A technique for designing Earth-Mars low-thrust transfers ......Earth-Mars low-thrust transfers...

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A technique for designing Earth-Mars low-thrust transfers culminating in ballistic capture

G. Aguiar F. Topputo

Delft University of Technology Astrodynamics & Space Missions

[email protected]

Politecnico di Milano Aerospace Science and Technology

[email protected]

mailto:[email protected]


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Outline1. Introduction 2. Concept 3. Assumptions 4. Ballistic capture 5. Low-thrust targeting

6. Results 7. Conclusions

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Introduction

Retrieved from http://www.busek.com/index_htm_files/70010819D.pdf (visited on

21/11/2017)

Retrieved from http://www.busek.com/index_htm_files/70008517E.pdf (visited on

21/11/2017)

What are the characteristics of Earth–Mars transfers that combine ballistic capture with low-thrust propulsion?

http://www.busek.com/index_htm_files/70008517E.pdf



Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Concept

Mars

to Sun t0tf

td

Mars

Earth

Powered TOF

Ballistic TOF

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

Assumptions

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rd !⃗d

rE + RSOI,E !⃗E

(Casado, 2017)

A (m2) mwet (kg) CR

0.52 26 1.1

mBC (kg)≈ 20.5

T (mN) Isp (s)[0.66,1.24]

[1400,2640]

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Ballistic capture

Choose conditions to test

Run classification algorithm

Choose dynamics

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Ballistic capture Choose conditions to test


Choose dynamics

2B TB SRP NSGMars Sun Mercury – Neptune Cannonball 20x20

Required for capture

May facilitate capture

Improves validity of results

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Choose dynamics

Ω0 (º) i0 (º) e0

0 22.5 0.99

Reduce search space

Maximise chances of

capture

ω0 (º) hp0 (km)[0, 359] [250, 4RM]

Consistent with past work

n6

Past work

t0 - t01 (days)[0, 800]

Includes synodic period

t01 ≡ 08 MAY 2024 Mars at periapsis

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Choose dynamics

#6-1 ≡ $6 ∩ %-1

$1 %1

…

&⃗0

?

(Luo et al., 2014)

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

-4 -2 0 2 4rp0cos( 0) (LU)

-4

-3

-2

-1

0

1

2

3

4

r p0si

n(0) (

LU)

1

1.5

2

2.5

3

3.5

4

S (T

U)

104

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Ballistic capture

t0 = t01 + 000 dayst0 = t01 + 050 dayst0 = t01 + 100 dayst0 = t01 + 150 days

TM = 687 days

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

-4 -2 0 2 4rp0cos( 0) (LU)

-4

-3

-2

-1

0

1

2

3

4

r p0si

n(0) (

LU)

1

1.5

2

2.5

3

3.5

4

S (T

U)

104

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Ballistic capture

t0 = t01 + 000 dayst0 = t01 + 050 dayst0 = t01 + 100 dayst0 = t01 + 150 dayst0 = t01 + 200 dayst0 = t01 + 250 dayst0 = t01 + 300 dayst0 = t01 + 350 dayst0 = t01 + 400 dayst0 = t01 + 450 dayst0 = t01 + 500 dayst0 = t01 + 550 dayst0 = t01 + 600 days

TM = 687 days

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

t = t

01 -

800

day

s

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Ballistic capture

t = t01

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

t = t

01 -

800

day

st =

t01

- 6

00 d

ays

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Ballistic capture

t = t01

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

t = t

01 -

800

day

st =

t01

- 6

00 d

ays

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Ballistic capture

t = t

01 -

400

day

s

t = t01

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Low-thrust targeting

Capture orbits

Run numerical method

Define control problem

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

Low-thrust target. Capture orbits



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2BSun

Required for transfer

'⃗d !⃗d md '⃗f !⃗f mf td tf≈ '⃗E(td) !⃗E(td) mwet '⃗C(tf) !⃗C(tf) free t0 - ΔtTOF free

J-mf

t0 - t01 (days) ΔtTOF (days)[0, 800] [1200, 2200]

t0tf

td

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

Low-thrust target.

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Direct collocation

Variables

• Discrete states • Discrete controls • Final time

Constraints

• Defect constraints • Boundary conditions • Pointwise path constraints

• Good convergence • Easy initial guess

Capture orbits



Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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'⃗d !⃗d md '⃗f !⃗f mf≈ '⃗E(td) !⃗E(td) mwet ≈ '⃗M(tf) !⃗M(tf) free

td

tftd tf Jt0 - ΔtTOF ≈ t0 -mf

Rendezvous with Mars(no capture)

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

Rendezvous with Mars

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(no capture)

0 200 400 600 800Arrival date (days after t01)

1300

1400

1500

1600

1700

1800

1900

2000

2100

2200

TOF

(day

s)

5

5.5

6

6.5

7

7.5

Requ

ired

mas

s of

pro

pella

nt (k

g)

min(Δm) ∈ [4.9, 5.1] kg

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions


1300

1400

1500

1600

1700

1800

1900

2000

2100

2200

TOF

(day

s)

5

5.5

6

6.5

7

7.5

Requ

ired

mas

s of

pro

pella

nt (k

g)

min(Δm) ∈ [4.7, 4.9] kg

Results

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(with ballistic capture)

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Conclusions• The spacecraft requires roughly the same fuel

regardless of Earth departure or Mars arrival dates;

• Ballistic capture does not carry additional costs, when compared to simply rendezvousing with the planet;

• 5 kg of propellant are required to reach Mars and get ballistically captured (20% of the spacecraft’s mass at departure);

• The spacecraft needs to fly for at least 3.6 years.

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Thank you for your attention.

G. Aguiar F. Topputo

Delft University of Technology Astrodynamics & Space Missions

[email protected]

Politecnico di Milano Aerospace Science and Technology

[email protected]

Questions?



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References

• Casado, Á. S. (2017). Preliminary Systems Design of a Stand-Alone Interplanetary CubeSat to Mars (Unpublished master’s thesis). Universidad Carlos III de Madrid, Politecnico di Milano.

• Luo, Z.-F., Topputo, F., Bernelli-Zazzera, F., & Tang, G. J. (2014). Constructing ballistic capture orbits in the real Solar System model. Celestial Mechanics and Dynamical Astronomy, 120(4), 433–450. doi: 10.1007/s10569-014-9580-5

Images

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Backup slides

A technique for designing Earth-Mars low-thrust transfers culminating in ballistic capture

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions-4 -2 0 2 4

rp0cos( 0) (LU)

-4

-3

-2

-1

0

1

2

3

4

r p0si

n(0) (

LU)

1

1.5

2

2.5

3

3.5

4

S (T

U)

104

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Ballistic capture

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Ballistic capture

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Ballistic capture

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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Ballistic capture

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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1300140015001600170018001900200021002200

TOF

(day

s)

2.5

3

3.5

4

4.5

5

θ(t f) (

360

deg)

Rendezvous with Mars(no capture)

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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1300140015001600170018001900200021002200

TOF

(day

s)

2.5

3

3.5

4

4.5

5

θ(t f) (

360

deg)

Results(with ballistic capture)

Introduction

Concept

Assumptions

Ballistic

Low-thrust

Results

Conclusions

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1300140015001600170018001900200021002200

TOF

(day

s)

0

100

200

300

400

500

600

700

800

900

Ballis

tic T

OF

(day

s)

Results(with ballistic capture)

A technique for designing Earth-Mars low-thrust transfers ......Earth-Mars low-thrust transfers...

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