Variational Quantum Algorithms (VQAs) are hybrid methods that use classical optimizers and quantum circuits to solve different minimization problems. Due to similarities with neural networks, these circuits might be called quantum neural networks, as they are composed of many layers of quantum gates whose parameters must be optimized to minimize a given loss function. This work's objective is to use a VQA for solving systems of coupled differential equations that describe the satellite's motion in the presence of orbital perturbations. We implement the VQA for propagating an orbit with atmospheric drag and gravitational perturbation considering the effects of the J2 term - Earth's second zonal harmonic that's used to describe the variation of the gravitational potential due to the planet's oblate geometry. After solving a simplified two-dimensional version of the problem, we propagate the actual 3D orbit and compare the VQA solution to the numerical one. Finally, we discuss the existing challenges and opportunities of this method and how to improve it in future works.