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Derive tidal force upon star (approximation: divide star in 2)

  1. Dec 23, 2016 #1
    1. The problem statement, all variables and given/known data
    Spherical,homogeneous star with radius R orbiting black hole at distance ## r_p >>R ## .Derive the tidal force acting upon the star by dividing the star into two equal parts and making the necessary approximations.

    2. Relevant equations
    The tidal force equation of ## a \propto \frac{ R }{ {r_p}^3} ## is not a given.
    3. The attempt at a solution
    I calculated the force acting on the nearest and farthest hemisphere from the black hole.
    Nearest: ##dF_1= \frac{G M_o dm}{{(r_p-R+r)}^2} ## where ## M_o ## is the mass of the black hole and ## dm= \rho \pi r^2 dr ## the mass of a disk with thickness dr . By integrating from 0 to R I got ## F_1= \frac{3GM_o M(2r_p-R)}{4r_p R^2} ##.
    For the farthest hemisphere ## dF_2=\frac{G M_o dm}{{(r_p+R-r)}^2} \Longrightarrow F_2= \frac{3GM_o M(2r_p+R)}{4r_p R^2} ##
    By substracting these,I get the tidal force ## \Delta F= F_1-F_2=\frac{3}{2} \frac{GM_oM}{R r_p} ## which is definitely not in agreement with the actual physics of the problem,since it should be proportional to R.
    Can someone point me to where I went wrong?
     
  2. jcsd
  3. Dec 24, 2016 #2

    haruspex

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    You seem to have defined r here as the distance from the point of the star nearest the black hole to the disk. The disk's radius will not be r.
     
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