Definition of an Ellipse
An ellipse is a closed, two-dimensional geometric shape defined as the set of all points in a plane where the sum of the distances from two fixed points (called foci) is constant. It is one of the conic sections, formed by the intersection of a cone with a plane that does not pass through the apex and is not parallel to the base, an element of the cone, or perpendicular to the axis.
Key Properties of an Ellipse
The two foci (F1, F2) are critical to its definition. An ellipse also has a major axis (the longest diameter passing through both foci) and a minor axis (the shortest diameter, perpendicular to the major axis at the center). The semi-major axis is half the major axis, and the semi-minor axis is half the minor axis. Eccentricity measures how elongated the ellipse is, with 0 representing a perfect circle and values closer to 1 indicating a more elongated shape.
Practical Example in Astronomy
Planets in our solar system, including Earth, orbit the Sun in elliptical paths, not perfect circles. According to Kepler's First Law of Planetary Motion, the Sun is located at one of the two foci of each planet's elliptical orbit. This explains why a planet's distance from the Sun varies throughout its year, leading to phenomena like perihelion (closest point) and aphelion (farthest point).
Applications Beyond Astronomy
Elliptical shapes have diverse applications. In optics, elliptical reflectors are used to concentrate light or sound to a single focal point, as seen in some spotlights or 'whispering galleries' where sound waves reflect to a specific location. In engineering, elliptical gears can provide variable speed ratios, and their strong structural properties are utilized in architectural designs and bridge construction.