## ellipse
foci (singular: focus), is constant (see
figure 2). If the two foci coincide then the ellipse is a circle.
The ellipse is symmetric with respect to both its axes, and is a closed
curve. The line passing through the foci is called the major axis of the ellipse; half this is the semi-major axis, a. The line passing through the center of the ellipse (the
midpoint of the foci) at right angles to the major axis is called the minor
axis, half of which is the semi-minor axis, b.
An ellipse centered at the origin of an x-y coordinate system with
its major axis along the x-axis is defined by the equationx^{2}/a^{2} + y^{2}/b^{2}
= 1
The shape of an ellipse is expressed by a number called the eccentricity, e, which is related to a and b by the formula b^{2}
= a^{2}(1 - e^{2}). The eccentricity is a
positive number less than 1, or 0 in the case of a circle. The greater the
eccentricity, the larger the ratio of a to b, and therefore
the more elongated the ellipse. The distance between the foci is 2ae.
The area enclosed by an ellipse is π ab. The circumference of an
ellipse is 4aE(e), where the function E is the complete
elliptical integral of the second kind.
## Elliptical orbitsThe closed path followed by one object that is gravitationally bound to another – for example, by one of the stars in a binary star system or a spacecraft in Earth orbit. That the orbits of the planets are ellipses, not circles, was first established by Johannes Kepler based on the careful observations of Tycho Brahe.## Related categories• PLANE CURVES• CELESTIAL MECHANICS | |||||||||

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