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Astronomy/Eccentricity of an Ellipse

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Expert: - 2/16/2005


Question
Is there any way to calculate the eccentricity of an ellipse when ONLY the semi-major axis is given? If so, do you know how to do this or  where can I find how to do this? Thanks!

Answer
Hello.

Unfortunately, the sort of calculation you seek is not possible. This is because the figure known as an ellipse - changes limits between two quantities - which we call c and a (the semi-major axis).

The eccentricity indicates a measure of the departure from circularity - so needs a ratio of BOTH a and c to define it.

First, what is c?

It is the square root of the difference between the semi-major axis squared, and the semi-minor axis squared:

c = (a^2  -  b^2)^ 1/2

Note that when c = 0 we have a = b. (One constant, fixed radius: e.g. r = a = b)

This means the figure is a perfect circle.

When, however, a > b then the shape alters to elliptical.

In the most extreme case - where c = a, the ellipse reduces to a line segment - bearing the foci (F1, F2)

Again, in general, since the shape of an ellipse requires TWO descriptors, or parameters- one need to know BOTH a and c to calculate the eccentricity, e:

e =  c/ a

There is no other way to do it - using only the semi-major axis a.  

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Philip Stahl

Expertise

I have forty years of experience in Astronomy, specifically solar and space physics. My specialties include the physics of solar flares, sunspots, including their effects on Earth and statistics as applied to astronomical investigations.

Experience

Astronomy: more than forty years experience starting with construction of my own simple telescopes. Worked at university observatory in college, doing astrographic measurements. M.Phil. degree in Physics/Solar Physics and more than ten years as researcher.

Organizations
American Astronomical Society (Solar Physics and Dynamical Astronomy divisions), American Mathematical Society, American Geophysical Union

Publications
Solar Physics (journal), The Journal of the Royal Astronomical Society of Canada, The Proceedings of the Meudon Solar Flare Workshop (1986), The Proceedings of the Caribbean Physics Conference (1985). Books: 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level'.

Education/Credentials
B.A. Astronomy, M. Phil. Physics

Awards and Honors
American Astronomical Society Studentship Award (1984), Barbados Government Award for Solar Research

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