An ellipse is a closed curve generated by a plane intersecting a conical shape. It has focal points and a focal property. Circles are a subset of ellipses. The polar equation is used to determine perihelion and aphelion in orbits. Johannes Kepler discovered elliptical orbits, and Isaac Newton detailed the law of universal gravitation.
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. While any particular formula for these shapes may seem quite complex, they are a common shape in natural systems such as orbital planes in space and on the atomic scale.
An oval is another generic name for an ellipse, both being closed convex curves in which any line drawn from two points on the curve will lie within the boundaries of the curve. 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, passing through its center and both of its farthest ends, any two points on the line that are equally distant from the center are described as focal 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 focal points of F1 and F2 are in the same position 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 furthest points in a body’s orbit, such as the Earth around the Sun. Taking the position of F1 on the major axis as the position of the Sun, the point on the ellipse closest to F1 would be perihelion. The furthest point of the ellipse, on the opposite side of F2, would be aphelion, or the furthest point of the Earth in its orbit of the Sun. The effective polar equation is used to calculate the radius of an orbit at any time . It may seem complicated when written in algebraic form, but it becomes apparent when labeled diagrams accompany it.
Johannes Kepler, who in 1609 published his decades-long research into the orbit of Mars in the book entitled Astronomia Nova, which literally means A New Astronomy, found that the orbits of the planets around the sun had positions of elliptical points. This discovery was later set forth by Isaac Newton in 1687 when he published Philosophiae Naturalis Principia Mathematica, literally The Principles. He detailed Newton’s law of universal gravitation which governs the mass of bodies orbiting in space.
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