The only difference made by the Earth's own movements in this case is, that as its motion is slower than and in the same direction as that of the inferior planet, the times between two successive conjunctions or elongations will be longer than if the Earth were at rest.

382. As seen from the Earth, the superior planets appear to reach stationary points in the same manner, but for a different reason. At the moment a superior planet appears stationary, the Earth, as seen from that planet, has reached its point of eastern or western elongation. In fact, let P in Fig. 43 repre

FIG. 43. Diagram explaining the Retrogradations, Elongations, and Stationary Points of Planets.

sent a superior planet at rest, and let the inferior planet represented be the Earth. From the western elongation through superior conjunction, the motion of the planet. referred to the stars beyond it will be direct-i.e. from *1 to *2, as shown by the outside arrow; when the Earth is at its eastern elongation, as seen from the planet, the planet as seen from the Earth will appear at rest, as we are advancing for a short time straight to it. When this point is passed, the apparent motion of the planet will be reversed; it will appear to retrograde from *2 to *1, as shown by the inside arrow.

383. As in the former case, the only difference when

we deal with the planet actually in motion, will be that the times in which these changes take place will vary with the actual motion of the planet; for instance, it will be much less in the case of Neptune than in the case of Mars, as the former moves much more slowly.

384. In consequence of the Earth's motion, the period in which a planet regains the same position with regard to the Earth and Sun is different from the actual period of the planet's revolution round the Sun. The time in which a position, such as conjunction or opposition, is regained, is called a synodic period. They are as follow for the different planets :

Mercury.
Venus

Mars

Mean Solar
Days.
115.87

583'92

779'94

Now these synodic periods are the periods actually observed, and from which the times of revolution of the planets round the Sun, or their periodic times, have been found out. This is easily done, as follows: Let us represent the periodic times of any two planets by O and I; O representing the outside planet of the two, and I the inside one; and let us begin with the Earth and Mercury. As the periodic time is the time in which a complete circuit round the Sun, or 360°, is accomplished; in one day, as seen from the Sun, the portion of the orbit passed over would be equal to 360° divided by I and O; or I 360° 360° 360°,

and

the difference between these, or I

360°

Ο

will be the number of degrees which the inside planet gains daily on the outside one.

385. The actually observed interval from one conjunction of the two planets to the next, we will represent by T; but it is evident that in this time the inner one has gained exactly one complete revolution, or 360°, upon the outer one; in fact, the outer one will have advanced a certain distance, and the inner one will have completed a revolution, and in addition advanced the same distance before the two planets are together again. Therefore, 360°

T

will represent the daily rate of separation, which we

In this case we want to know I, or the periodic time of Mercury, and we know by observation, T, the synodic period of Mercury and the Earth, which is given in the previous table as 115.87 days, and O, the time of revolution of the Earth = 365 256 days. We therefore transpose the equation to get the unknown quantity on one side, and the known ones on the other: we get

386. Next let us take the Earth and Jupiter. In this case, as Jupiter is now the outside planet, we must transpose equation (1):—

as O, or the periodic time, is the unknown quantity, and I and T are the two known ones. Proceeding as before,

The periodic time of Jupiter is therefore 4332'9 days.

387. We may also use equation (1) when, having the periodic times of two planets given, we wish to determine their synodic time. In this case T is the unknown quantity, and I and O the known ones. Let us take the Earth and Mars, whose periodic times are nearly 365 256 and 6869 respectively. We have

LESSON XXXII.—Apparent Movements of the Planets (continued). Inclinations and Nodes of the Orbits. Apparent Paths among the Stars. Effects on Physical Observations. Mars. Saturn's Rings.

388. If the motions of the planets were confined to the plane of the ecliptic, the motions, as seen from the Earth, would be along the same path as that followed by the Sun; but as we have seen, the orbits are all inclined somewhat to that plane. Here is a table of the present inclinations, and positions of the ascending nodes (Art. 233):—

389. A moment's thought will convince us that the apparent distance of a planet from the plane of the ecliptic will be greater, as seen from the Earth, if the planet is near the Earth at the time of observation; and it also follows that as the distance of the planet from the Earth must thus be taken into account, the distance above or below the plane of the ecliptic will not appear to vary so regularly when seen from the Earth as it would do could we observe it from the Sun.

390. Moreover, it should be clear that when the pianet is at a node, it will always appear in the ecliptic.