10.5 天体测量

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  天体测量

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  Astrometry is one of the oldest methods that astronomers have for studying the motion of stars. The name says it all: astrometry is the process of measuring the positions of objects in the sky. This technique has been used to measure parallax (distances) to stars and proper motions (motions in the plane of the sky) and to detect binary star orbits.  More recently, astronomers have tried to detect exoplanets with this technique. This technique has not been very successful from ground-based telescopes because distortions from the atmosphere ("twinkling" of stars) blurs out the spatial position of stars and therefore does not permit precise enough measurements.  However, astrometry as a planet detection technique is about to explode onto the scene with the launch of the by the European Space Agency.
  ::天文学是天文学家研究恒星运动的最古老的方法之一。 名字上写道: 天体测量是测量天体位置的过程。 这一技术被用于测量星体的等距(距离)和适当的运动(天空的平面运动)并探测二进制恒星轨道。 最近, 天文学家试图用这种技术探测外行星。 地基望远镜的这一技术并不十分成功, 因为大气层的扭曲(星体的“交汇”)模糊了恒星的空间位置,因此无法进行精确的测量。 然而,欧洲航天局发射时,行星探测技术的天体测量技术即将在现场爆炸。

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  The basic idea behind astrometry for exoplanet detection is depicted in . Astronomers obtain a series of pictures over time (a "time series") and use at least three reference stars (which have nearly constant positions) to measure the changing position of the host star in the plane of the sky.
  ::用于探测外行星的天体测量背后的基本想法在 . 天文学家在一段时间内获得一系列图片(一个“时间序列”),并使用至少三个参考恒星(这些恒星几乎具有恒定位置)来测量主星在天平上的位置变化。

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  Q1. How is astrometry (or the "astrometric technique") different from Direct Imaging or from the Doppler method?
  
  ::问题1. 天体测量(或“天体测量技术”)与直接成像或多普勒方法有何不同?

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  With direct imaging, astronomers obtain an actual image of the planet. To confirm that the planet is not a background source, additional observations are taken over time, verifying orbital motion of the planet candidate.  But the big difference between direct imaging and astrometry is that with direct imaging the planet is observed.
  ::通过直接成像,天文学家获得了地球的真实图像。为了确认地球不是一个背景来源,随着时间的流逝,将进行更多的观测,以核实候选行星的轨道运动。但是,直接成像和天体测量之间的巨大区别是,用直接成像观察地球。

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  Like the Doppler (or "radial velocity") technique, astrometry is an "indirect" method - the planet is not seen, but its existence is inferred by the gravitation effect that the planet exerts on the host star. However, different things are being measured with Doppler and Astrometric techniques; the radial velocity technique measures the changing speed of the star along one dimension: the line of sight. The fundamental data are measurements of radial velocity over time.  Astrometry measures the changing position (not speed) of the star projected onto the two-dimensional plane of the sky. The fundamental data are positions (angles and angular separations) over time.
  ::与多普勒(或“半径速度”)技术一样,天体测量是一种“间接”方法——没有看到行星,但其存在则通过行星对宿主恒星施加的引力效应推断出来。然而,正在用多普勒和天体测量技术测量不同的事物;半径速度技术测量恒星在一个维度上的变化速度:视线线。基本数据是测量时间的辐射速度。天体测量测量测量测量卫星在射入天体二维平面上的位置变化(而不是速度)。基本数据是长期的方位(矩形和角分离)。

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  Because astrometric measurements are made in two dimensions (x, y in the plane of the sky), the astrometric orbital model measures the true mass of the planet; it does not suffer from the unresolved inclination of orbital models from the radial velocity method.
  ::由于天体测量是在两个维度(天平上的x, y)上进行的,天体轨道模型测量地球的真正质量;轨道模型的未解决倾角不会因辐射速度法的轨道模型而受到影响。

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  The changing position of the host star is determined by the mass and the orbit of the planet. The main equation to keep in mind is:
  ::恒星恒星位置的变化取决于行星质量和轨道。要铭记的主要方程式是:

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  $\begin{align*}{M}_{star}\ast {\alpha }_{star} = {m}_{planet}\ast {\alpha }_{planet}\end{align*}$      [Eqn 1]
  ::Mstarstar=mplanetplanet[第1款]

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  Where:
  ::此处:

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  • $\begin{align*}{M}_{star}\end{align*}$ is the mass of the star
    ::Mstar是恒星的质量
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  • $\begin{align*}{\alpha }_{star}\end{align*}$ is the angular separation between the star and the center of mass
    ::α恒星是恒星与质量中心之间的角分离
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  • $\begin{align*}{m}_{planet}\end{align*}$ is the mass of the planet
    ::mplanenet 是地球的质量
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  • $\begin{align*}{\alpha }_{planet}\end{align*}$ is the angular separation between the (unseen) planet and the center of mass.
    ::α大陆网是(看不见的)行星与质量中心之间的角分离。

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  The first thing to do is to use the distance to the star to convert $\begin{align*}{\alpha }_{star}\end{align*}$ and $\begin{align*}{\alpha }_{planet}\end{align*}$ into physical distances in Astronomical Units, or AU's. Referring back to the section on measuring stellar distances, use:
  ::首先要做的是使用离恒星的距离将α星和αplanet转换成天文单位或AU的物理距离。

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  $\begin{align*}{r}_{star} = {\alpha }_{star}\ast {D}_{star}\end{align*}$
  ::恒星 * 星星 * 星星 * 星星星 *

