It is sometimes a source of wonder that the planets move in ellipses instead of circles, but it is easily seen from Fig. 20 that the planet, _P_, could not by any possibility move in a circle, since the direction of its motion at _P_ is not at right angles with the line joining it to the sun as it must be in a circular orbit, and even if it were perpendicular to the radius vector the planet must needs have exactly the right velocity given to it at this point, since either more or less speed would change the circle into an ellipse. In order to produce circular motion there must be a balancing of conditions as nice as is required to make a pin stand upon its point, and the really surprising thing is that the orbits of the planets should be so nearly circular as they are. If the orbit of the earth were drawn accurately to scale, the untrained eye would not detect the slightest deviation from a true circle, and even the orbit of Mercury (Fig. 17), which is much more eccentric than that of the earth, might almost pass for a circle. [Illustration: FIG. 21. An impossible orbit.] The orbit _P 2_, which lies between the parabola and the straight line, is called in geometry a hyperbola, and Newton succeeded in proving from the law of gravitation that a body might move under the sun's attraction in a hyperbola as well as in a parabola or ellipse; but it must move in some one of these curves; no other orbit is possible.[1] Thus it would not be possible for a body moving under the law of gravitation to describe about the sun any such orbit as is shown in Fig. 21. If the body passes a second time through any point of its orbit, such as _P_ in the figure, then it must retrace, time after time, the whole path that it first traversed in getting from _P_ around to _P_ again--i. e., the orbit must be an ellipse. [1] The circle and straight line are considered to be special cases of these curves, which, taken collectively, are called the conic sections. Newton also proved that Kepler's three laws are mere corollaries from the law of gravitation, and that to be strictly correct the third law must be slightly altered so as to take into account the masses of the planets. These are, however, so small in comparison with that of the sun, that the correction is of comparatively little moment.