Planetary Configurations

The apparent motions of the planets are quite complicated, partly because they reflect the motion of the Earth around the Sun (Fig. 7.3). Normally the planets move eastward (direct motion, counterclockwise as seen from the Northern hemisphere) when compared with the stars. Sometimes the motion reverses to the opposite or retrograde direction. After a few weeks of retrograde motion, the direction is changed again, and the planet continues in the original direction. It is quite understandable that the ancient astronomers had great difficulties in explaining and modelling such complicated turns and loops.

Figure 7.4 explains some basic planetary configurations. A superior planet (planet outside the orbit of the Earth) is said to be in opposition when it is exactly opposite the Sun, i. e. when the Earth is between the planet and the Sun. When the planet is behind the Sun, it is in conjunction. In practise, the planet may not be exactly opposite or behind the Sun because the orbits of the planet and the Earth are not in the same plane. In astronomical almanacs oppositions and conjunctions are defined in terms of ecliptic longitudes. The longitudes of a body and the Sun differ by 180° at the moment of opposition; in conjunction the longitudes are equal. However, the right ascension is used if the other body is

Fig. 7.3. (a) Apparent motion of Mars during the 1995 opposition. (b) Relative positions of the Earth and Mars. The projection of the Earth-Mars direction on the infinitely distant celestial sphere results in (a)

Conjunction

Upper conjunction

Greatest eastern elongation

/ Inferior conjunction

Earth Opposition

Fig. 7.4. Planetary configurations. The angle a (Sun-object-Earth) is the phase angle and e (Sun-Earth-object) is the elongation not the Sun. Those points at which the apparent motion of a planet turns toward the opposite direction are called stationary points. Opposition occurs in the middle of the retrograde loop.

Inferior planets (Mercury and Venus) are never in opposition. The configuration occurring when either of these planets is between the Earth and the Sun is called inferior conjunction. The conjunction corresponding to that of a superior planet is called upper conjunction or superior conjunction. The maximum (eastern or western) elongation, i. e. the angular distance of the planet from the Sun is 28° for Mercury and 47° for Venus. Elongations are called eastern or western, depending on which side of the Sun the planet is seen. The planet is an "evening star" and sets after the Sun when it is in eastern elongation; in western elongation the planet is seen in the morning sky as a "morning star".

The synodic period is the time interval between two successive events (e. g. oppositions). The period which we used in the previous chapters is the sidereal period, the true time of revolution around the Sun, unique

Upper conjunction

for each object. The synodic period depends on the difference of the sidereal periods of two bodies.

Let the sidereal periods of two planets be P1 and P2 (assume that Pi < P2). Their mean angular velocities (mean motions) are 2n/P1 and 2n/P2. After one synodic period P1>2, the inner planet has made one full revolution more than the outer planet: 2n 2n

P1 P2

The angle Sun-planet-Earth is called the phase angle, often denoted by the Greek letter a. The phase angle is between 0° and 180° in the case of Mercury and Venus. This means that we can see "full Venus", "half Venus", and so on, exactly as in the phases of the Moon. The phase angle range for the superior planets is more limited. For Mars the maximum phase is 41°, for Jupiter 11°, and for Neptune only 2°.

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