Add Wilkin (1996) solution as special case to Sec 5

will-henney / bowshock-shape

Calculate shape of wind-wind bowshocks

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Add Wilkin (1996) solution as special case to Sec 5 #54

Closed will-henney closed 6 years ago

will-henney commented 7 years ago

[x] Calculate R90 and Rc
[ ] Look at asymptotic tail behaviour

will-henney commented 7 years ago

Jorge has calculate R_90 and R_c

will-henney commented 7 years ago

Jorge has made an attempt to fit a parabola to the tail. The main problem is that we will never find a good fit over a wide range in x. We should concentrate on the range x = 0 -> -5 as we did with the CRW shapes. Also, we should use the same techniques as in sec 5.3. In principle, we ought to get the right result by taking the limit $\beta \to 0$ of eq. (69) and (70), but this is problematic because the coefficients won't converge.

will-henney commented 7 years ago

In fact, I think I have shown that the asymptotic behavior for x -> -infinity is cubic, not quadratic. So that explains why a parabola will not fit over a large range of x. But this doesn't matter, since we are only interested in the thetas that give theta' = 90 for a reasonable range of inclinations, which is probably up to theta = 150 or so.