Effectiveness of the de-orbiting practices in the MEO region

The Medium Earth Orbit (MEO) region is becoming in- The disposal zone is, in principle, well separated both creasingly exploited as the number of navigation constel- from the GPS operational orbit and from the GALILEO lations grows with the advent of the European GALILEO planned orbit. Unfortunately the picture is more compli- and the Chinese COMPASS systems. There is the need cated. In a number of recent papers (e.g. [2] [5] [12]) the for an effective disposal strategy of satellites at end- instability of the navigation constellations disposal orbits, of-life able to prevent any possible damage of opera- showing an increase of the eccentricity that could lead to tional satellites. This strategy has to take into account dangerous crossings of the operational orbits, was stud- the known instability of nearly circular disposal orbits in ied. Figure 1 shows the eccentricity evolution over 100 MEO. These orbits show an increase of the eccentricity years, for a GPS like orbit propagated with increasing so- that could lead to dangerous crossings of the operational phisticated dynamical models, from a simple case with orbits. only the gravity monopole term, plus luni-solar pertur- bations, to a full model with Earth gravity harmonics up to degree and order 10 and luni-solar perturbations. The first long term effects of the 2 : 1 geopotential resonance (due to the fact that the orbital period of the navigation constellations equals approximately half a sidereal day) appear when the harmonics up to l = 3 and m = 3 are included (see e.g. [12]). The real striking change in the pace of the eccentricity growth happens when a full model including Earth gravity harmonics and luni- solar perturbation is assumed. The eccentricity undergoes a very long term (quasi-secular) perturbation that, at the end of the 100-year time span, leads to a value more than 3 times larger than in the case without luni-solar pertur- bations. This is due to a so-called luni-solar resonance. Moreover, it is worth noting how, in the case where a full dynamical model is applied (including luni-solar pertur- bations), the eccentricity growth drops significantly go- ing from the case where a 3 × 3 gravity field is used (the uppermost red curve) to a 4 × 4 gravity field (the top ma- genta line) and then to the full model with a 10 × 10 field. This, most probably, means that the shape of the ellipsoid, represented by the simple spherical harmonics expansion up to degree and order three, undergoes a stronger res- onance with the Sun and the Moon perturbations. The caveat that should be taken by this example is that sim- ulating, or analytically calculating, an approximate prob- lem with few harmonics might overestimate the perturba- tion effect. The FOP orbital propagator [13] used in this paper takes into account this fact. The nature of this instability, linked to luni-solar reso- nances, is briefly recalled. Then the effect of different disposal strategies on the long term evolution of the MEO environment is analyzed. It is shown how the disposal of satellites at end-of-life into well separated storage zones, above the constellations operational orbits, is capable of limiting the collision risk for operational satellites to very low values for long time spans (200 years). Moreover, a disposal into eccentric orbits not only keeps the collision risk to very low values, but also has the advantage of re- ducing the lifetime of the disposed satellites, thus free- ing the orbital environment from the uncontrolled space- craft.