Changes between Version 1 and Version 2 of u/johannjc/scratchpad23


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Timestamp:
02/09/17 11:33:25 (8 years ago)
Author:
Jonathan
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  • u/johannjc/scratchpad23

    v1 v2  
    1717$v_\phi = \omega(r - R^2/r) \sin \theta$
    1818
    19 Then one just needs to use
     19which takes into account the angular momentum of the wind as it leaves the surface of the planet.  Then one just needs to use
    2020
    2121$v \times B = 0$
     
    2525$\nabla \cdot B = 0$
    2626
    27 to solve for the steady state magnetic field.  We can write $B = \alpha v$ to satisfy the first constraint, and then the divergence in spherical coords to get
     27to solve for the steady state magnetic field.  We can write $B = \alpha v$ to satisfy the first constraint, and then the divergence of B in spherical coords to get
    2828
    2929$\alpha = \frac{R^2 B_r(R) }{r^2 v_p(r)}$
    3030
    31 
    3231which has nearly the same $1/r^2$ dependence as in the Parker Spiral - although it takes into account the actual parker velocity.
    33 
    34