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How to check a statement about orbital angles of exoplanets?

  1. Apr 23, 2015 #1
    Hi, everybody. Mi name is Fabio Onier Osorio Pelaez and I'm from Colombia.

    I hope to be finishing my Bachelor´s degree in Physics at University of Antioquia by next August. I'm doing my final project on the detection of planets by the Radial Velocity technique and I have a question about an statement of Christophe Lovis and Debra Fischer in a paragraph in the third page or their article (page 29 in the book Exoplanets). I quote the complete paragraph emphasizing the statement in which I am interested:

    "The unknown inclination angle ##i## prevents us from measuring the true mass of the companion ##m_2##. While this is an important limitation of the RV technique for individual systems, this fact does not have a large impact on statistical studies of exoplanet populations. Because inclination angles are randomly distributed in space, angles close to 90° (edge-on system) are much more frequent than pole-on configurations. Indeed, the distribution function for ## i ## is given by ## f(i)di=\sin(i)di ##. As a consequence, the average value of ##\sin(i)## is equal to ##\pi/4## (0.79). Moreover, the a priori probability that ##\sin(i)## is larger than 0.5 is 87%."

    I wondered if you may tell me how did they conclude that. I'll be thankful if you can help me with that information. It will be very useful for my work.
  2. jcsd
  3. Apr 23, 2015 #2

    Simon Bridge

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    Welcome to PF;
    The authors tell you: "Because the inclination angles are randomly distributed...."
  4. Apr 23, 2015 #3


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    To give you another hint, imagine a six-sided die (i.e. a cube) being thrown. Pick any one pair of opposite sides - these represent the poles of the orbital arrangement. The remaining four sides represent the edges. As you can already see, there's more possibilities of an edge-on result (4 of 6) than of a pole-on result (2 of 6).
    Generalise the cube to a sphere and see if you can get the same result the authors got.
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