Without any formal application of mathematics we may readily see that the swifter the motion of the body at _P_ the shorter will be the time during which it is subjected to the sun's attraction at close range, and therefore the force exerted by the sun, and the resulting change of motion, will be small, as in the orbits _P 1_ and _P 2_. On the other hand, _P 5_ and _P 6_ represent orbits in which the velocity at _P_ was comparatively small, and the resulting change of motion greater than would be possible for a more swiftly moving body. What would be the orbit if the velocity at _P_ were reduced to nothing at all? What would be the effect if the body starting at _P_ moved directly away from _1_? [Illustration: FIG. 20.--Different kinds of orbits.] The student should not fail to observe that the sun's attraction tends to pull the body at _P_ forward along its path, and therefore increases its velocity, and that this influence continues until the planet reaches perihelion, at which point it attains its greatest velocity, and the force of the sun's attraction is wholly expended in changing the direction of its motion. After the planet has passed perihelion the sun begins to pull backward and to retard the motion in just the same measure that before perihelion passage it increased it, so that the two halves of the orbit on opposite sides of a line drawn from the perihelion through the sun are exactly alike. We may here note the explanation of Kepler's second law: when the planet is near the sun it moves faster, and the radius vector changes its direction more rapidly than when the planet is remote from the sun on account of the greater force with which it is attracted, and the exact relation between the rates at which the radius vector turns in different parts of the orbit, as given by the second law, depends upon the changes in this force.