Dynamical properties of the Molniya satellite constellation: long-term evolution of orbital eccentricity

Abstract

The aim of this work is to analyze the orbital evolution of the mean eccentricity given by the Two-Line Elements (TLE) set of the Molniya satellites constellation. The approach is bottom-up, aiming at a synergy between the observed dynamics and the mathematical modeling. Being the focus the longterm evolution of the eccentricity, the dynamical model adopted is a doublyaveraged formulation of the third-body perturbation due to Sun and Moon, coupled with the oblateness effect on the orientation of the satellite. The numerical evolution of the eccentricity, obtained by a two-degree-of-freedom model assuming different orders in the series expansion of the third-body effect, is compared against the mean evolution given by the TLE. The results show that, despite being highly elliptical orbits, the second order expansion catches extremely well the behavior. Also, the lunisolar effect turns out to be non-negligible for the behavior of the longitude of the ascending node and the argument of pericenter. The role of chaos in the timespan considered is also addressed. Finally, a frequency series analysis is proposed to show the

Investigation on a Doubly-Averaged Model for the Molniya Satellites Orbits

“…Using the Delaunay variables we noticed that the larger the amplitudes the deeper the periodic fluctuation, while the periods help us to identify which harmonics produce long-term oscillations and which ones give rise to near-resonant or resonant terms. Finally, the results concerning the ratio between amplitudes and the corresponding frequency confirm that the dynamics is governed by the second order lunisolar perturbation, as found numerically in [1]. In addition to the harmonics corresponding to 2g and 2g ± h, already taken into account in [16], the long-term behaviour is strongly influenced also by perturbing terms associated with the argument h and with some arguments involving the lunar ascending node.…”

“…Finally, from Tab. 7 we can conclude that the second order lunisolar effect is the dominant perturbation on the long-term dynamics, as already found numerically in [1].…”

“…(2) µ is the gravitational parameter of the Moon, ε is the angle between the ecliptic and the equatorial plane, and y s = 0 for s even while y s = 1 2 for s odd. The analytical expansions of the Kaula's inclination functions and of U l,±s m , the Hansen coefficients and the coefficients ε m , ε s , k 1 , k 2 , k 3 can be found in [4,10,11].…”