The Moon revolve around the Earth or the Sun

Celestial mechanics. Modeling and simulation of a complex dynamic system using a system of differential equations.
The objective of this task is to model and simulate the movement of the Moon around the Earth and the Sun.
They can use the article “The Equations of Planetary Motion and Their Numerical Solution” as a base. But they must use vector operations.
The initial conditions of the physical system, positions and velocities, must be real. Enter https://ssd.jpl.nasa.gov/horizons/app.html#/ and the following
screen appears Select
vector table:

  1. The planet is selected
  2. The data time is selected
  3. Press Generate Ephemeris and the data is obtained
    Problem . Does the Moon revolve around the Earth or the Sun? What is the trajectory that the Moon follows during a year?

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