orbits near the Moon:  the L1 northern, L1 southern, L2 northern, and L2 southern families.
The particular orbit selected for Gateway is an NRHO of the L2 southern family with an orbit period selected for a 9:2 Lunar Synodic Resonance (LSR) and phasing set for avoidance of eclipses by the Earth [1].

[Figure: Figure 2:  15 Year NRHO Reference Trajectory.  The figure on the left shows the trajectory in the Earth-centered Sun-Earth rotating frame, illustrating the 9:2 LSR pattern for eclipse avoidance.  The figure on the right shows the trajectory in the familiar Moon-centered Earth-Moon rotating frame.]

The selection of this specific orbit was based on several criteria.

An L2 family NRHO was initially selected because of better visibility to the lunar far side for communications [8].  Additionally, the L2 NRHOs in the range of interest have better stability characteristics compared to L1 NRHOs in a similar range, leading to lower orbit maintenance requirements in propellant and ∆V [4] [6].

A southern family NRHO was selected because this offers lower ∆V and propellant requirements for Orion returning from the NRHO.  This is due to the geometry of returning to a splashdown in Earth’s northern hemisphere.  The southern family also has the advantage of very good communications coverage to the surface for sites near the lunar south pole [8] [12], which is currently a region of interest [13] [14].

An NRHO with a Lunar Synodic Resonant (LSR) period was deemed desirable as it offered the possibility of avoiding eclipses, particularly eclipses by the Earth [15], which can have durations well in excess of current hardware limits for the Gateway and Orion spacecraft. (More on this later.)  Both 4:1 and 9:2 LSR cases were considered.  The 9:2 LSR NRHO was ultimately selected because it offered a relatively low perilune radius [15], which is advantageous for surface access [9].
Characteristics of the Reference Trajectory

The Gateway NRHO reference trajectory is captured in a SPK-type kernel compatible with the SPICE ephemeris system created at the NASA Jet Propulsion Laboratory (JPL) [16].  (SPICE SPK-type kernels are binary files which store ephemeris data [17].)  The full trajectory kernel is available on the JPL website [18].

The reference trajectory represents an orbit with the characteristics already described for Gateway:  an NRHO of the L2 southern family with an orbit period selected for a 9:2 Lunar Synodic Resonance and phasing set for avoidance of eclipses by the Earth.

The Gateway NRHO reference trajectory spans 15 years, from January 2, 2020 to February 11, 2035.  The trajectory is continuous in position, with small velocity adjustments (or discontinuities) occurring every NRHO rev near apolune.  These adjustments are necessary to maintain the stability of the NRHO in the ephemeris gravity model.  The adjustments are quite small, with an average magnitude of only 1.86 mm/s per NRHO rev.

It’s important to note that this is an idealized reference trajectory, intended to be generic to the particulars of specific spacecraft and mission designs.  The only perturbations considered are those from the n-body gravitation model in the ephemeris.  No other perturbations or errors were considered:  no solar pressure, no drag, no spacecraft noise, no navigational errors, no insertion errors, etc.

[Figure: Figure 3:  Eclipse History for NRHO Reference Trajectory.]

The velocity adjustments are small compared to the additional errors and perturbations that would typically be expected for an actual spacecraft, and also when compared to the actual correction maneuvers that would be required to maintain the orbit [4] [6].

Also, no active phase control was applied in the generation of the trajectory.  It is a “natural” trajectory, in that sense, and accomplishes eclipse avoidance by virtue of a judicious selection of initial conditions only.

Figure 2 shows the reference trajectory displayed in two frames:  an Earth-Centered Sun-Earth rotating frame, and a Moon-centered Earth-Moon rotating frame.  In the Earth-Moon rotating frame, on the right, we can see the familiar NRHO shape, albeit with 15 years of variations.

In the Sun-Earth rotating frame, on the left, we can see how the LSR orbit accomplishes eclipse avoidance:  by setting up a repeating geometrical pattern in the Sun-Earth frame, which consistently avoids passing through the Earth’s shadow (along the axis opposite the Sun). Note that the elliptical shapes on this axis are projections of the Earth’s outer shadow, or penumbra.