The Science of the StarsMaunder, E. Walter (Edward Walter)
History
The Science of the Stars
Maunder, E. Walter (Edward Walter)
Astronomy
These curves are what are known as the "+conic sections+"--that is,
they are the curves found when a cone is cut across in different
directions. Their relation to each other may be illustrated thus. If
we have a very powerful light emerging from a minute hole, then, if we
place a screen in the path of the beam of light, and exactly at right
angles to its axis, the light falling on the screen will fill an exact
circle. If we turn the screen so as to be inclined to the axis of the
beam, the circle will lengthen out in one direction, and will become an
ellipse. If we turn the screen still further, the ellipse will
lengthen and lengthen, until at last, when the screen has become
parallel to one of the edges of the beam of light, the ellipse will
only have one end; the other will be lost. For it is clear that that
edge of the beam of light which is parallel to the screen can never
meet it. The curve now shown on the screen is called a +parabola+, and
if the screen is turned further yet, the boundaries of the light
falling upon it become divergent, and we have a fourth curve, the
+hyperbola+. Bodies moving under the influence of {35} gravitation can
move in any of these curves, but only the circle and ellipse are closed
orbits. A particle moving in a parabola or hyperbola can only make one
approach to its attracting body; after such approach it continually
recedes from it. As the circle and parabola are only the two extreme
forms of an ellipse, the two foci being at the same point for the
circle and at an infinite distance apart for the parabola, we may
regard all orbits under gravitation as being ellipses of one form or
another.
Public-domain text, read in full here on John Shaqi.
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