Speaker
Mr
Fabien Gachet
(University of Rome 'Tor Vergata')
Description
The long-term dynamics of the geostationary (GEO) region has been studied both numerically (Chao, 2005; Anselmo and Pardini, 2007) and analytically (Chao and Baker, 1983; Chao, 2006; Valk et al., 2008; Rosengren and Scheeres, 2013), and some of these results contributed to the IADC guidelines for disposal of objects in the GEO region.
In this work, we revisit the dynamics of this region through the application of canonical perturbation theory, and we apply our results to study the peculiar dynamical behavior of high area-to-mass ratio space debris.
More specifically, previous works focused on the evolution of objects *around* a nominal solution called the forced equilibrium solution. Here, instead we focus on the nature of the equilibrium solution itself. Thanks to a higher order normal form, we demonstrate that this equilibrium is actually a lower dimensional object containing slow frequencies. This means that even placed at this pseudo-equilibrium, an object will exhibit periodic variations of its elements, which can be large. We give an analytical expression of these variations, valid for long time scales.
To this end, we considered the Hamiltonian of the system accounting for all major perturbations in GEO : the Earth gravitational potential at order and degree 2, the third body perturbations from the Sun and the Moon from Montenbruck and Gill (2000), and the solar radiation pressure. Using canonical perturbation theory, we perform a rigorous averaging of the 8 degrees of freedom Hamiltonian by the method of normal forms via Lie Series (Hori, 1966; Deprit, 1969).
The fast terms are then eliminated by a series of canonical transformation, revealing the long-period evolution of the different elements.
This allows us to derive the forced equilibrium of this averaged Hamiltonian which is a lower dimensional object containing 5 slow frequencies defining a quasi-periodic orbit, which shows the actual nature of this pseudo--equilibrium.
We obtain through a back-transformation of the canonical transformation made from the forced equilibrium, the analytical time-explicit evolution of all elements at this equilibrium.
This analytical result is compared to the numerical integration of the full model before averaging, and gives satisfying accuracy.
The long term evolution of the inclination and eccentricity for an object at the equilibrium are particularly analyzed showing strong dependence on the area-to-mass ratio.
We highlight that in addition to the geopotential at order and degree 2, we use a realistic model for the Sun and the Moon from Montenbruck and Gill (2000), where the Moon and the Sun are on elliptical, inclined orbits with a variation of their argument of perigee and right ascension of the ascending node.
As noted in Valk et al. (2008), having a fixed Sun-Earth distance in the estimation of solar radiation pressure (an assumption made in previous studies, such as Chao (2006)) would induce spurious long-period terms in eccentricity and inclination evolution.
This also ensures that the solar radiation pressure which derives from the position of the Sun is correctly modeled.
Another novelty of the approach is that the Hamiltonian is derived in cylindrical coordinates since the geometry of the GEO region is very suitable for this coordinate system, therefore our approach does not need the disturbing function expansions making it simple to develop, and our results are directly translatable in Keplerian elements without singularity.
The time-explicit solutions also give direct access to the equilibrium without scanning the whole phase space, and the long-term behavior described by these formulas can be used for disposal studies.
| Applicant type | First author |
|---|
Primary author
Mr
Fabien Gachet
(University of Rome 'Tor Vergata')
Co-authors
Prof.
Alessandra Celletti
(University of Rome 'Tor Vergata')
Dr
Christos Efthymiopoulos
(Academy of Athens)
Prof.
Giuseppe Pucacco
(University of Rome 'Tor Vergata')
