Astrophysics   Sunqm-3s4: Using {N,n} QM Structure and Multiplier N’ to Analyze Saturn’s (And Other Planets’) Ring Structure

Authors: Yi Cao

All Saturn rings do follow p{N,n} QM structure. By using planet’s Earth-sized core as pCore{0,1} and r1, Saturn’s inner core, outer core, surface, B-ring, and moons of Mimas, Enceladus, Tethys, Dione, and Rhea, are almost perfectly at pCore{0,n=1..9//3} orbits or sizes. Also Uranus’ major ring (ε ring), and its minor moons Portia, Puck, and its major moons Miranna, Arial, Umbriel, Titania, Oberon, are at orbit of pCore{0,n//2} with n ≈ 3, 3, 4, 5, 6,7, 9, and 10 approximately. All major rings of gas/ice planet are at Δn = +1 out of planet’s surface (if using their Earth-sized core as r1). For Neptune and Uranus, both of their surfaces are at pCore{0,2//2} size, and their major rings are at pCore{0,3//2} orbit. For Saturn and Jupiter, both of their surfaces are at around pCore{0,3//3} size, and their major rings are at pCore{0,4//3} orbit. By comparing between similar massed planets, the pCore{N,n} QM structure analysis suggests that Uranus’ ring is younger than that of Neptune’s, and Saturn’s ring is younger than that of Jupiter’s. Saturn’s major ring (B-ring, base frequency n=4)’s inner edge can be described by a multiplier n’ = 4*3^6 - 167 = 2749, its outer edge can be described by n’ = 4*3^6 +225 = 3141, and its thickness can be described by n’ =4*3^25 = 3.39E+12. Saturn’s A, B, C, D rings may follow the radial probability density distribution curve. We can use p{N,n} QM and r^2 *|R(n,l)|^2 *|Y(l,m)|^2 to build Saturn major ring’s true 3D structure probability function as shown in equation-4.