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With the development of aerospace science and technology, more and more probes are expected to be deployed around extraterrestrial planets. In this paper, some special orbits around Jupiter, Saturn, Uranus, and Neptune are discussed and analyzed. The design methods of some special orbits are sorted out, considering the actual motion parameters and main perturbation forces of these four planets. The characteristics of sun-synchronous orbits, repeating ground track orbits, and synchronous planet orbits surrounding these plants are analyzed and compared. The analysis results show that Uranus does not have sun-synchronous orbits in the general sense. This paper also preliminarily calculates the orbital parameters of some special orbits around these planets, including the relationship between the semi-major axis, the eccentricity and the orbital inclination of the sun-synchronous orbits, the range of the regression coefficient of the sun-synchronous repeating ground track orbits, and the orbital parameters of synchronous planet orbits, laying a foundation for more accurate orbit design of future planetary probes.