Currently, 285 natural satellites orbiting the eight solar system major planets have been discovered, exhibiting a wide range of orbital and physical properties. Most previous studies of natural satellites focus only on satellites of one particular planet, or one satellite group. This paper introduces a new orbital parameter, denoted as ``n', which is independent of planetary characteristics but dependent on stellar parameter. It is defined as the natural logarithm of the semi-major axis of the orbit in units of the solar radius. It is found that moons of the different planets all exhibit a bimodal distribution of n values, with the majority falling within the $n\gtrsim2$ range, followed by a smaller number within the $n\lesssim-1$ range, and very few located in the intermediate region. Analysis of satellite physical parameters and orbital parameters with respect to n reveals common features among satellites of the six major planets. Firstly, satellites with high orbital eccentricity and inclination tend to have n values around 3.5, and they are irregular satellites of the giant planets. Secondly, satellites with n values between $-1$ and 1 are typically characterized by large volume, high mass, high albedo, and slow rotation rates. In addition, we identified 11 candidate exomoon candidates from the literature and found that massive ones also tend to fall within the $-1 < n < 1$ range, with less massive ones in other ranges. These consistent patterns suggest that the formation mechanisms of satellites in the solar system for different planets and for the potential exomoons may share similar formation mechanism.