Precise orbits for the lunar navigation system: challenges in the modeling of perturbing forces and broadcast orbit representation

In the framework of the European Space Agency’s Moonlight program, a satellite navigation system is planned for positioning, navigation, timing, and communication on the Moon.  The constellation will consist of three or four lunar orbiters in eccentric orbits – with periselene above the northern hemisphere and aposelene above the southern hemisphere; the latter is of special interest in terms of future lunar missions. The eccentric orbits introduce a challenge for precise orbit determination, because large gravity perturbations due to the lunar gravity field occur in the periselene passes, whereas the aposelene passes are associated with the smallest gravity gradients and thus the largest errors in orbit determination.

We evaluate the non-gravitational and gravitational perturbing forces acting on lunar orbiters in eccentric orbits. The simulated orbits consider lunar gravity field based on the GRAIL mission, gravity perturbations from the Sun, Earth, and planets considering Earth’s oblateness, tidal deformations, direct solar radiation pressure with lunar and Earth eclipses, albedo, antenna thrust, and relativistic effects. We discuss three methods of proposed representation of the broadcast orbits: based on Keplerian parameters and a set of one-per-revolution corrections (GPS-like or Galileo-like), based on Chebyshev polynomials with a variable number of coefficients and arc-length representation, and based on a series of positions and velocities (GLONASS-like). We discuss the advantages and limitations of all three representations and accuracies provided by different approaches depending on the number of assumed coefficients and arc lengths. Finally, we discuss the impact of inconsistent treatment of the origin, scale, and orientation of the lunar reference frame on the determined positions on the Moon.