Parabolas in Telescope Design
Demonstration of how a parabola focuses light from a plane wave source.
parabola: a mathematical term for the conic section obtained by cutting a cone with a plane parallel to its generator (or 'edge').
Parabola - A geometric curve followed by a body that moves with a speed exactly equal to escape velocity
Parallax - The shift in the direction of a star caused by the change in the position of the Earth as it moves about the Sun ...
PARABOLA
A parabola is a conic section, a curve that is a set of points (P) such that the distance from a line (the directrix) to P is equal to the distance from P to focus F. Parabolas have an of 1.
Parabola vs. sphere
If cross-sections of a spherical surface and a parabolic surface were made by slicing each surface in half, these would be the shapes you would see.
Parallax ...
Parabola
In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface....
with the summation of an infinite series
Series (mathematics) ...
gives a parabola, with a any number. Usually (though not always) y is isolated, so that the formula has the form
y = f(x) ...
Sphere versus Parabola.
Most radio telescopes use a parabolic antenna to focus the energy received to a single point. The antenna is then pointed at the object of interest using a flexible mount.
parabola (NASA Thesaurus / NASA SP-7, 1965) An open curve all points of which are equidistant from a fixed point, called the focus , and a straight line. See conic section.
The mirrors are usually a section of a rotated parabola. High energy particle telescopes detect a flux of particles, usually originating at an astronomical source.
History ...
Applying Newton's method, he presupposed a parabola as an approximation for each orbit. Among the 24 parabolas, 3 were identical in size and superimposed in space.
The orbits of comets are very elongated; some are long ellipses, some are nearly parabolic (see parabola), and some may be hyperbolic.
He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x).
Another system which forms real images consists of a set of two orthogonal parabolas of translation, off which incident X-rays reflect successively, as first proposed in 1948 by Kirkpatrick and Baez.
The airplane does this by flying in up-and-down parabolas. At the top of the parabola, people and objects inside the airplane are in free fall for about 20-30 seconds at a time.
Java applet illustrating properties of a parabola
For a given central force, increasing the velocity causes the orbit to change from a circle to an ellipse to a parabola to a hyperbola, with the changes occurring at certain critical velocities.
The sun is a small target for a meteorite coming from infinity to hit, and if this considerable quantity reaches its mark, a much greater amount will circulate round the sun in parabolas, ...
The orbit of such a body will be a parabola with the Sun as its focus. As the comet gets closer to the Sun its velocity increases reaching a maximum at its closest point whereupon is starts its journey back out to the outer reaches of the solar ...
Imagine an inverted parabola with its minimum value at = 0; the configuration of the field can be represented as the position of a ball rolling on this curve. In the stable configuration it nestles in the bottom of the potential well at = 0.
After rough Foucault measurements on 10%, 70% and 90% zones indicated that the mirror may be close to parabola, I assembled the optical tube outside (altitide bearings were not ready at that time yet) and took a look at Polaris.
Lord Rosse then used a steam-driven machine to grind the mirror to the necessary shape, that of a parabola, which brings the light reflecting off the mirror to a focus further up within the telescope tube.
An open orbit has the shape of a hyperbola (when the velocity is greater than the escape velocity), or a parabola (when the velocity is exactly the escape velocity).
A circle has an eccentricity of 0.0, a parabola 1.0.
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The inclination of a planetary orbit is measured with respect to the plane of the earth's orbit.
0 = a perfect circle; any figure between 0 and 1 = an ellipse; 1 = a parabola; any figure greater than 1 = a hyperbola. Eccentricity may sometimes be expressed as a percentage.
Newton's gravitational theory also predicts that in general, the orbit of an object can be any of the four conic sections: circle, ellipse, parabola and hyperbola; as well as the straight line.
Comet orbits vary in eccentricity between an ellipse and a parabola and have known periods from 3 to 1000s of years. The names of such periodic comets are prefaces with “P/' (e.g., Comet P/Halley).
Parabolas have an eccentricity of 1. Neptune, Venus, and Earth are the planets with the least eccentric orbits in our solar system. Pluto and Mercury are the planets with the most eccentric orbits in our solar system.
The conic sections are the ellipse, the parabola, and the hyperbola, curves that are used to describe the path or bodies moving in space. The circle is a special case of the ellipse, an ellipse with an eccentricity of zero.
He is also well known for inventing the method of solving cubic equations by intercepting a parabola with a circle.
Omar Khayyam the Writer and Poet ...
Eccentricity: The measure of the degree of elongation of an ellipse. For example, a circle has an eccentricy of 0, and a parabola (an open figure) an eccentricity of 1. The deviation of an orbit from a perfect circle.
Figure 16. Basic design for a reflecting telescope. The curved mirror is in the shape of a parabola and this allows it to bring all of the light to a focus in one location.
In 1731 he gave a demonstration of the fact noted by Newton that all curves of the third order were projections of one of five parabolas.
Any curve produced by the intersection of a plane and a right circular cone. Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola.
Comets, however, have very large eccentricities, often approaching one, the value for a parabola. Such highly eccentric orbits are just as possible as circular orbits, as far as the laws of motion are concerned.
Converging reflectors always have concave surfaces. The section shape is the arc of a circle in simple cases; the arc of a parabola is needed for more precise work. As these mirrors have positive power, they are sometimes called positive mirrors.
Hole-In-One (PDF, 468 KB): Participants experiment with a parabola and simulate the collection of ions onto the target of the concentrator to model the Genesis Solar Wind Concentrator.
Grade Level: K-4 ...
 See also: Orbit, Distance, Solar, Earth, Sun
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