ellipse

Ellipse A closed curve that is symmetrical about two perpendicular axes and has one axis longer than the other. The longer axis is the major axis; the other is called the minor axis. The ellipse belongs to the family of curves known collectively as conic sections because they can all be generated by slicing through a solid cone in different ways. The other types of conic section are the circle, the parabola and the hyperbola. The shape of the orbit of a body moving under the influence of a central gravitational force is necessarily one of the conic sections. The ellipse is important in celestial mechanics since closed orbits are invariably elliptical. (The special case of the circle is rarely achieved naturally.) Planets have elliptical orbits around the Sun. When a body is in an elliptical orbit under a gravitational force, the object providing the gravitational attraction lies at one focus of the ellipse. There are two foci located on the major axis, each the same distance (c) from the centre of the ellipse (see illustration). The more elongated the ellipse, the greater the value of c in relation to the semimajor axis (a). The ratio c/a defines the eccentricity (e) of the ellipse, which must be more than zero but less than unity (e = 0 for a circle; e = 1 for a parabola. The size of the semiminor axis (b) is linked to a and e by the formula . The sum of the distances between any point on an ellipse and the two foci is a constant with the value 2a. This property means that an ellipse can be drawn with the help of a loop of string fixed between two points. A pencil moved so that the loop remains just taut will trace out an ellipse.