Download - Advanced method of virtual trajectories for the preliminary design of gravity-assist missions
Advanced method of virtual trajectoriesfor the preliminary design of gravity-assist missions
Sergey TrofimovKeldysh Institute of Applied Mathematics
Moscow Institute of Physics and Technology
Maksim ShirobokovKeldysh Institute of Applied Mathematics
Moscow Institute of Physics and Technology
Content
• Motivation
• Method of virtual trajectories
• Benefits and flaws
• Test case: flight to Jupiter
• Conclusion
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Gravity-assist interplanetary missions
Two stages of a mission to any planet and its moon system:• – takes most of flight time and imposes
principal restrictions on the mission timeline• – fine adjustment of the moon orbit
insertion conditions
Gravity assists (swing-bys) are of vital importance for saving fuel and increasing the scientific payload
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Cruise
Orbital tour
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 recalculating the whole optimization procedure)
• To do all of this without involving skilled specialists in astrodynamics
These goals are rather challenging in case of multiple gravity-assist (MGA) trajectory design
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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 trajectories
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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 (DSM)
At most one DSM is allowed on each heliocentric arc
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Some basic concepts and assumptions
1) 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 chosen
3) 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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Discretization of planetary orbitsand beams of virtual trajectories
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Beam of heliocentric arcs with different elevation angles
2
1
1 2
1 1 cos2cos cos cospar
vv r r
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Patching of incoming and outgoing planetocentric hyperbolic arcs
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Screening of VT database
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Refinement of near-feasible trajectories
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Comparison of computational costs
Number of gravity
assists
CPU time for VT database screening and refinement,
min*
CPU time for classical Lambert-based approach,
min*
1 0.5-2 2-32 3-6 10-153 8-15 60-804 20-40 >200
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*All values of computational time are relative to a PC with 2.13 GHz CPU and 2Gb RAM
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 when constructing a database of VT
− Requires considerable hard disk space for saving all of VT databases
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Sample problem: transfer to JupiterObjective functional:
Constraints:
No conjunctions during performing GAs or DSMs
To check some standard planetary sequences: EVJ, EVEJ, EEVJ, EVEEJ
minV
2020,2025launchT
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3 km/sV
EVEEJ: similar to the baseline trajectory of Jupiter Ganymede Orbiter (JGO) mission
194 m/s6.02 yrs
11 / 03 / 2020flight
launch
VT
t
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EVEEJ: similar to the baseline trajectory of Jupiter Ganymede Orbiter (JGO) mission
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In synodic (Earth co-rotating) frame
EVEEJ: similar to the baseline trajectory of proposed Ganymede Lander mission
146 m/s8.16 yrs
22 / 05 / 2023flight
launch
VT
t
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EVEEJ: similar to the baseline trajectory of proposed Ganymede Lander mission
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In synodic (Earth co-rotating) frame
ConclusionBased 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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Thank you for attention