How do I calculate the length of the major axis of an ellipse? I have the eccentricity and the length of the semi-major axis.

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    $\begingroup$ You multiply the length of the semi-major axis by 2. You don't need the eccentricity. The semi-major axis is half the major axis by definition. $\endgroup$ – Ron Maimon May 8 '12 at 4:28

As wikipedia points out, the eccentricity $\epsilon$ of an ellipse obeys the equation $$\epsilon=\sqrt{1-\left(\frac{b}{a}\right)^2}$$ where $a$ and $b$ are respectively the semi-major and semi-minor axes of the ellipse.

  • 2
    $\begingroup$ Um, the question asked for major axis from semimajor axis--- the answer is "multiply by 2". $\endgroup$ – Ron Maimon May 8 '12 at 4:29
  • $\begingroup$ @Ron: sounds like an answer to me... $\endgroup$ – J. M. isn't a mathematician May 8 '12 at 6:21

Multiply the semi-major axis by 2, and that's the major axis.


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