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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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    $\begingroup$ No, it is definitely not okay for your semi-major axis to be negative for the same reasons you cannot have a negative radius. $\endgroup$
    – Kyle Kanos
    Nov 6, 2013 at 17:04
  • $\begingroup$ So then how do I compute semi-major axis $a$ for a parabolic/hyperbolic orbit (i.e. $e >= 1$)? Would you care to answer? $\endgroup$
    – feralin
    Nov 6, 2013 at 20:33
  • $\begingroup$ 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. $\endgroup$
    – Kyle Kanos
    Nov 6, 2013 at 20:42
  • $\begingroup$ 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. $\endgroup$
    – fibonatic
    Nov 7, 2013 at 0:24
  • $\begingroup$ @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... $\endgroup$
    – feralin
    Nov 7, 2013 at 2:31

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