The ancient Greeks introduced the study of certain kinds of curves called "conic sections."  These include ellipses, parabolas, and hyperbolas.  Centuries later,  Johannes Kepler discovered that ellipses are precisely what is needed to describe the orbits of planets revolving around the sun.  Isaac Newton then found a mathematical explanation based on his Law of Universal Gravitation.  The orbit of our Moon revolving around the Earth is also an ellipse, as are the orbits of the moons of Jupiter around that planet.  Here are some links which will provide an introduction to ellipses , to Kepler's Laws , and to the  quantity called the eccentricity.
 
 

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