Solar Sailing Kinetic Energy Impactor (KEI) Bernd Dachwald Ralph - - PowerPoint PPT Presentation

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters Summary and Conclusions

Solar Sailing Kinetic Energy Impactor (KEI) Mission Design Tradeoffs for Impacting and Deflecting Asteroid 99942 Apophis

Bernd Dachwald

German Aerospace Center (DLR) Mission Operations Section Oberpfaffenhofen, 82234 Wessling, Germany bernd.dachwald@dlr.de

Ralph Kahle

German Aerospace Center (DLR) Space Flight Technology Section Oberpfaffenhofen, 82234 Wessling, Germany ralph.kahle@dlr.de

Bong Wie

Arizona State University Department of Mechanical & Aerospace Engineering Tempe, AZ 85287, USA bong.wie@asu.edu

AIAA/AAS Astrodynamics Specialist Conference 21–24 August 2006, Keystone, CO

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters Summary and Conclusions

Outline

Introduction The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol Mission Design Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact Variation of Mission Design Parameters Sail Temperature Limit Solar Sail Degradation Summary and Conclusions

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Near-Earth Asteroids (NEAs)

◮ The orbits of NEAs intersect or pass near the orbit of

Earth

◮ 838 NEAs with a diameter d 1 km are currently

known

◮ The entire population contains perhaps more than 1 000

• bjects of this size

◮ All NEAs with MOID ≤ 0.05 AU and d 200 m are

Potentially Hazardous Asteroids (PHAs)

◮ There are currently 790 known PHAs, 161 of them with

d 1 km

◮ Even asteroids that do not intersect Earth’s orbit may

evolve into Earth-crossers, since their orbits are chaotic, having a relatively short dynamical lifetime (∼ 107 years)

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

The Case of 99942 Apophis

◮ In June 2004, a NEA with a diameter of about 320 m was

discovered (firstly designated 2004 MN4 and later 99942 Apophis)

◮ Very close encounter with Earth on 13 Apr 2029 ◮ With a non-negligible probability subsequent very close

encounter or even impact on 13 Apr 2036 or later

◮ Currently estimated probability that Apophis impacts the

Earth in 2036 is 1/45 000

◮ Earth impact velocity of about 12.6 km/s ◮ Released energy would equal about 875 Megatons of TNT ◮ Whether or not Apophis will impact the Earth in 2036 or

later will be decided by its close encounter in 2029. (If the asteroid passes through one of several so-called “gravitational keyholes” (∅ ≈ 600 m), it will get into a resonant orbit and impact the Earth in one of its later encounters, if no counter-measures are taken)

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Solar Sail Kinetic Energy Impactors (KEIs)

(Multiple) KEIs impact Apophis at perihelion from a trajectory that is retrograde w.r.t. Apophis’ orbit (⇒ vimp ≈ 75 km/s)

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Scenario I

(fictional)

• 1. In 2013 (very favorable radar and optical observations), it is found

that in its 2029-encounter Apophis is likely to fly through the 2036-keyhole ⇒ resonant return to hit the Earth in 2036

• 2. At 01 Jan 2020, a solar sail KEI is launched from Earth

◮ 160 m × 160 m, 168 kg solar sail assembly ◮ 150 kg impactor ◮ ac = 0.5 mm/s2 ◮ Tlim = 240◦C ◮ C3 = 0 km2/s2

• 3. After having attained a trajectory that is retrograde to Apophis’
• rbit, the solar sail KEI is brought onto a collision trajectory, from

where it can impact Apophis in 2026 in the case that Apophis is still likely to fly through the keyhole Two kinds of collision trajectories are investigated:

◮ A trajectory that maximizes vimp ◮ An exactly retrograde orbit (ERO) that encounters

Apophis at every perihelion and aphelion passage

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Scenario I

(fictional)

• 1. In 2013 (very favorable radar and optical observations), it is found

that in its 2029-encounter Apophis is likely to fly through the 2036-keyhole ⇒ resonant return to hit the Earth in 2036

• 2. At 01 Jan 2020, a solar sail KEI is launched from Earth

◮ 160 m × 160 m, 168 kg solar sail assembly ◮ 150 kg impactor ◮ ac = 0.5 mm/s2 ◮ Tlim = 240◦C ◮ C3 = 0 km2/s2

• 3. After having attained a trajectory that is retrograde to Apophis’
• rbit, the solar sail KEI is brought onto a collision trajectory, from

where it can impact Apophis in 2026 in the case that Apophis is still likely to fly through the keyhole Two kinds of collision trajectories are investigated:

◮ A trajectory that maximizes vimp ◮ An exactly retrograde orbit (ERO) that encounters

Apophis at every perihelion and aphelion passage

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Scenario I

(fictional)

