Page:Popular Astronomy - Airy - 1881.djvu/147

Rh planet is moving at that point. If, then, it can be shown that when the planet is nearest to the sun it moves with a greater velocity, it will follow that, though the attractive force is greater than when farthest from the sun, its orbit may not be more curved than when it is farthest from the sun.

For this purpose, I introduced to you the model, represented in Figure 36. I pointed out to you that the tension of the cord EF, acting in the direction EF, does produce the effect of keeping in equilibrium the tension of the two other cords, one acting in the direction of EA, and the other in the direction EB; and therefore, a force acting in the direction EF, does produce two forces acting in the directions AE, BE. This is what we mean by the resolution of forces. The way in which I desire to apply this consideration to the motion of the planets is this. The sun's attraction acting in the direction MS, Figure 30, can there be resolved into two forces, in conformity with the law just mentioned; one in the direction of the line OM, touching the orbit, or in the same direction as the motion of the planet, and the other force in the direction NM, perpendicular to the orbit. As regards this part of the force which is perpendicular to the orbit, its effect may be considered as similar to that of the force of gravity on the cannon ball; its action is square to the planet's path at that time, and its tendency is to curve the planet's path. But the other resolved part pushes the body along in its orbit, so that the planet, instead of being allowed to go on in one uniform speed, is by the sun's attraction accelerated in its course. This amounts to so great a quantity that, at the time the planet has arrived at the part L of its orbit, it is going at a very great speed. When the planet has arrived at the part of the orbit