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SUMMARY:A fast an efficient algorithm for the computation of distant retro
grade orbits
DTSTART;VALUE=DATE-TIME:20181109T120000Z
DTEND;VALUE=DATE-TIME:20181109T123000Z
DTSTAMP;VALUE=DATE-TIME:20220528T224434Z
UID:indico-contribution-3864@indico.esa.int
DESCRIPTION:Speakers: Martin Lara (GRUCACI - University of La Rioja)\nAn a
lgorithm for the computation of distant retrograde orbits is presented. It
is based on the computation of an approximate analytical solution of the
restricted three body problem in the Hill problem approximation that prov
ides accurate estimations of two basic design parameters. Notably\, these
parameters can be used for the computation of initial conditions of orbits
that are periodic on average\, and almost periodic in the original proble
m. Following application of iterative differential corrections results in
the initial conditions and period of a true periodic orbit with the charac
teristics fixed by the design parameters.\n\nThe analytical solution consi
st roughly of a drifting ellipse\, whose guiding center moves around the p
rimary with long-period oscillations\, and in which the linear growing of
the phase of the satellite is modulated with long-period variations. The a
nalytical solution splits in two parts of different nature. The first one
provides the periodic corrections needed for converting osculating element
s into the mean ones that describe the long-term evolution of the dynamics
. The second part of the analytical solution gives the time history of the
mean elements in the form of five Lindstedt series\, which are needed for
describing:\n- the time scale in which the Lindstedt series evolve (1 ser
ies)\n- the time evolution of the guiding center of the reference ellipse
(2 series)\n- the linear frequency with which the satellite evolves\, on a
verage (1 series)\n- the long-period modulation of the phase of the satell
ite (1 series)\n\nThe use of the algorithm is illustrated with different e
xamples\, ranging from the typical case of 1:1-resonant distant retrograde
orbits\, in which the satellite remains always far away enough from the p
rimary\, to the challenging case of higher order resonances in which the a
mplitude of the libration of the guiding center of the orbit can take the
satellite much closer to the primary.\n\nhttps://indico.esa.int/event/224/
contributions/3864/
LOCATION: Single 107
URL:https://indico.esa.int/event/224/contributions/3864/
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