Changes between Version 1 and Version 2 of u/johannjc/scratchpad23
- Timestamp:
- 02/09/17 11:33:25 (8 years ago)
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u/johannjc/scratchpad23
v1 v2 17 17 $v_\phi = \omega(r - R^2/r) \sin \theta$ 18 18 19 Then one just needs to use19 which takes into account the angular momentum of the wind as it leaves the surface of the planet. Then one just needs to use 20 20 21 21 $v \times B = 0$ … … 25 25 $\nabla \cdot B = 0$ 26 26 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 get27 to 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 28 28 29 29 $\alpha = \frac{R^2 B_r(R) }{r^2 v_p(r)}$ 30 30 31 32 31 which has nearly the same $1/r^2$ dependence as in the Parker Spiral - although it takes into account the actual parker velocity. 33 34