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When using formulas that describe a 2d orbit around a planetary body:

  • is it actually OK for the semi-major axis $a$ to be negative?
  • when $a$ is negative, it is impossible to compute mean anomaly from time, so what is the equivalent of mean anomaly for parabolic or hyperbolic orbits, assuming that $a$ can be negative?
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feralin
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    No, it is definitely not okay for your semi-major axis to be negative for the same reasons you cannot have a negative radius. – Kyle Kanos Nov 06 '13 at 17:04
  • So then how do I compute semi-major axis $a$ for a parabolic/hyperbolic orbit (i.e. $e >= 1$)? Would you care to answer? – feralin Nov 06 '13 at 20:33
  • You can't for a parabolic orbit (it's an undefined term). For a hyperbolic orbit, you do it the same way as an elliptic orbit: use geometry. – Kyle Kanos Nov 06 '13 at 20:42
  • But if you evaluate the equation for the semi-major axis, $a=\frac{r\mu}{2\mu-rv^2}$, for $e\geq 1$ you do get negative values. And is you use negative values in other equations which discribe orbital motion, they work just fine. – fibonatic Nov 07 '13 at 00:24
  • @fibonatic if I use $a < 0$, then $\sqrt{\frac{\mu}{a^3}}$, the "slope" of mean anomaly with respect to time, is imaginary. That doesn't work, and that is what my question is all about... – feralin Nov 07 '13 at 02:31
  • This is not correct, since the slope should be proportional to $\sqrt{\frac{\mu}{a^3(1-e^2)^3}}$ which would be complex for a positive $a$ when $e>1$. – fibonatic Nov 07 '13 at 12:26

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