Letters on Astronomy: in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent AstronomersOlmsted, Denison
Science
Letters on Astronomy: in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers
Olmsted, Denison
Astronomy
You have already learned, that when a body is acted on by two forces, in
different directions, it moves in the direction of neither, but in some
direction between them. If I throw a stone horizontally, the attraction
of the earth will continually draw it downward, out of the line of
direction in which it was thrown, and make it descend to the earth in a
curve. The particular form of the curve will depend on the velocity with
which it is thrown. It will always _begin_ to move in the line of
direction in which it is projected; but it will soon be turned from that
line towards the earth. It will, however, continue nearer to the line of
projection in proportion as the velocity of projection is greater. Thus,
let A C, Fig. 33, be perpendicular to the horizon, and A B parallel to
it, and let a stone be thrown from A, in the direction of A B. It will,
in every case, commence its motion in the line A B, which will therefore
be a tangent to the curve it describes; but, if it is thrown with a
small velocity, it will soon depart from the tangent, describing the
line A D; with a greater velocity, it will describe a curve nearer the
tangent, as A E; and with a still greater velocity, it will describe the
curve A F.
[Illustration Fig. 33.]
As an example of a body revolving in an orbit under the influence of two
forces, suppose a body placed at any point, P, Fig. 34, above the
surface of the earth, and let P A be the direction of the earth's
centre; that is, a line perpendicular to the horizon. If the body were
allowed to move, without receiving any impulse, it would descend to the
earth in the direction P A with an accelerated motion. But suppose that,
at the moment of its departure from P, it receives a blow in the
direction P B, which would carry it to B in the time the body would fall
from P to A; then, under the influence of both forces, it would descend
along the curve P D. If a stronger blow were given to it in the
direction P B, it would describe a larger curve, P E; or, finally, if
the impulse were sufficiently strong, it would circulate quite around
the earth, and return again to P, describing the circle P F G. With a
velocity of projection still greater, it would describe an ellipse, P I
K; and if the velocity be increased to a certain degree, the figure
becomes a parabola, L P M,--a curve which never returns into itself.
[Illustration Fig. 34.]
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