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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.
     
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  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

    Bandersnatch

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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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