Advanced method of virtual trajectories for the preliminary design of gravity-assist missions Sergey Trofimov Keldysh Institute of Applied Mathematics Moscow Institute of Physics and Technology Maksim Shirobokov Keldysh Institute of Applied Mathematics Moscow Institute of Physics and Technology
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Advanced method of virtual trajectories for the preliminary design of gravity-assist missions Sergey Trofimov Keldysh Institute of Applied Mathematics.
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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
2/20
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
3/20
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
4/20
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 trajectories5/20
Classes of trajectories considered
Basic 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
6/20
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
7/20
Discretization of planetary orbitsand beams of virtual trajectories
8/20
Beam of heliocentric arcs with different elevation angles
2
1
1 2
1 1 cos
2cos cos cospar
v
v r r
9/20
Patching of incoming and outgoing planetocentric hyperbolic arcs
10/20
Screening of VT database
11/20
Refinement of near-feasible trajectories
12/20
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 2-3
2 3-6 10-15
3 8-15 60-80
4 20-40 >200
13/20
*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
14/20
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
15/20
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
16/20
EVEEJ: similar to the baseline trajectory of Jupiter Ganymede Orbiter (JGO) mission
17/20
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
18/20
EVEEJ: similar to the baseline trajectory of proposed Ganymede Lander mission
19/20
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