Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-entry

Abstract

This paper investigates the long-term evolution of spacecraft in Highly Elliptical Orbits (HEOs). The single averaged disturbing potential due to luni-solar perturbations, zonal harmonics of the Earth gravity field is written in mean Keplerian elements. The double averaged potential is also derived in the Earth-centered equatorial system. Maps of long-term orbit evolution are constructed by measuring the maximum variation of the orbit eccentricity to identify conditions for quasi-frozen, long-lived libration orbits, or initial orbit conditions that naturally evolve toward re-entry in the Earth's atmosphere. The behavior of these long-term orbit maps is studied for increasing values of the initial orbit inclination and argument of the perigee with respect to the Moon's orbital plane. In addition, to allow meeting specific mission constraints, quasi-frozen orbits can be selected as graveyard orbits for the end-of-life of HEO missions, in the case re-entry option cannot be achieved due to propellant constraints. On the opposite side, unstable conditions can be exploited to target Earth re-entry at the end-of-mission.

Phase space description of the dynamics due to the coupled effect of the planetary oblateness and the solar radiation pressure perturbations

“…Moreover, the concept proposed will hold certainly in the cases described above, where the two perturbations -oblateness and solar radiation pressure -play a major role, but it will be of high interest to see how the solutions presented may persist under the effect of an additional effect and under which conditions they remain the skeleton of the long-term dynamics. For orbits at the Earth, the key case will be the dynamics due to lunisolar gravitational perturbations for Highly Elliptical Orbits [25] and in the geosynchronous region (e.g., [26,27]).…”

On the Dominant Lunisolar Perturbations for Long-Term Eccentricity Variation: The Case of Molniya Satellite Orbits

“…Following, e.g., [15], the oblateness of the Earth does not produce any effect on the actions G and H, but it causes a precession, or regression, of g and h, which is usually used to approximate the evolution of the angles, as already mentioned before. From the last two equations of the system, Equation (11), we notice that the angles undergo secular drifts, caused by both the oblateness and the lunar and solar mean terms, and periodic effects, given by integrating the oscillating terms whose amplitude is proportional to the partial derivatives of the harmonic coefficients. Since the Laplace radius is around 7.7 R ⊕ [17], higher than the Molniya one, and is the geocentric distance at which the order of magnitude of the precession caused by the lunisolar perturbation is equivalent to the one caused by the Earth's oblateness, the following approximation…”

“…From Equation (11), it is noteworthy that Ġ, and thus the mean eccentricity, only depends on the harmonics showing ġ in the argument. On the other hand, only harmonics depending on h affect Ḣ; therefore, the orbital inclination depends on the harmonics having g or h in the argument.…”

“…Another novelty with respect to past works is that lunisolar effects are usually studied with a second-order doubly averaged model but the geocentric orbits of the third bodies are taken as circular. Under this assumption, the third-order disturbing function vanishes, thanks to the analytical expressions of the eccentricity functions appearing in it [11], and the argument of pericenter of the perturbing bodies is not well-defined; hence, they do not appear in the power series development of the disturbing functions. Here, we will provide the general treatment.…”

Dynamical evolution of artificial satellites and space debris in near earth region

“…While end-of-life (EOL) disposal options are well established for missions in LEO (atmospheric decay) and GEO (near circular graveyards), existing mitigation guidelines do not fully regulate the whole, usable circumterrestrial orbital space, such as high-eccentricity science missions (HEO); e.g., NASA's Magnetospheric Multiscale Mission (MMS) [Williams, 2012] and ESA's INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) [Eismont et al, 2003]. The non-negligible collision risks posed by these LEO-GEO transiting spacecraft has motivated both theoretical study and practical implementation [Armellin et al, 2015;Colombo, 2015;Merz et al, 2015].…”