方式
around. It’s just kind of fun to plug
举个例子 把金星和地球
in the numbers that roughly correspond
大概对应的数字代入其中
to like Venus and Earth for example. And,
会很有意思
of course, it’s not exactly 8 to 13 ratio
当然啦 这个8比13的比例并不精确
but it gives the 5 pointed symmetry
但由8+5=13
because 8 plus 5 is 13.
可以推知五点对称
Today’s episode has been brought to you
本集精彩由机智网提供
by Brilliant. Now we often focus on all
我们最近经常关注他们的这些
their great math courses, like these ones,
高质量数学课 诸如此类
but it seems appropriate today to let
然而这是一个合适的时机
you know they happen to have this epic
向大家介绍它们即将推出的
course on Gravitational Physics. As you
这部史诗级的引力物理学课程
can see it’s jam
如你所见
packed with stuff relating to today’s
这里遍布了
video,
与这期视频有关的内容
but going much much deeper of course.
当然 深度要远大于此
Brilliant is fun, it’s engaging; it’s
机智网不仅引人入胜
educational of course, but most
寓教于乐 更重要的是
importantly it’s really interactive. Why
它的最大亮点——互动性
not visit today and see what a great
不如立即行动
resource they’ve created?
去看看他们创造的绝妙资源宝库吧
Maybe sign up if it’s for you; or give a
自用请注册登录
subscription as a gift to that person
点击订阅作为礼物
who already has everything.
送给那个无所不有的人
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点击屏幕上的链接进入网站
going to Brilliant.org/Numberphile,
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the address on the screen.
可以享受八折优惠
Thanks Brilliant for supporting today’s episode.
感谢机智网对本集的赞助

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