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SUMMARY:Efficient design of low lunar orbits based on Kaula recursions
DTSTART;VALUE=DATE-TIME:20181109T120000Z
DTEND;VALUE=DATE-TIME:20181109T123000Z
DTSTAMP;VALUE=DATE-TIME:20220528T222148Z
UID:indico-contribution-4142@indico.esa.int
DESCRIPTION:Speakers: Martin Lara (GRUCACI - University of La Rioja)\nPrel
iminary design of artificial satellite missions commonly relays on the use
of simplified models that comprise the bulk of the dynamics. In the case
of the gravitational potential\, the amplitude of long-term oscillations o
f the orbital parameters is roughly one order of magnitude larger than the
short-period oscillations. Because of that\, dealing with just the few mo
re relevant zonal harmonics of the potential is generally suitable for the
initial steps of the procedure. In addition\, the long-term evolution of
the orbital parameters is customarily investigated through averaging proce
dures that remove the higher frequencies of the motion\, in this way notab
ly speeding the process of mission design.\n\nHowever\, there are cases in
which the use of simplified models is not an option and full zonal potent
ial models must be used instead. The paradigm is provided by the moon\, wh
ere\, due to the irregular character of the moon gravity field\, mission d
esigning of low altitude lunar orbits needs to deal with tens of\, contrar
y to just a few\, zonal harmonics. The analytical approach is still possib
le\, but the requirement of handling huge expressions formally usually dis
courages mission planners\, who then resort to numerical procedures. Still
\, useful compact recursions for dealing analytically with the problem exi
st in the literature since many years ago\, yet limited to the equations o
f the averaged flow.\n\nBased on Kaula’s popular work\, we re-derive the
long-term potential of the zonal problem in closed form and show that Kau
la’s approach in orbital elements provides much more efficient formulas
for the construction of the mean elements potential that recent alternativ
e proposals in the literature. The necessity of having available efficient
expressions for the long-term zonal potential\, from which the evolution
equations of the orbit are directly derived\, is illustrated with applicat
ion to the design of low lunar orbits.\n\nhttps://indico.esa.int/event/224
/contributions/4142/
LOCATION: 103 and 105 combined
URL:https://indico.esa.int/event/224/contributions/4142/
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