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