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解释开普勒行星运动定律 – 译学馆
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解释开普勒行星运动定律

Explained In 5 Questions: Kepler's Law of Planetary Motion | Encyclopaedia Britannica

5个问题阐释开普勒行星运动定律
SPEAKER 1: Kepler’s first law of planetary motion states
开普勒行星运动第一定律说明
that all planets move about the Sun in elliptical orbits having
所有椭圆形轨道上围绕太阳运转的行星
the Sun as one of the foca.
都以太阳为一个焦点
But what does that actually mean?
但这是什么意思呢?
Well an ellipse is a shape that resembles a kind of squashed circle.
一个椭圆类似于一种扁扁的圆
Its foci are two points within the ellipse that describe its shape.
它的焦点是椭圆里决定形状的两个点
For any point on the ellipse,
椭圆上的每一点
the sum of that points distances to the two foci is the same.
到两个焦点的距离之和都是一样的
The further apart the foci are, the more squashed the ellipse is.
两个焦点的间距越远 椭圆越扁
If the foci become so close that they are only one focus,
如果两个焦点足够近 直到成为一个点
you just have a circle.
那轨道就是一个圆
In reality orbits are never perfectly circular.
实际上轨道绝不可能是完全的圆
But we do know that the Sun will always be one
但我们肯定太阳始终是
of the foci of the elliptical path of an orbit.
所有椭圆轨道的一个焦点
Knowing that the Sun is a focus of the planet’s orbit
知道太阳是行星轨道的一个焦点
can tell us a lot about the shape of that orbit.
可以帮我们更多地了解轨道形状
Kepler tells us that orbits are ellipses,
开普勒告诉我们轨道是椭圆形的
which are like circles with some added eccentricity.
就像用离心率处理后的圆形
But what is eccentricity?
那什么是离心率呢?
How do you figure it out?
你如何将它算出?
Eccentricity measures how flattened an ellipse is compared to a circle.
离心率是一个椭圆对比一个圆的扁平度
We calculate it using this equation.
我们用这个公式进行计算
So what does that mean? Well,
是什么意思呢?
a is the semi-major axis,
a表示半长轴
or half the distance along the long axis of the ellipse.
或者说椭圆长轴的一半
And b is the semi-minor axis,
b表示短半轴
or half the distance along the short axis of the ellipse.
或者说椭圆短轴的一半
The equation is a way to compare these
这个等式是用轴的比值
axes to describe how squashed the ellipse is.
来描述椭圆的扁平度
An ellipse with zero eccentricity would just be a regular old circle.
离心率为0的椭圆就是一个正圆
As eccentricity increases, the ellipse gets flatter and flatter
随着离心率的增加 椭圆变得越来越扁
until it just looks like a line.
直到它看上去像一条线
An orbit with an eccentricity greater
当轨道的离心率大于1时
than one is no longer an ellipse but a parabola
它不再是椭圆 并且当e为1时
if e is equal to one a hyperbola it e is greater than one.
是一条抛物线 当e大于1时是双曲线
For example, the giveaway that Oumuamua, the first interstellar comet,
比如 奥陌陌 第一颗星际彗星
was not from around here was that its eccentricity was 1.2.
它不在这附近运行 它的离心率是1·2
The eccentricity of Earth’s orbit is only 0.0167.
地球的轨道离心率仅为0·0167
Kepler’s third law states that the squares
开普勒第三定律说明
of the sidereal periods of revolution
行星的恒星周期的平方
of the planets are directly proportional to the cubes
与它们距太阳的
of their mean distances from the Sun.
平均距离的立方成正比
Which what does that mean?
这意味着什么呢?
Basically it’s saying that how long a planet takes to go around the Sun,
可以说行星围绕太阳运转一圈的时间
its period,
其周期
is related to the mean of its distance from the Sun.
跟它与太阳的距离的平均值有关
That is the square of the period divided by the cube
即平均距离的立方除以
of the mean distance is equal to a constant.
周期的平方是一个常数
For every planet, no matter its period or distance,
对于每一颗行星 不管是周期还是距离
that constant is the same number.
这个常数都是相同的
Kepler’s second law tells us
开普勒第二定律说明
that a planet moves more slowly when it’s further from the Sun.
行星距太阳越远 它运行得越慢
But why should that be? Well,
为什么会这样呢?
as a planet orbits
行星围绕太阳运行时
the Sun it may not keep a constant speed
它可能不会维持在一个速度
but it does maintain its angular momentum.
但它会维持它的角动量
Angular momentum is equal to the mass
角动量等于
of the planet times the distance of the planet
行星质量乘以它到太阳的距离
to the Sun times the velocity of the planet.
再乘以行星的速度
Since the angular momentum doesn’t change, when the distance increases
因为角动量不会变
the velocity has to decrease.
所以当距离增加时 速度会降低
That means when the planet gets further from the Sun it slows down.
表示行星远离太阳时它的速度会变慢
Kepler’s second law deals with the speed of planets orbiting the Sun.
开普勒第二定律研究的是行星绕太阳的速度
So does it tell us
它告诉我们
at what point the Earth is moving at top speed?
地球在哪个点的速度最快
The second law tells us
第二定律说明
that the Earth moves fastest when it’s closest to the Sun,
地球距太阳最近时或者说在近日点时
or at its perihelion.
地球的公转速度最快
That happens in early January.
这发生在一月初
At that point Earth is about 92 million miles from the Sun.
这个点上 地球距太阳约9千2百万英里
Meanwhile it’s at its slowest in early July,
它的速度在7月初最慢
at its furthest point from the Sun, or aphelion.
在距太阳最远的点 或者说远日点时
That greatest distance is about 95 million miles.
最大距离约为9千5百万英里
That difference of 3 million miles might sound like a lot
三百万英里的差值可能听起来很大
but Earth’s orbit is so vast that it’s actually merely circular.
但地球的轨道范围太广 以至于其实际上接近一个圆

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视频概述

视频形象地就轨道焦点、轨道离心率与轨道形状、行星速度与距太阳的距离等因素展现了行星运行规律。

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视频来源

https://www.youtube.com/watch?v=AKbfR5KHUm4

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