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  Where $\begin{align*}{r}_{star}\end{align*}$ is the distance between the star and the center of mass in AU and $\begin{align*}{D}_{star}\end{align*}$ is the distance from our solar system to the star in units of parsecs.  Then, equation 1 becomes:
  ::恒星是恒星与AU和Dstar中质量中心之间的距离,Dstar是太阳系与恒星之间的距离,以分析为单位。然后,等式1变成:

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    $\begin{align*}{M}_{star}\ast {r}_{star} = {m}_{planet}\ast {r}_{planet}\end{align*}$      [Eqn 2]
  ::Mstar*rstar=mplanet*rplanet[英文第2页]

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    Q2. Calculate the Astrometric Displacement of the Sun
  
  ::Q2. 计算太阳的天体偏移

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  1. The mass of Jupiter is 0.001 times the mass of the Sun and Jupiter orbits at a distance of about 5 AU from the Sun. What is the astrometric displacement (in AU) of the Sun because of Jupiter?
     ::木星的质量是太阳和木星轨道质量的0.001倍,距离太阳大约5AU。由于木星的原因,太阳的天体迁移(在非盟)是多少?
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  2. The mass of Saturn is 1/3 the mass of Jupiter and Saturn orbits at a distance of about 10 AU from the Sun. What is the astrometric displacement (in AU) of the Sun because of Saturn?
     ::土星质量是木星和土星轨道质量的1/3,距离太阳约10AU。 土星的天体迁移(在非盟)是多少?
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  3. If Saturn (at 10AU) had the same mass as Jupiter, would the astrometric displacement of the Sun be smaller or larger than the displacement from the real Jupiter at 5AU?
     ::如果土星(在10AU时)与木星质量相同,太阳的天体移位是否小于或大于5AU时实际木星的移位?
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  4. Can you picture the total astrometric orbit of the Sun that is caused by both Jupiter and Saturn?
     ::你能想象一下由木星和土星造成的太阳的总天体轨道吗?

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  Notice that even if you know the mass of the star (from its spectral type) and the distance between the star and the center of mass with astrometry, there are still two unknowns in equation 2: the mass of the planet and the semi-major axis of the planet. However, astrometric observations also reveal the orbital period, so we can use Kepler's Laws to derive the semi-major axis of the planet. Then, if you know the mass of the star and measure the astrometric displacement of the star, you can solve for the planet mass.
  ::请注意,即使您知道恒星的质量( 从其光谱类型) 和恒星与星体中心之间的距离以及天体测量, 方程式中仍然有两个未知点: 行星的质量以及行星的半主轴。 然而, 天体测量观测还揭示了轨道周期, 这样我们就可以使用开普勒的定律来得出行星的半主轴。 然后, 如果您知道恒星的质量, 并且测量恒星的天体偏移, 您可以解决行星质量问题 。

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  Astrometry of multi-planet systems
  ::多大陆板系统的天体测量

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  Consider our solar system. With 8 planets, this is a good example of a multi-planet system. What does Kepler's Third Law tell you about the orbital periods of our planets? The star wobble demo in the downloaded  package (Extrasolar Planets simulations)  will allow you to add in an arbitrary number of solar system planets and see the gravitational effect on the Sun that might be observed if we were observing from above the orbital plane. However (this is an important point), to fully model an astrometric orbit, astronomers must observe the star through a large fraction of one complete orbit.  This would require about 12 years of observations to detect Jupiter or 30 years for Saturn.  How long will the fly?
  ::考虑我们的太阳系。 有8个行星, 这是多行星系统的一个好例子。 Kepler的第三个法律告诉了你我们行星的轨道周期吗? 下载的包件( 太阳行星模拟) 中的恒星波状演示将允许您添加任意数量的太阳系行星, 并查看如果我们从轨道平面上观测到的对太阳的引力效应。 然而( 这是一个重要点 ) , 要充分模拟一个天体测量轨道, 天文学家必须通过一个完整轨道的很大一部分来观察恒星。 这将需要大约12年的观察来探测木星, 或者需要30年的时间来观察土星。 飞行要多久?

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    Q3. Astrometric Displacement of the Sun - a Bird's Eye view
  
  ::Q3. 太阳的天体迁移——鸟类眼观

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  Run the , selecting only Jupiter. Then run the simulation selecting only Saturn.  Does this match the result you expected from Q2 parts a and b?
  
  ::运行,只选择木星。然后运行模拟,只选择土星。这是否与您期望从 Q2 a 和 b 部分得到的结果相符?

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  Now run the  selecting both Jupiter and Saturn. Does this result match your picture from Q2 part d?
  ::现在运行选中的木星和土星。 此结果是否匹配您在 Q2 部分 d 中的照片 ?

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  How do the astrometric influences of Mercury, Venus, Earth, Mars, and Pluto compare to the influence of Jupiter, Saturn, Uranus, and Neptune.
  ::与木星、土星、天王星和海王星的影响相比,水星、金星、地球、火星和冥王星的天体测量影响如何?

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  The astrometric motion of the Sun is depicted in the   below. These positional measurements assume a bird's eye view looking down onto the orbital plane of the solar system.
  ::以下描述了太阳的天体运动。这些位置测量假设鸟的眼观向下看太阳系的轨道平面。

  

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  The time series astrometric motion of the Sun from the gravitational tug of the orbiting planets. What is the approximate period of the largest loops of orbital motion for the Sun? What planet in our solar system has a similar period? Why doesn't the astrometric orbit of the Sun look like a single closed circle or ellipse?
  ::太阳从轨道行星引力拖动中的时间序列天体测量运动。 太阳轨道运动的最大环圈的大约时间是什么时候? 我们太阳系中哪个行星有类似的时间段? 为什么太阳的天体测量轨道看起来不像一个封闭的圈或椭圆?