轨道运动

播放段落

Orbital Motion
::轨道运动

播放段落

We commonly talk about satellites orbiting Earth. But what does that really mean? When a satellite, space shuttle, or some other object is orbiting a planet, it maintains a circular orbit around the planet a constant off the surface. Manmade satellites typically orbit between 200 and 400 miles. For example, the International Space Station (ISS) orbits at 370 km, or 230 miles.
::我们通常谈论卫星环绕地球。但这意味着什么?当一颗卫星、航天飞机或其他物体环绕一个行星时,它维持一个环绕地球的轨道,一个固定在地表之外的恒定轨道。人造卫星一般在200至400英里之间运行。例如,国际空间站(ISS)轨道为370公里,或230英里。

播放段落

The ISS has an average of 7.66 km/sec tangential to its orbit. An orbiting satellite is close enough to be acted upon by Earth’s gravity. This force is constantly pulling the satellite in toward the center of the earth – it is a and causes a . At this height, however, Earth’s gravity is only about 8.7 m/s ² . As was discussed in Motion in Two Dimensions: , the velocity and centripetal acceleration are perpendicular.
::国际空间站的轨道平均相切值为7.66公里/秒。轨道卫星离地球引力足够近,可以运行。这一力量不断将卫星拉向地球中心 — — 地球中心是其中的一个,并造成一个。然而,在这一高度,地球的重力只有大约8.7米/秒。 正如在两个方面运动中所讨论的:速度和子宫加速度是垂直的。

播放段落

NASA scientists, in designing this and all other satellites, must carefully calculate the velocity necessary to keep the satellite orbiting. To keep the satellite from falling back to Earth, the horizontal velocity must be large enough. The satellite must travel far enough horizontally that it follows the curve of the planet, as shown below.
::美国航天局科学家在设计这颗卫星和所有其他卫星时,必须仔细计算卫星轨道运行所需的速度。为了防止卫星返回地球,水平速度必须足够大。卫星必须沿着地球曲线水平飞行,如下文所示。

播放段落

When the satellite is orbiting in this way, it is falling straight down towards Earth. Imagine standing in an elevator when the bottom drops out from under you. The elevator, you, and anything you might have had with you all fall straight down. If you had a backpack on your back, the of the books can no longer be felt because the books are in free fall as well. A similar thing is happening in the space shuttle or orbiting satellite, where objects are weightless.  
::当卫星以这种方式在轨道上运行时,它正直接掉向地球。 想象一下当底部从你下面掉下来时, 站在电梯里。 电梯, 你, 你, 以及你可能拥有的任何东西, 都直接掉下来。 如果你背上有一个背包, 书本就再也无法感受到了, 因为书本也自由掉落。 类似的事情正在发生在航天飞机或轨道卫星上发生, 在那里, 物体是无重的。

播放段落

For a full description of weight, look at Forces: Mass versus Weight. In sum, weight is the result of the force of gravity being opposed by the normal force .  As we just learned, objects in orbit are in free fall; they have nothing exerting a normal force against them and thus no weight.
::对于重量的完整描述,请看力量:质量对重量。总之,重量是重力受到正常力反对的结果。正如我们刚刚了解到的,轨道上的物体处于自由坠落状态;它们没有正常力量来对付它们,因此没有重量。

 

播放段落

Examples
::实例

播放段落

Example 1  
::例1

播放段落

Consider a satellite of the earth orbiting at 225 km above the surface of the earth.  Keep in mind that this is NOT the radius of the satellite’s orbit.  The satellite’s orbit is measured from the center of the earth, so its radius will be the radius of the earth, 6.37 × 10 ⁶  m, plus the 225,000 m.  The mass of the earth is 5.98 × 10 ²⁴ kg.  What is the velocity of the satellite?
::考虑地球轨道卫星在地球表面225公里上方运行。 记住这不是卫星轨道的半径。 卫星的轨道是从地球中心测量的, 因此其半径将是地球半径6. 37×106米, 加上22.5万米。 地球质量是5. 98× 1024公斤。 卫星的速度是多少?

