132. _Apparent Motion of a Superior Planet._--In order to deduce the apparent motion of a superior planet from the real motions of the earth and planet, let _S_ (Fig. 149) be the place of the sun; 1, 2, 3, etc., the orbit of the earth; _a_, _b_, _c_, etc., the orbit of Mars; and _CGL_ a part of the starry firmament. Let the orbit of the earth be divided into twelve equal parts, each described in one month; and let _ab_, _bc_, _cd_, etc., be the spaces described by Mars in the same time. Suppose the earth to be at the point 1 when Mars is at the point _a_, Mars will then appear in the heavens in the direction of 1 _a_. When the earth is at 3, and Mars at _c_, he will appear in the heavens at _C_. When the earth arrives at 4, Mars will arrive at _d_, and will appear in the heavens at _D_. While the earth moves from 4 to 5 and from 5 to 6, Mars will appear to have advanced among the stars from _D_ to _E_ and from _E_ to _F_, in the direction from west to east. During the motion of the earth from 6 to 7 and from 7 to 8, Mars will appear to go backward from _F_ to _G_ and from _G_ to _H_, in the direction from east to west. During the motion of the earth from 8 to 9 and from 9 to 10, Mars will appear to advance from _H_ to _I_ and from _I_ to _K_, in the direction from west to east, and the motion will continue in the same direction until near the succeeding opposition. The apparent motion of a superior planet projected on the heavens is thus seen to be similar to that of an inferior planet, except that, in the latter case, the retrogression takes place near inferior conjunction, and in the former it takes place near opposition. [Illustration: Fig. 150.] 133. _Aspects of a Superior Planet._--The four aspects of a superior planet are shown in Fig. 150, in which _S_ is the position of the sun, _E_ that of the earth, and _P_ that of the planet. When the planet is on the opposite side of the earth to the sun, as at _P_, it is said to be in _opposition_. The sun and the planet will then appear in opposite parts of the heavens, the sun appearing at _C_, and the planet at _A_. When the planet is on the opposite side of the sun to the earth, as at _P''_, it is said to be in _superior conjunction_. It will then appear in the same part of the heavens as the sun, both appearing at _C_. When the planet is at _P'_ and _P'''_, so that a line drawn from the earth through the planet will make a right angle with a line drawn from the earth to the sun, it is said to be in _quadrature_. At _P'_ it is in its western quadrature, and at _P'''_ in its eastern quadrature. [Illustration: Fig. 151.] 134. _Phases of a Superior Planet._--Mars is the only one of the superior planets that has appreciable phases. At quadrature, as will appear from Fig. 151, Mars does not present quite the same side to the earth as to the sun: hence, near these parts of its orbit, the planet appears slightly gibbous. Elsewhere in its orbit, the planet appears full.