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  • 开普勒行星运动法

    A drawing depicting the elliptical orbits of planets around the sun, illustrating Kepler's First Law.

    Though a drawing, not an accurate portrayal of the solar system, the elliptical appearance of the orbits is correct. The elliptical orbits around the sun are not limited to the planets; comets, asteroids, and other orbiting objects also follow elliptical paths. 
    ::太阳周围的椭圆轨道并不局限于行星;彗星、小行星和其他轨道物体也遵循椭圆路径。

    Kepler’s Laws
    ::开普勒的法律

    Fifty years before Newton proposed his three laws of motion and his law of universal gravitation, Johannes Kepler (1571 – 1630) published a number of astronomical papers with detailed descriptions of the motions of the planets.  Included in those papers were the findings that we now refer to as Kepler’s Laws of Planetary Motion. These are summarized below.
    ::在牛顿提出其三项运动法及其普遍引力法50年前,约翰内斯·开普勒(1571 - 1630年 ) ( 1531 - 1630年 ) ( 1531 - 1630年 ) 彩蛋 ( 1571 - 1630 ) 彩蛋 彩蛋 ) 彩蛋 发表了数篇载有行星运动详细描述的天文论文。 这些文件中包括我们目前称为开普勒行星运动法的研究结果。 这些结论概述如下。

    Kepler’s First Law 
    ::开普勒的第一法

    The path of each planet around the sun is an ellipse with the sun at one focus.
    ::太阳周围每个行星的路径 是一个有太阳焦点的椭圆

    An Elliptical Orbit Of A Planet Around The Sun At One Focus.

    Though it seems at first glance that this law is incorrect (the sun appears to be in the center of our orbit), remember that a perfect circle is an ellipse with the foci in the same place. Since the Earth's orbit is nearly circular, the sun appears to stay in the center.
    ::尽管乍一看,这一法律似乎不正确(太阳似乎处于我们轨道的中心 ) , 但要记住,完美的圆圈是在同一地方有方形的椭圆形。 由于地球轨道几乎是圆形的,太阳似乎停留在中间。

    Kepler’s Second Law  
    ::开普勒的第二法

    As a planet moves in its orbit, a line from the sun to the planet sweeps out equal areas in equal times.
    ::当一个行星在其轨道上移动时,从太阳到地球的一条线会同时扫出平等的区域。

    Kepler'S Second Law Showing Equal Areas Swept Out By A Planet In Orbit.

    The image above illustrates this relationship. Though the green wedges may appear significantly different in area, Kepler's second law states that the areas are equal if the planet travels along the perimeter of the segments in equal periods of time. From this, we can clearly see that the planet moves with greater when it is near the sun and slower when it is far away.
    ::以上图像说明了这种关系。 虽然绿色的网点在面积上看起来可能大不相同,但开普勒的第二项法律指出,如果行星在相同时间沿各区段的周界行走,那么区域是平等的。 从这一点上,我们可以清楚地看到,当地球靠近太阳时,其移动会更大,而远处则会更慢。

    Use the simulation below to observe a planet in orbit around a star . Start by adjusting the eccentricity, which is a measure of how elliptical its orbit is. What do you notice as its eccentricity increases? Does it appear to speed up or slow down along its journey? Try to apply Kepler’s first and second laws to make predictions about the planet’s orbital motion before pressing play.
    ::使用下面的模拟来观察环绕恒星的轨道上的行星。 从调整偏心度开始,这是测量其轨道如何的尺度。 当它的偏心度增加时,你注意到什么?它似乎在加速或放慢其旅程?尝试应用开普勒的第一和第二条定律来预测行星的轨道运动,然后按下播放。

    Kepler’s Third Law
    ::开普勒的第三法律

    The ratio of the squares of the periods of any two planets revolving around the sun is equal to the ratio of the cubes of their average from the sun.
    ::任何两个围绕太阳旋转的行星周期的平方比例等于它们平均的立方体与太阳的比例。

    ( T 1 T 2 ) 2 = ( r 1 r 2 ) 3

    :伤心T1T2)2=(r1r2)3

    This is the only one of Kepler's three laws that deals with more than one planet at a time.
    ::这是开普勒三部法律中唯一一部 一次处理不止一个行星的法律

    This equation can be reworked to reveal that the ratio between the period and the radius of the planet's orbit is always the same:
    ::这一方程式可以重新拟订,以表明地球轨道周期和半径之间的比率始终相同:

    ( T 1 ) 2 ( r 1 ) 3 = ( T 2 ) 2 ( r 2 ) 3

    :伤心T12(r1)3=(T2)(r2)3

    In truth, it has been calculated that this ratio holds for all the planets in our solar system, in addition to moons and other satellites. 
    ::事实上,据计算,除了卫星和其他卫星之外,这一比率还适用于太阳系中的所有行星。

