开普勒定律

在谈到轨道和开普勒定律时，我会详细介绍这一点的。

We 'll talk about this much later when we deal with orbits and with Kepler 's Law .

开普勒定律的数学解释及现代证明

Mathematical Explanations and Modern Demonstrations about Kepler Law

今天我们要讨论，行星轨道，和著名的开普勒定律。

Today , I will talk to you about elliptical orbits and Kepler 's famous laws .

用矢量法证明开普勒三定律

Three Kepler Laws Proved by Means of Vector

这是开普勒第一定律。

That 's Kepler 's law number one .

开普勒三定律发现的启示&兼谈李约瑟难题

Revelation from the foundation of the Kepler Laws & A discussion on the Joseph Needham 's Problem

单位时间扫过的面积为常量，这就是开普勒三定律之一。

The rate of sweeping out of area is a constant-this is one of three Kepler laws .

开普勒第三定律，就是你们在考试中和，作业中推导出的：，周期的平方等于，4π的平方乘以1，加上r2的三次方。

Kepler 's Third Law , which you derived on your exam as well as on an assignment : r1 the period squared equals four pi squared times r1 plus r2 to the power three .

利用几何方法研究开普勒第二定律

Study on the secondly kepler 's law using a geometric method

开普勒第三定律表达式的一种新的推导方法

The new Derivation for Third Law of Kepler

开普勒第三定律与谐和思想

Kepler 's Third Law and His Harmonics

开普勒第三定律给出了一个关于力的本质的更为具体的说明。

Kepler 's third law gave a more specific hint about the nature of the force .

让我们比较天王星和地球的轨道，来检验一下开普勒第三定律。

Let us test kepler 's third law for the orbit of Uranus compared with that of earth .

因此我想告诉你们，一些关于开普勒第二定律的知识。

So , I want to tell you a bit about Kepler 's second law of celestial mechanics .

开普勒第二定律当然也对，如果东西远离了。

But , Kepler 's law would also be true , actually , if things were going away .

如何用向量来解释开普勒第二定律？

So , let 's try to see , what does Kepler 's law say in terms of vectors ?

，开普勒第二定律-，奇怪他是怎么发现的，惊世的成就。

- Kepler 's second law is & quite bizarre how he found that out , an amazing accomplishment .

所以，开普勒第二定律说，加速度平行于位置矢量。

OK , so , in fact , what Kepler 's second law says is that the acceleration is parallel to the position vector .

开普勒第二定律说到，首先每个行星的运动都保持在同一平面内。

So , what Kepler 's second law says is that the motion of planets is , first of all , they move in a plane .

其实有三个定律，让我先来告诉你们开普勒第二定律，其中对向量有一个很好的解释。

So , there 's actually three laws , but let me just tell you about the second one that has a very nice vector interpretation .

太阳以什么力量用于行星，使之遵循开普勒发现的定律运行呢？

What sort of force does the sun exert on the planets which causes the planets to move according to the laws which Kepler has discovered ?

利用几何方法及计算机模拟研究开普勒第二定律，运算结果面积速度近似为常量，本文中精度为10-13。

Using a geometric method and computer simulation , the second Kepler 's Law is studied . The calculated result shows that the areal velocity is approximately constant with an accuracy of 10 - 13 .

事实上，如果你观察带电粒子，在点电荷引起的电场中的运动，它也满足开普勒第二定律。

So , actually , if you look at motion of charged particles in an electric field caused by a point charged particle , it also satisfies Kepler 's law , satisfies the same law .

所有这些通过多普勒，顿移测量得到，但如果你知道r1和，那就知道，所以你知道开普勒，第三定律中的这部分。

All these things come out of the Doppler shift measurements , r2 but if you know r1 and you know r2 , r1 + r2 then you also know r1 plus r2 , so you know this part in Kepler 's Third Law .

在向心力的一些论述之后，他推出了开普勒的第三定律。

After some treatment of centripetal force , he deduces Kepler 's third law .

接着开普勒提出了他的定律，他说行星基本上是绕太阳作椭圆运动，它们在椭圆上有特殊的运动规律。

And then Kepler came with these laws that said basically that planets move in an ellipse around the sun , and that they move in a very specific way along that ellipse .