Method of Virtual Trajectories for the Preliminary Design of Multiple Gravity-Assist Interplanetary...
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Transcript of Method of Virtual Trajectories for the Preliminary Design of Multiple Gravity-Assist Interplanetary...
Method of Virtual Trajectories for the Preliminary Design of Multiple Gravity-Assist Interplanetary
Trajectories
Sergey TrofimovKeldysh Institute of Applied Mathematics, RAS
Moscow Institute of Physics and Technology
Michael OvchinnikovKeldysh Institute of Applied Mathematics, RAS
Maksim ShirobokovKeldysh Institute of Applied Mathematics, RAS
Moscow Institute of Physics and Technology
64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Contents
• Motivation for inventing a method
• Method of virtual trajectories (MVT)
• Benefits and flaws of the MVT
• Test case: Flight to Jupiter
• Conclusions
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Mission feasibility studyWhen studying the mission feasibility, a designer wants:• To quickly estimate the best V, the transfer time and
launch windows for a number of planetary sequences• To have an option of varying some mission constraints
and imposing new ones (ideally without repeating the whole optimization procedure)
• To do all of this without involving skilled specialists in astrodynamics
These demands are difficult to meet in case of multiple gravity-assist (MGA) trajectory design
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Method of virtual trajectories• Based on the fact that the orbits of planets are
changing very slowly
• For a given planetary sequence, a database of all
“geometrically feasible” trajectories can be
constructed once and for all (“for all” means at
least for several decades)
• The second, fast computing step: to screen and
refine such a database of virtual trajectories4/17
64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Classes of trajectories consideredBasic class of trajectories:
• Coast heliocentric conic arcs
• Powered gravity assists (single impulse at the pericenter)
Method of VT was also adapted to the trajectories with
• non-powered gravity assists
• deep space maneuvers (DSMs)
At most one DSM is allowed on each heliocentric arc
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Some basic concepts and assumptions1) The orbits of planets:• assumed to be closed curves fixed in space• are discretized (i.e., represented as a 1D mesh)
2) Virtual trajectory (VT):• consists of heliocentric conic arcs• sequentially connecting the mesh points on the orbits of planets
included in the planetary sequence chosen3) A virtual trajectory is referred to as near-feasible if a spacecraft
moving along it would fly by the mesh node on the planet’s orbit approximately (within some time tolerance) at the same time with the planet itself
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Discretization of planetary orbitsand beams of virtual trajectories
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2
1
1 2
1 1 cos
2cos cos cospar
v
v r r
64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Patching of incoming and outgoing planetocentric hyperbolic arcs
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Powered GA maneuvers Unpowered GA maneuvers
64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Screening of a VT database and refinement of near-feasible trajectories
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Pruning infeasible trajectories Refinement of near-feasible ones
64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Comparison of computational costs
Number of gravity
assists
CPU time for VT database screening and refinement,
min*
CPU time for standard Lambert-based approach,
min*
1 0.5-2 2-3
2 3-6 10-15
3 8-15 60-80
4 20-40 >200
*All values of computational time are relative to a PC with 2.13 GHz CPU and 2Gb RAM
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Benefits and flaws of the VT method+ One and the same set of databases can be used
many times for the design of various missions+ Easy handles with imposing different additional
constraints, without extra computational cost− Sensitive to step sizes during the discretization
of planets’ orbits− Requires considerable hard disk space for saving
all the VT databases (from 10 MB up to 1 GB for a long planetary sequence with 5 GAs)
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Sample problem: Transfer to JupiterObjective function:
Constraints:
No conjunctions during performing GAs or DSMs
To check some standard planetary sequences: EVJ, EVEJ, EEVJ, EVEEJ
minV
2020,2025launchT
3 km/sV
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
EVEEJ with powered GA maneuvers
194 m/s6.02 yrs
11 / 03 / 2020flight
launch
VT
t
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
EVEEJ with DSMs and unpowered GAs
88 m/s6.03 yrs
13 / 03 / 2020flight
launch
VT
t
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This trajectory is similar to the baseline trajectory of Jupiter Ganymede Orbiter (JGO) mission
64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Comparison of trajectories obtained usingthe MVT with DSMs and in the JGO mission
JGO trajectory MVT with DSMs
Launch 11/03/2020 13/03/2020
Venus flyby 01/07/2020 30/06/2020
First Earth flyby 27/04/2021 27/04/2021
Second Earth flyby 28/07/2023 28/07/2023
Jupiter approach 04/02/2026 25/03/2026
in EV 0 0.01
in VE 0 0.07
in EE 39 88
in EJ 0 0.4
Escape velocity, km/s 3.39 3.41
Approach velocity , km/s 5.50 5.58
Duration, year 5.9 6.0
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
ConclusionsBased on a number of beforehand computed databases of
virtual trajectories, a mission designer can:
• quickly estimate the possible mission timeline options
(planetary sequence, launch date, transfer time)
• pick and choose the planetary sequence which is best
suited to various constraints and scientific requirements
• change his mind and impose new constraints without a
serious increase in time of mission feasibility analysis
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64th International Astronautical Congress (IAC) 23-27 September 2013, Beijing, China
Acknowledgments
• Russian Academy of Sciences (RAS), Presidium
Program “Fundamental Issues in Investigation
and Exploration of Solar System”, Subprogram
“Mission Scenarios and Trajectory Design”
• Russian Foundation for Basic Research (RFBR),
Grant No. 13-01-00665
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