IX. That the apparent motions of the sun and moon are not so complicated as those of the planets will be clear at once if we remember that the sun's apparent motion is caused by our seeing the sun projected against the celestial sphere in the ecliptic, the path cut out by the plane of the earth's orbit, while in the case of the moon, what we see is the moon's actual motion around the earth projected against the celestial sphere in the great circle traced by the moon's own orbital plane produced to an indefinite extent. These motions are further complicated by the rotation of the earth on its own axis, causing the rising and setting of the sun and the moon. These two bodies, however, always appear to be moving directly on in their courses, each completing a revolution around the earth in a definite time, the sun in a year, the moon in 29-1/2 days. What we see in the case of the planets, on the other hand, is a complex motion compounded of the effects of the earth's daily rotation, its yearly revolution around the sun, and the planets' own revolutions in different periods of time in elliptical orbits around the sun. These complex planetary motions are characterized by the peculiar oscillations known as 'direct' and 'retrograde' movements. [Illustration: Fig. 4.] The motion of a planet is said to be _direct_ when it moves in the direction of the succession of the zodiacal signs; _retrograde_ when in the contrary direction. All of the planets have periods of retrograde and direct motion, though their usual direction is direct, from west to east. Retrograde motion can be explained by reference to the accompanying diagrams. In Fig. 4, the outer circle represents the path of the zodiac on the celestial sphere. Let the two inner circles represent the orbits of the earth and an inferior planet, Venus, around the sun, at S. (An _inferior_ planet is one whose orbit around the sun is within that of the earth. A _superior_ planet is one whose orbit is outside that of the earth.) V, V' and V", and E, E', and E" are successive positions of the two planets in their orbits, the arc VV" being longer than the arc EE" because the nearer a planet is to the sun, the greater is its velocity. Then when Venus is at V and the earth at E, we shall see Venus projected on the celestial sphere at V{1}. When Venus has passed on to V' the earth will have passed to E' and we shall see Venus on the celestial sphere at V{2}. The apparent motion of the planet thus far will have been direct, from west to east in the order of the signs. But when Venus is at V" and the earth at E" Venus will be seen at V{3} having apparently moved back about two signs in a direction the reverse of that taken at first. This is called the planet's retrograde motion. At some point beyond V", the planet will appear to stop moving for a very short period and then resume its direct motion. In Fig. 5, the outer arc again represents the path of the zodiac on the celestial sphere.