EDIT: Re-framed [here](https://physics.stackexchange.com/questions/657091/how-inaccurate-are-the-positions-of-the-planet-and-moon-in-my-simple-solar-syste) to be more on-topic.

I am building a model of a simplified, fictional sun-planet-moon solar system (not the real Sun-Earth-Luna system) **to calculate astronomical events like eclipses and lunar phases and the positions of the sun and moon in the sky of the planet at a given time**, and want to know if there's anything I'm missing that would affect the accuracy of the model over the scale of several hundred years (that isn't being purposefully left out; see below). I want to be physically accurate within the restricted scope of the model.

In the model, all orbits are circular and in the same plane. At $t = 0$ the three bodies are colinear, with the moon located between the sun and the planet. The sun-planet-moon barycenter is located at the origin. The sun and the planet-moon barycenter both orbit the sun-planet-moon barycenter in 360 days; the planet and the moon both orbit the planet-moon barycenter in $\frac{360}{13}$ (≈27.69) days, with one synodic month (time between full/new moons) being exactly 30 days. The following diagram **(very much NOT to scale)** illustrates these motions:

[![View of the solar system model from the north pole looking down](https://i.stack.imgur.com/Cfou6.gif)](https://i.stack.imgur.com/Cfou6.gif)

* The center of the sun has coordinates (-SunBarycenterDistance cos($t$), -SunBarycenterDistance sin($t$))
* The center of the planet has coordinates (PlanetOrbitRadius cos($t$) + PlanetBarycenterDistance cos(13$t$), PlanetOrbitRadius sin($t$) + PlanetBarycenterDistance sin(13$t$))
* The center of the moon has coordinates (PlanetOrbitRadius cos($t$) - MoonOrbitRadius cos(13$t$), PlanetOrbitRadius sin($t$) - MoonOrbitRadius sin(13$t$))

Where

* SunBarycenterDistance is the distance between the sun-planet-moon barycenter and the center of the sun, calculated based on the masses of the sun and the planet-plus-moon subsystem: (PlanetBarycenterDistance \* (MassPlanet + MassMoon)) / (MassSun + MassPlanet + MassMoon)
* PlanetOrbitRadius is the distance between the planet-moon barycenter and the sun-planet-moon barycenter, calculated based on the mass of the sun and the orbital period of the planet: cbrt((TimePlanetOrbit² \* G \* MassSun) / (4π²))
* PlanetBarycenterDistance is the distance between the planet-moon barycenter and the center of the planet: (MoonOrbitRadius \* MassMoon) / (MassPlanetPlusMoon)
* MoonOrbitRadius is the distance between the planet-moon barycenter and the center of the moon: cbrt((TimeMoonOrbit² \* G \* MassPlanet) / (4π²))
* G is the gravitational constant

Things I am purposefully leaving out:

* non-circular orbits causing changes in orbital velocity at different points in the orbit; as mentioned above, the model's orbits are circular
* apsidal precession; because the orbits are circular, there are no apsides
* nodal precession; because the orbits are in the same plane, there are no orbital nodes
* precession of the equinoxes and the difference between sidereal and solar years caused by general relativity and the oblateness of the sun and planet; I'm still working out how to calculate this and want to include it in the future, but I'm leaving it out for now
* perturbations from other bodies; the model only considers the one sun, one planet, and one moon, with no other masses acting on these three bodies

Aside from these effects that I am purposefully leaving out of the model, are there any effects or motions that should be considered?