    Try to apply Kepler’s third law in the simulation below to help you determine the right launch date to get a spacecraft to land on Mars. Then, because this law holds for all planets in our solar system, try other launches from Venus to Earth or from Mars to Venus.
    ::尝试在下面的模拟中应用开普勒的第三个法律来帮助您确定让航天器降落在火星的正确发射日期。 然后,由于这一法律对太阳系中的所有行星都适用,所以尝试从金星到地球或从火星到金星的其他发射。

    Example
    ::示例示例示例示例

    The planet Venus has a mean distance from the sun of 108.2 ×10 6 km and a period of 0.615 years. The planet Mars has an average mean distance from the sun of 227.9 ×10 6 km and a period of 1.88 years. Do these planets follow Kepler’s third law?
    ::金星行星与太阳的平均距离为108.2×106公里,时长为0.615年,火星与太阳的平均距离为227.9×106公里,时长为1.88年。 这些行星是否遵循开普勒的第三定律?

    The average mean distance of Venus divided by the average mean distance of Mars = 0.475.  The period of Venus divided by the period of Mars = 0.327.
    ::金星的平均平均距离除以火星的平均平均距离=0.475。金星的平均距离除以火星的时期=0.327。

    The square of the period ratio is 0.107 and the cube of the mean distance ratio is 0.107.  It is clear that these two planets follow Kepler’s third law.
    ::周期比率的平方是0.107,平均距离比率的立方是0.107。 很明显,这两个行星都遵循开普勒的第三个定律。

    Summary
    ::摘要

    • Kepler’s first law: The path of each planet around the sun is an ellipse with the sun at one focus.
      ::开普勒的第一道定律:太阳周围每个行星的路径都是以太阳为焦点的椭圆。
    • Kepler’s second law: Each planet moves such that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal periods of time.
      ::开普勒的第二定律:每个行星的移动方式都使得从太阳到地球的假想线在相同的时间段内扫出平等的区域。
    • Kepler’s third law: The ratio of the squares of the periods of any two planets revolving around the sun is equal to the ratio of the cubes of their average distance from the sun.
      ::开普勒的第三项法律:两个行星环绕太阳周期的平方比例等于它们与太阳平均距离的立方体比例。

    Review
    ::回顾

    1. The average mean distance of the earth from the sun is 149.6 ×10 6 km and the period of the earth is 1.0 year.  The average mean distance of Saturn from the sun is 1427 ×10 6 km. Using Kepler’s third law, calculate the period of Saturn.
      ::地球与太阳的平均平均平均距离是149.6×106公里,地球的周期是1.0年。土星与太阳的平均平均距离是1427×106公里。使用开普勒的第三个定律计算土星的周期。
    2. Which of the following is one of Kepler's Laws of Planetary Motion?
      1. Planets move in elliptical orbits with the Sun at one focus.
        ::行星移动在椭圆轨道上,以太阳为焦点。
      2. Gravitational force between two objects decreases as the distance squared.
        ::两个对象之间的引力随着距离平方而下降。
      3. An object in motion remains in motion.
        ::活动对象仍在活动。
      4. Inner planets orbit in a different direction that outer ones.
        ::内行星运行的方向与外行星不同

      ::以下哪一个是开普勒行星运动定律?行星以太阳为焦点移动在椭圆轨道上。两个物体之间的引力随着距离平方而下降。一个在运动的物体仍在运动中。内行星以与外行星不同的方向运行。
    3. If a planet's orbital speed is 20 km/s when it's at its average distance from the sun, which is most likely orbital speed when it is nearest the sun?
      1. 10 km/s
        ::10公里/秒
      2. 15 km/s
        ::15公里/秒
      3. 20 km/s
        ::20公里/秒
      4. 25 km/s
        ::25公里/秒

      ::如果一个行星的轨道速度是20公里/秒,如果它距离太阳的平均距离是20公里/秒,那么太阳距离最近时最有可能是轨道速度? 10公里/15公里/秒/20公里/秒/25公里/秒。

    Explore More
    ::探索更多

    Use this resource to answer the questions that follow.
    ::使用此资源回答下面的问题 。

    1. What is the shape of a planetary orbit?
      ::行星轨道的形状是什么?
    2. How are the areas swept out by the line able to be equal, when the line is much longer at some times than others?
      ::当这条线在某些时候比其他时间长得多时,这条线扫出的地区如何能够平等?
    3. What is the T in Kepler's third law? What is the r?
      ::开普勒第三定律的T是什么?