So, I want to tell you a bit about Kepler's second law of celestial mechanics. 因此我想告诉你们,一些关于开普勒第二定律的知识。
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. 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。
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. 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。
But, Kepler's law would also be true, actually, if things were going away. 开普勒第二定律当然也对,如果东西远离了。
And, you'll see that if we reformulate Kepler's Law in terms of vectors, and if we work a bit with these vectors, we are going to end up with something that's actually completely obvious to us now. 如果用公式表达的话就会用到向量,如果用向量的话,我们就需要一些对我们显而易见的方法,来解决它。
So, let's try to see, what does Kepler's law say in terms of vectors? 如何用向量来解释开普勒第二定律?
We'll talk about this much later when we deal with orbits and with Kepler's Law. 在谈到轨道和开普勒定律时,我会详细介绍这一点的。
After some treatment of centripetal force, he deduces 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。
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. 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。
Let us test kepler's third law for the orbit of Uranus compared with that of earth. 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。
That's Kepler's law number one. 这是开普勒第一定律。
Kepler's third law gave a more specific hint about the nature of the force. 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。
So, what Kepler's second law says is that the motion of planets is, first of all, they move in a plane. 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。
OK, so, in fact, what Kepler's second law says is that the acceleration is parallel to the position vector. 所以,开普勒第二定律说,加速度平行于位置矢量。
-Kepler's second law is& quite bizarre how he found that out, an amazing accomplishment. ,开普勒第二定律-,奇怪他是怎么发现的,惊世的成就。
Kepler's Third Law and His Harmonics 开普勒第三定律与谐和思想
Kepler's Third Law is an important law for the research of planets 'movement. Its derivations in some mechanics textbooks are either neglected or over-complicated. Kepler第三定律是研究星体运动的一条重要定律,但在力学教材中,对其证明或者忽视,或者过于繁琐。
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. 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。
Study on the secondly kepler's law using a geometric method 利用几何方法研究开普勒第二定律