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SUMMARY:Trajectory Optimization of a Low-Thrust Geostationary Orbit Insert
ion Maneuver for Spacecraft Total Ionizing Dose Reduction
DTSTART;VALUE=DATE-TIME:20181109T090000Z
DTEND;VALUE=DATE-TIME:20181109T093000Z
DTSTAMP;VALUE=DATE-TIME:20220528T101858Z
UID:indico-contribution-4102@indico.esa.int
DESCRIPTION:Speakers: Alexander Starchenko (Research Institute of Applied
Mechanics and Electrodynamics of Moscow Aviation Institute)\nWe consider t
he problem of optimal low-thrust spacecraft geostationary orbit (GEO) inse
rtion from initial circular orbit with 800 km height and 51.6 degrees incl
ination. Minimal time for electric propulsion insertion of considered nucl
ear powered heavy spacecraft [1] is about 117 days. Significant amount of
this time (~90 days) the spacecraft spends in regions with harsh space rad
iation environment inside the Van Allen radiation belts. To reduce an abso
rbed total ionizing dose (TID) for onboard electronic systems we propose a
method of changing shape of the insertion trajectory and examine efficien
cy of this method. The main idea of the proposed method is to consider TID
as a part of state variables set and to add the equation for TID change o
ver the time to the equations of motion. Then if we add to the low-thrust
optimal time GEO insertion problem [2] with the new set of state variables
a condition of fixed TID at the end of transfer\, one could obtain trajec
tories with lower final TID values. The obtained optimal control problem w
as solved using the maximum principle for one orbit time-averaged equation
s of motion. For numerical solution of corresponding boundary value proble
ms we used the numerical continuation method with the predictor-corrector
scheme. Numerical integration of considered ODEs was performed using the D
OP853 integrator code.\n\nThe dose calculation for obtained trajectories w
e performed with CmdLineAe9Ap9 [3] software and Python scripts using AE8/A
P8 MIN\, AE8/AP8 MAX and AE9/AP9 electron and proton flux models of the Va
n Allen Radiation belts. In order to tackle discontinuities in right parts
of ODEs we constructed a two-step spline approximation scheme of dose rat
e function. The first step is cubic smoothing spline approximation for noi
se level reduction of the CmdLineAe9Ap9 dose rate data. The second step co
nsists of high-order (11th or higher) usual spline interpolation of the sm
oothing spline values. High-order order spline is needed to meet smoothnes
s conditions of the right parts for Dormand-Prince ODE integration method.
\n\nWe managed to reduce the final TID values by 25-38% (depending on the
flux model) of final TID value on the minimal time GEO insertion trajector
y. The duration of GEO insertion transfer is increased by no more than 7%
of the minimal insertion duration. The additional required characteristic
velocity for obtained trajectories is 320-560 m/s (depending on the flux m
odel) with respect to the minimal time insertion trajectory.\n\nReferences
\n[1] Legostaev V. P. et al.\, Prospects for and Efficiency in Application
of Space Nuclear Power Plants and Nuclear Electrorocket Propulsion System
s\, Space Engineering and Technology\, 2013\, No. 1.\, P. 4-15. (in Russia
n).\n[2] Petukhov V. G. Optimization of Multi-Orbit Transfers Between Nonc
oplanar Elliptic Orbits\, Cosmic Research\, 2004\, Vol. 42\, No. 3\, P. 25
0-268.\n[3] https://www.vdl.afrl.af.mil/programs/ae9ap9/downloads.php\n\nh
ttps://indico.esa.int/event/224/contributions/4102/
LOCATION: 103 and 105 combined
URL:https://indico.esa.int/event/224/contributions/4102/
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