mellanus orbits

Omen mass: 341 Mearth
Zwonmu mass: 0.95 Msol

Earth GM: 3.98600436e14 m^3/s^2
Sun GM:   1.3271244e20  m^3/s^2

Omen GM:   1.35922749e17 m^3/s^2
Zwonmu GM: 1.26076818e20 m^3/s^2

Omen Horseshoe half-width accounting for Omen and Zwonmu mass: 0.0355342316 * SMA

Mellanus inner SMA: 0.806293382au = 1.20619773e11 m
Omen SMA:           0.836      au = 1.2506382e11 m
Mellanus outer SMA: 0.865706618au = 1.29507867e11 m

Mellanus inner period: 271.316538 days
Omen period:           286.293878 days
Mellanus outer period: 301.851079 days

synodic period:
1/S = 1/E - 1/P
S = synodic period
E = inferior planet
P = exterior planet

Inner mellanus synodic period:
1/271.316538 - 1/286.293878 = 1/5186.2523
Outer mellanus synodic period:
1/286.293878 - 1/301.851079 = 1/5554.86274

5186.2523 days = 14 years 2 months 15 days
5554.86274 days = 15 years 2 months 19 days

Omen Hill Sphere:
8891538366.662882 meters

Omen radius: 68,335,000m

Omen angular size at close approach: 0.880681595 degrees