播放段落

Since the centripetal force keeping this satellite traveling in orbit is provided by the gravitational force of the earth, we can set the formula for centripetal force equal to the formula for gravitational force.
::由于将这颗卫星留在轨道上的子胎力是由地球引力提供的,我们可以设定子胎力的公式与引力的公式相等。

播放段落

$\begin{array}{r}{F}_c=\frac{m{v}^2}{r}and{F}_g=\frac{G{m}_1{m}_2}{d^2}\end{array}$
::Fc=mv2r和Fg=Gm1m2d2

播放段落

$\begin{array}{r}\frac{G{m}_E{m}_s}{r^2}=\frac{m_s{v}^2}{r}sov=\sqrt{\frac{G{m}_E}{r}}\end{array}$
::GmEmsr2=msv2rso v=GmEr =gmEr =msv2r =msv2r = gmEr = gmEr = gmEr =msv2r

播放段落

$\begin{array}{r}v=\sqrt{\frac{(6.67\times {10}^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2)(5.98\times {10}^{24}\text{kg})}{6.60\times {10}^6\text{m}}}=7770\text{m/s}\end{array}$
:6.67×10-11 Nm2/kg2)(5.98×1024公斤) 6.60×106 m=7770 mm/s)

播放段落

Example 2
::例2

播放段落

Set the equation for Newton’s law of gravity equal to the equation for centripetal force shown below and derive an equation for the period of a planet around the earth.
::设定牛顿重力定律的方程, 等同以下显示的子宫力的方程, 并得出地球周围行星的方程 。

播放段落

$\begin{array}{r}{F}_g=\frac{G{m}_E{m}_s}{r^2}\text{and}{F}_c=\frac{4{\pi }^2{m}_{sat}r}{T^2}\end{array}$
::Fg=GmEmsr2和Fc=42 mssatrT2

 

播放段落

$\begin{array}{r}\frac{G{m}_E{m}_s}{r^2}=\frac{4{\pi }^2{m}_{s}r}{T^2}\text{and}T=2\pi \sqrt{\frac{r^3}{G{m}_E}}\end{array}$
::GmEmsr2=42msrT2和T=2°r3GmE

播放段落

Use the Space Station simulation below to observe how adjusting the initial radius of a satellite in orbit affects its orbital period, as well as the overall shape of the orbit:
::利用以下空间站模拟观测轨道上卫星最初半径的调整如何影响轨道周期以及轨道的总体形状:

播放段落

Summary
::摘要

播放段落
• A satellite in a circular orbit accelerates toward the object it is orbiting at a rate equal to the acceleration of gravity at its orbital radius.
  ::一颗卫星在环绕轨道上加速接近其轨道轨道的物体,速度相当于其轨道半径重力加速率。
播放段落
• As in a falling elevator, objects in orbit are in constant freefall.
  ::与坠落的电梯一样,轨道上的物体始终处于自由坠落状态。
播放段落
• Objects in free fall have no normal force acting upon them, and thus no weight.
  ::物体在自由坠落时,没有正常的力量对其采取行动,因此没有重量。

播放段落

Review
::回顾

播放段落
1. Sally’s mass on the earth is 50. kg.
   播放段落
   1. What is her weight on the earth?
      ::她在地球上的重量是多少?
   播放段落
   2. What is her weight on the moon?
      ::她对月球的重量是多少?
   播放段落
   3. What is her mass on the moon?
      ::她在月亮上是什么质量?
   
   ::萨莉在地球上的重量是50公斤。她在地球上的重量是多少?她在月球上的重量是多少?她在月球上的重量是多少?她在月球上的重量是多少?
播放段落
2. The radius of the planet Mercury is 2.43 × 10 ⁶ m and its mass is 3.2 × 10 ²³  kg.
   播放段落
   1. Find the speed of a satellite in orbit 265,000 m above the surface.
      ::在地面上空265,000米的轨道上找到一颗卫星的速度。
   播放段落
   2. Find the period of the satellite.
      ::找到卫星的周期。
   
   ::行星半径为2.43×106米,质量为3.2×1023公斤。在轨道上265 000米处找到一颗卫星的速度。
播放段落
3. A geosynchronous orbit is an orbit in which the satellite remains over the same spot on the earth as the earth turns. This is accomplished by matching the velocity of the satellite to the velocity of the turning earth. The orbital radius of a geosynchronous satellite is 4.23 × 10 ⁷ m (measured from the center of the earth).
   播放段落
   1. What is the speed of the satellite in orbit?
      ::轨道卫星的速度是多少?
   播放段落
   2. What is its period?
      ::期限是多少?
   
   ::地球同步轨道是一个轨道,卫星在地球转动的同一地点停留在地球的轨道上。通过将卫星的速度与转动地球的速度相匹配来实现这一点。地球同步卫星的轨道半径是4.23×107米(从地球中心测量)。轨道卫星的速度是多少?时间是多少?

播放段落

Resources
::资源

播放段落

What makes the moon go around the Earth? Watch this video to find out.
::是什么让月亮环绕地球?