Eccentricity (mathematics) Totally Explained

Everything about Eccentricity Mathematics totally explained

In mathematics, the eccentricity, denoted e or

varepsilon

, is a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.
In particular,

The eccentricity of a circle is zero.
The eccentricity of an (non-circle) ellipse is greater than zero but less than 1.
The eccentricity of a parabola is 1.
The eccentricity of a hyperbola is greater than 1 but less than infinity.

Furthermore, two conic sections are similar if and only if they've the same eccentricity.

Definitions

For every conic section, there exist a fixed point F, a fixed line L and a non-negative number e such that the conic section consists of all points whose distance to F equals e times their distance to L. e is called the eccentricity of the conic section.
The linear eccentricity of a conic section, denoted c or e, is the distance between its center and its focus (or one of its two foci).

Alternative Names

The eccentricity is sometimes called first eccentricity to distinguish it from the second eccentricity and third eccentricity defined for ellipses (see below). The eccentricity is also sometimes called numerical eccentricity.
In the case of ellipses and hyperbolas the linear eccentricity is sometimes called half-focal separation.

Notation

Two notational conventions are in common use:

e for the eccentricity and c for the linear eccentricity.

varepsilon

for the eccentricity and e for the linear eccentricity. We will use the first one in this article.

Values

conic section	equation	eccentricity (e)	linear eccentricity (c)
circle	$x^2+y^2=r^2$	$0$	$0$
ellipse	$frac ight)$	$o!varepsilon$

Quadrics

The eccentricity of a three-dimensional quadric is the eccentricity of a designated section of it. For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (for example in the equatorial plane).

Celestial Mechanics

In celestial mechanics, for bound orbits in a spherical potential, the definition above is informally generalized. When the apocentre distance is close to pericentre distance, the orbit is said to have low eccentricity; when they're very different, the orbit is said be eccentric or having eccentricity near unity. This definition coincides with the mathematical definition of eccentricity for ellipse, in Keplerian, for example,

1/r

potentials.

Further Information

Get more info on 'Eccentricity Mathematics'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://eccentricity__mathematics.totallyexplained.com">Eccentricity (mathematics) Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.