126. _Apparent Motion of an Inferior Planet._--When the planet is at _P_, if it could be seen at all, it would appear in the heavens at _A_. As it moves from _P_ to _P'_, it will appear to move in the heavens from _A_ to _B_. Then, as it moves from _P'_ to _P''_, it will appear to move back again from _B_ to _A_. While it moves from _P''_ to _P'''_, it will appear to move from _A_ to _C_; and, while moving from _P'''_ to _P_, it will appear to move back again from _C_ to _A_. Thus the planet will appear to oscillate to and fro across the sun from _B_ to _C_, never getting farther from the sun than _B_ on the west, or _C_ on the east: hence, when at these points, it is said to be at its _greatest western_ and _eastern elongations_. This oscillating motion of an inferior planet across the sun, combined with the sun's motion among the stars, causes the planet to describe a path among the stars similar to that shown in Fig. 145. [Illustration: Fig. 146.] 127. _Phases of an Inferior Planet._--An inferior planet, when viewed with a telescope, is found to present a succession of phases similar to those of the moon. The reason of this is evident from Fig. 146. As an inferior planet passes around the sun, it presents sometimes more and sometimes less of its bright hemisphere to the earth. When the earth is at _T_, and Venus at superior conjunction, the planet turns the whole of its bright hemisphere towards the earth, and appears _full_; it then becomes _gibbous_, _half_, and _crescent_. When it comes into _inferior conjunction_, it turns its dark hemisphere towards the earth: it then becomes _crescent_, _half_, _gibbous_, and _full_ again. 128. _The Sidereal and Synodical Periods of an Inferior Planet._--The time it takes a planet to make a complete revolution around the sun is called the _sidereal period_ of the planet; and the time it takes it to pass from one aspect around to the same aspect again, its _synodical period_. [Illustration: Fig. 147.] The synodical period of an inferior planet is longer than its sidereal period. This will be evident from an examination of Fig. 147. _S_ is the position of the sun, _E_ that of the earth, and _P_ that of the planet at inferior conjunction. Before the planet can be in inferior conjunction again, it must pass entirely around its orbit, and overtake the earth, which has in the mean time passed on in its orbit to _E'_. While the earth is passing from _E_ to _E'_, the planet passes entirely around its orbit, and from _P_ to _P'_ in addition. Now the arc _PP'_ is just equal to the arc _EE'_: hence the planet has to pass over the same arc that the earth does, and 360° more. In other words, the planet has to gain 360° on the earth. The synodical period of the planet is found by direct observation. 129. _The Length of the Sidereal Period._--The length of the sidereal period of an inferior planet may be found by the following computation:--