• 1. In 2013 (very favorable radar and optical observations), it is found

that in its 2029-encounter Apophis is likely to fly through the 2036-keyhole ⇒ resonant return to hit the Earth in 2036

• 2. At 01 Jan 2020, a solar sail KEI is launched from Earth

◮ 160 m × 160 m, 168 kg solar sail assembly ◮ 150 kg impactor ◮ ac = 0.5 mm/s2 ◮ Tlim = 240◦C ◮ C3 = 0 km2/s2

• 3. After having attained a trajectory that is retrograde to Apophis’
• rbit, the solar sail KEI is brought onto a collision trajectory, from

where it can impact Apophis in 2026 in the case that Apophis is still likely to fly through the keyhole Two kinds of collision trajectories are investigated:

◮ A trajectory that maximizes vimp ◮ An exactly retrograde orbit (ERO) that encounters

Apophis at every perihelion and aphelion passage

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Potential Trajectory for a Pre-2029-Impact

Trajectory that maximizes vimp

520 500 450 400 350 300

Sail Temp. [K] Apophis orbit Earth orbit Launch at Earth Retrograde Apophis impact

Mission duration: 6 years Impact velocity: 75.4 km/s

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Kinetic Energy Impacts Issues

◮ Effective impulse imparted to the asteroid is sum of pure kinetic

impulse of the impactor plus impulse due to “thrust” of material being ejected from impact crater

◮ Last term can be very significant, but magnitude depends strongly

upon density, yield strength, porosity, impactor mass, impact velocity ∆v = ξ mKEI mApophis vimp

◮ Enhancement factor for hard rock: ξ ≈ 2 ◮ Enhancement factor for soft rock: ξ ≈ 4 ◮ Enhancement factor for porous asteroids: ξ ≈ 1.16

⇒ ∆v = 3.73 × 10−9vimp

◮ Values are associated with large uncertainty ⇒ accurate modeling

and prediction of ejecta impulse is critical part of any kinetic-impact approach

◮ Risk that impact could result in fragmentation of the asteroid

(depends upon its composition and structure)

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

The Non-Perfectly Reflecting Solar Sail

The non-perfectly reflecting solar sail model parameterizes the optical behavior of the sail film by the optical coefficient set P = {ρ, s, εf, εb, Bf, Bb} The optical coefficients for a solar sail with a highly reflective aluminum-coated front side and with a highly emissive chromium-coated back side are: PAl|Cr = {ρ = 0.88, s = 0.94, εf = 0.05, εb = 0.55, Bf = 0.79, Bb = 0.55}

S0: solar constant (1368 W/m2) c: speed of light in vacuum r: radius r0: 1 astronomical unit (1 AU) ρ: reflection coefficient s: specular reflection factor εf and εb: emission coefficients of the front and back side, respectively Bf and Bb: non-Lambertian coefficients of the front and back side, respectively

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Simulation Model

Considerations for high-precision trajectory control:

◮ Solar sail bends and wrinkles,

depending on actual solar sail design

◮ Gravitational forces of all

celestial bodies

◮ Reflected light from close

celestial bodies

◮ Solar wind ◮ Finiteness of solar disk ◮ Finite low-precision attitude

control maneuvers

◮ Aberration of solar radiation

(Poynting-Robertson effect)

◮ Relativistic corrections

required for final targeting phase Allowed simplifications for mission feasibility analysis:

◮ Solar sail is a flat plate ◮ Solar sail is moving under sole

influence of solar gravitation and radiation

◮ Sun is a point mass and a

point light source

◮ Solar sail attitude can be

changed instantaneously

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction

The Hazard from Near-Earth Objects The Case of 99942 Apophis Kinetic Energy Impactor Deflection Scenario (I) Kinetic Energy Impacts Solar Sail Force Model Simulation Model Evolutionary Neurocontrol

Mission Design Variation of Mission Design Parameters Summary and Conclusions

Evolutionary Neurocontrol (ENC)

A smart global trajectory optimization method

◮ We used ENC to calculate near-globally optimal

trajectories

◮ ENC is based on a combination of artificial neural

networks with evolutionary algorithms

◮ ENC attacks trajectory optimization problems from the

perspective of artificial intelligence and machine learning

◮ ENC was implemented within a low-thrust trajectory

• ptimization program called InTrance (Intelligent

Trajectory optimization using neurocontroller evolution)

◮ InTrance requires only the target body/state and

intervals for the initial conditions as input to find a near-globally optimal trajectory for the specified problem

◮ InTrance works without an initial guess and does not

require the attendance of a trajectory optimization expert

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Scenario I

(fictional)

• 1. In 2013 (very favorable radar and optical observations), it is found

that in its 2029-encounter Apophis is likely to fly through the 2036-keyhole ