|(Note: in orbital diagrams, the sizes of the Sun and planets are NOT to scale)|
Synodic and Sidereal Periods of Revolution
As the planets move around the Sun, they change their positions relative to each other. Since the inner planets, in smaller orbits, move faster around the Sun and have shorter orbital periods, they continually gain on the outer planets, and occasionally lap them. The time required to do this is referred to as the synodic period of revolution, as opposed to the sidereal period of revolution, which is the time required for a planet to move once around the Sun relative to the stars, and is equal to the orbital period. (Note that this is similar to the difference between the sidereal period of rotation, which is the time required for a planet to turn once on its axis relative to the stars, and is usually defined as its rotation period, and the synodic period of rotation, which is the time required for a planet to turn once on its axis relative to the Sun, and is the length of its day.)
During a synodic period, there are four times when each planet is said to have a certain aspect relative to the other planet, and the Sun. If, as seen from one planet, the other one is in the same direction as the Sun, it is said to be at conjunction, or in conjunction with the Sun. If, on the other hand, a planet is in the opposite direction from the Sun, it is said to be at opposition. If the angle between the Sun and the planet is 90 degrees, or a quarter of a circle, the planet is said to be at quadrature -- Eastern quadrature, if the planet is 90 degrees to the east of the Sun, and Western quadrature, if the planet is 90 degrees to the west of the Sun. In the second diagram below, the Sun and the Earth are shown as fixed in position, while another planet moves around the Sun, from one aspect to another. Of course, the Earth is not fixed in position, but also moves around the Sun, as shown in the first diagram; but to us, living on the Earth, it appears as though we are fixed, and we can create that same illusion, in the second diagram, by simply rotating it around the Sun at the same rate that the Earth moves around the Sun, but in the opposite direction to the Earth's motion. So, since the planetary motions are shown as counter-clockwise in the first diagram (which is eastward, relative to the Sun and stars), the diagram has to be rotated clockwise, to make the Earth appear to be fixed in position.
The motion of the Earth and another planet around the Sun, showing both moving eastward (counter-clockwise, in this view) around the Sun, but at different rates.
The motion of an outer planet, as seen from a "fixed" Earth. Because this requires rotating the image backward at our orbital rate, which is faster than the motion of the outer planet, the outer planet appears to be moving backwards (westward = clockwise, in this view) relative to the Sun. Thus, it moves westward from conjunction to Western quadrature, then to opposition, then to Eastern quadrature, and back to conjunction.
Inferior and Superior Aspects
The discussion above presumes that the other planet can be seen in all directions, from the Earth. But this is only true for planets which have larger orbits than ours, or superior planets. (In this sense, superior means "higher than" the Earth, or more specifically, farther from the Sun than the Earth.) Mars, Jupiter, and the other outer planets can be seen at the aspects listed above. But Mercury and Venus, which are closer to the Sun, can never be opposite the Sun, or even at right angles to it, because that would require their orbits to be larger than ours, which is contradictory to their position. These inferior planets (meaning "lower than", or closer to the Sun than the Earth) have a different set of aspects than the outer planets.
Since inferior planets are closer to the Sun than we are, their elongation, or the angle between them and the Sun, can never be larger than a certain value, which is called their greatest elongation, and is typically about 45 degrees, as seen from the next planet out, because of the more or less regular spacing of the planets. Thus, Mercury's greatest elongation as seen from Venus is about 45 degrees, Venus' greatest elongation as seen from the Earth is about 45 degrees, and the Earth's greatest elongation as seen from Mars is about 45 degrees. This is only an approximate relationship, and only holds as true as the planets are evenly spaced, in their distance from the Sun; and because of the large gap between the orbits of Mars and Jupiter, Mars' greatest elongation, as seen from Jupiter, is less than 20 degrees, which is even closer to the Sun than the greatest elongation of Mercury, as seen from the Earth (which is about 27 degrees).
Obviously, the inner planet can never be seen at quadrature or opposition, if it can never be 90 or more degrees from the Sun; but there are still four aspects defined for the inner planet, as shown in the diagram below. There are two conjunctions, one with the inner planet between the Sun and the outer planet, and one with the two planets on opposite sides of the Sun, which are called inferior or superior conjunction, according to how far the inner planet is from the outer one; when they are closer, the inner planet is at inferior conjunction, passing between the Sun and the outer planet; when they are further, the inner planet is at superior conjunction, with the two planets on opposite sides of the Sun. The diagram below shows the aspects for an inferior planet.
The motion of an inner planet, as seen from a "fixed" Earth. Because the backward rotation at our orbital rate is slower than the faster motion of the inner planet, the inner planet appears to be moving forwards (eastward = counter-clockwise, in this view) relative to the Sun. Thus, it moves from inferior conjunction to greatest western elongation, then to superior conjunction, then to greatest eastern elongation, and finally back to inferior conjunction.
Relationship Between Superior and Inferior AspectsRetrograde MotionPlanetary Transits
As it happens, when the inner planet is at inferior conjunction, it would see the outer planet opposite the Sun, at opposition; so inferior conjunction and opposition are related, being the different views that each planet sees of the other, when one is in between the other and the Sun. Similarly, when an inner planet is seen at superior conjunction by an outer planet, the inner planet sees the outer planet at conjunction. So a "superior", or outer planet, has only one conjunction, which occurs when it sees the inner planet at superior conjunction; whereas an inner planet has an additional conjunction (inferior conjunction), which occurs when it sees the outer planet at opposition.
In a similar way, greatest elongations, which are the moments when the outer planet sees the inner planet as far to one side of the Sun or the other as possible, are related to quadratures, in that the inner planet sees the outer planet at eastern quadrature when the outer planet sees the inner planet at greatest western elongation, and the inner planet sees the outer planet at western quadrature when the outer planet sees the inner planet at greatest eastern elongation.