Are there any space objects for which the synodic period is equal to infinity?

The synodic period is equal to infinity when the periods of revolutions around the Sun of a certain planet and the Earth are equal for an observer from Earth. As you know, there is no such real planet. But in the solar system such a situation takes place: these are dusty satellites of the Earth for an observer from the Moon; asteroids “Greeks” and “Trojans” in orbit of Jupiter, and Jupiter itself in relation to each other; some satellites of the giant planets.