hyperbola: a conic section, its most common use in dialling is the shape of the declination lines on many types of dial.
Hyperbola - A curved path that does not close on itself. A body moving with a speed greater than escape velocity follows a hyperbola ...
HYPERBOLA
A hyperbola is a conic section (the intersection of a cone with a plane) that has two mirror-image branches. Hyperbolas have an eccentricity greater than 1.
For hyperbolas and prolate ellipses,
B = 1- e2
For oblate ellipses,
B = 1/(1-e2) boattail (NASA Thesaurus / NASA SP-7, 1965) The rear portion of an elongated body, as a rocket, having decreasing cross-sectional area toward the rear.
The spacecraft entered the Martian atmosphere on 4 July 1997 directly from its approach hyperbola at about 7300 m/s without going into orbit around the planet. The cruise stage was jettisoned 30 minutes before atmospheric entry.
If we assume that the bolograph of solar energy is simply a graph of amorphous radiation from an ideal radiator, so that the con- Temperature stants cl, c 2 , of Planck's formula determined terrestrially apply to it, the hyperbola of maximum ...
The total energy E of the comet, which is a constant of motion, will determine whether the orbit is an ellipse, a parabola, or a hyperbola.
Ellipse & Hyperbola Construction - An interactive sketch showing how to trace the curves of the ellipse and hyperbola. (Requires Java.)
Ellipse Construction - Another interactive sketch, this time showing a different method of tracing the ellipse.
(Tilt still more and you get hyperbolas--not only don't the trajectories close, but the directions of coming and going make a definite angle).
Java applet illustrating properties of an hyperbola
Java applet illustrating properties of a parabola ...
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).
In fact, the path of the spacecraft relative to Earth is a related geometric figure called a hyperbola. If we simply change the word ellipse to hyperbola, the modified version of Kepler's first law still applies, as does Kepler's second law.
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.
The others are the parabola, the circle, and the hyperbola. The ellipse is vitally important in astronomy as celestial objects in periodic orbits around other celestial objects all trace out ellipses.
The Agena second burn some 980 seconds later followed by Agena-Mariner separation injected the Mariner 2 spacecraft into a geocentric escape hyperbola at 26 minutes 3 seconds after lift-off.
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.
In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
of an asteroid is used to describe the dimensions of its orbit around the Sun, and its value determines the minor planet's orbital period ...
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.
If the polar distance of the Sun is equal to the observer's latitude, the shadow path of a gnomon's tip on a sundial will be a parabola; at higher latitudes it will be an ellipse and lower, a hyperbola.
Related Articles ...
In euclidean geometry space is postulated to be "flat", i.e., to be the three-dimensional analog of a plane. In noneuclidean geometry space is "curved", i.e., is the three-dimensional analog of a sphere or a hyperbola. [F88]
Germanium ...
 See also: Orbit, Distance, Sun, Second, Planet
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