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An ellipse is a geometric shape that is generated when a plane intersects a conical shape and produces a closed curve. Circles are a special subset of the ellipse. Though any particular formula for these shapes may seem rather complex, they are a common form in natural systems such as in orbital planes in space and at the atomic scale.
An oval is another general name for an ellipse, both being convex closed curves where any line drawn from two points on the curve will lie within the confines of the curve itself. The ellipse has a mathematical symmetry, however, that an oval doesn't necessarily have. If a line is drawn through the major axis of an ellipse, which is through its center and to both of its farthest ends, any two points on the line that are equally distant from the center are described as foci points F1 and F2. The sum of any two lines drawn from F1 and F2 to the circumference of the ellipse will add up to the total length of the major axis, and this is known as the focal property of the ellipse. When the foci points of F1 and F2 are in the same location on the major axis, this is the true definition of a circle.
Another ellipse equation is the polar equation, which is used to determine perihelion and aphelion for the closest and farthest points in a body's orbit, such as the Earth around the Sun. Taking the location of F1 on the major axis as being the location of the Sun, the closest point of the ellipse shape to F1 would be perihelion. The farthest point of the ellipse, on the opposite side of F2, would be aphelion, or the farthest point of the Earth in its orbit of the Sun. The actual polar equation is used to calculate the radius of an orbit at any one point in time. It can seem complicated when written out in algebraic form, but becomes self-evident when labeled diagrams accompany it.
The orbits of planets around the sun were first discovered to have ellipse point locations by Johannes Kepler, who published his ten-year-long research of the orbit of Mars in 1609 in the book entitled Astronomia Nova, literally meaning A New Astronomy. This discovery was later expounded upon by Isaac Newton in 1687 when he published Philosophiae Naturalis Principia Mathematica, literally The Principles. It detailed Newton's law of universal gravitation governing the mass of orbiting bodies in space.
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