Final answer:
The synodic periods of superior planets show a trend where they approach a value slightly longer than an Earth year as the distance from Earth increases, due to the slower orbital speeds of planets that are farther from the Sun.
Step-by-step explanation:
When observing the synodic periods of the superior planets (those outside of Earth's orbit), a trend becomes apparent related to their distance from the Sun and orbital periods.
The synodic period is defined as the time it takes for a planet to return to the same position in relation to the Earth and the Sun. According to Kepler's third law, the square of the orbital period (P) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit, which is indicative of its average distance from the Sun.
Jupiter, which is 5 AU from the Sun, has a synodic period of approximately 399 days. Saturn, at almost 10 AU, has a synodic period of about 378 days. As you look at planets with increasingly longer orbits like Uranus (19 AU) and Neptune (30 AU), their synodic periods also grow longer, moving closer to 370 days for Uranus and slightly increasing for Neptune.
The trend indicates that the synodic period of a superior planet approaches a value slightly longer than an Earth year as we consider planets farther from Earth. This happens because the farther a planet is from the Sun, the slower it moves in its orbit.
The Earth, moving faster in its orbit because it is closer to the Sun, takes approximately an Earth year to catch up and align with a superior planet. As the planets get farther away, the differences in orbital speed decrease; hence, the synodic periods converge towards an Earth year but do not surpass it significantly as the planets' orbital periods become much longer than Earth's.