Roberto Paoli

Al. I. Cuza University of Iasi

Analysis of Solar Radiation Pressure semi-secular resonances

The aim of this work is to provide new insights on the dynamics associated to the resonances which arise as a consequence of the coupling of the effect due to the oblateness of the Earth and the Solar Radiation Pressure (SRP) effect for an uncontrolled object with moderate to high area-to-mass ratio. In particular, we are going to focus on resonant terms whose associated resonant angles involve a linear combination of the argument of perigee, right ascension of the ascending node and mean anomaly of the Sun. Resonances involving semi-fast angles such as the Sun’s mean anomaly are called semi-secular in [1]. Analytical estimates for the location of the resulting resonant equilibrium points are provided, together with formulas to compute the maximum amplitude of the corresponding variation in the eccentricity, as a function of the initial conditions of the object and of its area-to-mass ratio. A classification based on the strength of the SRP resonances is provided. The estimates are validated using numerical tools, including the use of Fast Lyapunov Indicators (FLIs), to draw phase portraits and bifurcation diagrams. FLI maps depicting the location and overlapping of SRP resonances are presented. Finally, for the case of small eccentricities, we show how SRP resonances could be modeled in the context of either the Extended Fundamental Model by [2] or the Second Fundamental Model by [3].

[1] Celletti, A., Gales, C. \& Lhotka, C. (2019). Resonances in the Earth’s Space Environment.

[2] Breiter, S.. (2003). Extended Fundamental Model of Resonance. Celestial Mechanics and Dynamical Astronomy. 85. 209-218. 10.1023/A:1022569419866.

[3] Henrard, J., Lemaitre, A. A second fundamental model for resonance. Celestial Mechanics 30, 197–218 (1983). 10.1007/BF01234306

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Analysis of Solar Radiation Pressure semi-secular resonances
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