A High Earth, Lunar Resonant Orbit for Lower Cost Space Science Missions (2013) wrote:
The mission orbit selected for TESS early in the design process was the “P/2-HEO,” a high Earth orbit in
2:1 resonance with the Moon (i.e., having an orbital period of 13.7 days), first studied in depth by McGiffin 
and similar to the 3:1 lunar-resonant orbit of the IBEX mission . The P/2-HEO is eccentric, with perigee
above geostationary altitude (GEO) and apogee beyond the Moon’s orbital radius. The spacecraft reaches this
orbit via a gravity-assist flyby of the Moon. The P/2-HEO was selected for TESS to provide unobstructed
observation sectors and continuous light curves for the TESS all-sky survey.
Although TESS was the model
for this study, the results contained herein apply to space missions of any size that require a similar operating
environment and seek a low-V option.
The orbit-parameter selection process for the P/2-HEO was driven by three constraints imposed by TESS:
1) no eclipse can exceed 6 hours duration during the 4-year mission; 2) maintain mission-orbit perigee above
GEO (>6.6 RE) for four years; and 3) maintain mission-orbit perigee below 22 RE for four years to ensure
The P/2-HEO analysis draws upon on the initial work of McGiffin . A key result of this work is that
“lunar secular perturbations average, roughly, to zero, resulting in significant long term stability” when the
spacecraft apogee is offset 90 deg with respect to the Moon and when spacecraft apogees alternately lead
and trail the Moon
, as shown in the Earth-Moon rotating coordinate system in Fig. 1(a). Figure 1 shows the
3.5 phasing orbits, the transfer orbit, and the 25-year propagation of the P/2-HEO mission orbit, including
plots of the orbital elements. Although the orbit is high and subject to lunisolar perturbations, a proper
selection of initial conditions—in conjunction with resonance with the Moon—drives the orbital elements of
the P/2-HEO to oscillate rather than grow or shrink without bound.
Much of the subsequent analysis focuses
on finding those initial conditions that ensure such non-secular behavior and ensure that the oscillations are
bounded by the mission’s eclipse and perigee-range constraints.