Letters on Astronomy / in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers

by Denison Olmsted

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.

Fig. 34.

In Fig. 35, page 154, suppose the planet to have passed the point C, at the aphelion, with so small a velocity, that the attraction of the sun bends its path very much, and causes it immediately to begin to approach towards the sun. The sun's attraction will increase its velocity, as it moves through D, E, and F, for the sun's attractive force on the planet, when at D, is acting in the direction D S; and, on account of the small angle made between D E and D S, the force acting in the line D S helps the planet forward in the path D E, and thus increases its velocity. In like manner, the velocity of the planet will be continually increasing as it passes through D, E, and F; and though the attractive force, on account of the planet's nearness, is so much increased, and tends, therefore, to make the orbit more curved, yet the velocity is also so much increased, that the orbit is not more curved than before; for the same increase of velocity, occasioned by the planet's approach to the sun, produces a greater increase of centrifugal force, which carries it off again. We may see, also, the reason why, when the planet has reached the most distant parts of its orbit, it does not entirely fly off, and never return to the sun; for, when the planet passes along H, K, A, the sun's attraction retards the planet, just as gravity retards a ball rolled up hill; and when it has reached C, its velocity is very small, and the attraction to the centre of force causes a great deflection from the tangent, sufficient to give its orbit a great curvature, and the planet wheels about, returns to the sun, and goes over the same orbit again. As the planet recedes from the sun, its centrifugal force diminishes faster than the force of gravity, so that the latter finally preponderates.

Fig. 35.

I shall conclude what I have to say at present, respecting the motion of the earth around the sun, by adding a few words respecting the precession of the equinoxes.

The precession of the equinoxes is a slow but continual shifting of the equinoctial points, from east to west. Suppose that we mark the exact place in the heavens where, during the present year, the sun crosses the equator, and that this point is close to a certain star; next year, the sun will cross the equator a little way westward of that star, and so every year, a little further westward, until, in a long course of ages, the place of the equinox will occupy successively every part of the ecliptic, until we come round to the same star again. As, therefore, the sun revolving from west to east, in his apparent orbit, comes round to the point where it left the equinox, it meets the equinox before it reaches that point. The appearance is as though the equinox goes forward to meet the sun, and hence the phenomenon is called the precession of the equinoxes; and the fact is expressed by saying, that the equinoxes retrograde on the ecliptic, until the line of the equinoxes (a straight line drawn from one equinox to the other) makes a complete revolution, from east to west. This is of course a retrograde motion, since it is contrary to the order of the signs. The equator is conceived as sliding westward on the ecliptic, always preserving the same inclination to it, as a ring, placed at a small angle with another of nearly the same size which remains fixed, may be slid quite around it, giving a corresponding motion to the two points of intersection. It must be observed, however, that this mode of conceiving of the precession of the equinoxes is purely imaginary, and is employed merely for the convenience of representation.

The amount of precession annually is fifty seconds and one tenth; whence, since there are thirty-six hundred seconds in a degree, and three hundred and sixty degrees in the whole circumference of the ecliptic, and consequently one million two hundred and ninety-six thousand seconds, this sum, divided by fifty seconds and one tenth, gives twenty-five thousand eight hundred and sixty-eight years for the period of a complete revolution of the equinoxes.