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Homework Help: Planet transit to derive system parameters

  1. Oct 4, 2011 #1

    RHK

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    1. The problem statement, all variables and given/known data

    Measuring the flux of a star as a function of the time, the flux exhibit a decrease of 1.65% for 2h 56m, periodically every 57.22 days. Such decrease is ascribed to a planet transit.
    The continuous spectrum of the star is like a black body with T= 9500 K, and its bolometric luminosity is 22 times the bolometric luminosity of the Sun (that has a black body spectrum with T=5600K).
    Assuming that the planet transit is projected on the star equator, and that the planet is on a circular orbit, calculate:
    (i) The planet diameter;

    (ii) The orbit planet radius;

    (iii) The star mass.

    2. Relevant equations

    [itex]R_{sun} = 6.69*10^8 m[/itex]
    [itex]L_{bol}=4\pi R_s^2 \sigma T^4 [/itex]

    3. The attempt at a solution

    For the first point i can calculate the Sun bolometric luminosity with the same Stefan-Boltzmann law:
    [itex]L_{sun}=4\pi R_{sun}^2 \sigma T_{sun}^4 [/itex]

    and then calculate the bolometric luminosity of the star, that is 22*Lsun.
    This allow to obtain the stellar radius Rs by using the S-B law.
    Thus, the luminosity difference in the star is [itex]\Delta L= 4\pi(R_s^2 - R_{sun}^2) \sigma T_s^4 [/itex]
    where [itex]\Delta L= (100 - 1.65)\% L_s[/itex]

    Is it ok?
     
    Last edited: Oct 4, 2011
  2. jcsd
  3. Oct 7, 2011 #2

    RHK

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    Anyone can suggest if it's the correct way?
     
  4. Oct 7, 2011 #3

    RHK

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    I'm sorry: the correct eqaution is not (as reported):
    but: [itex]\Delta L= 4\pi(R_s^2 - R_{planet}^2) \sigma T_s^4 [/itex]

    What about this?
     
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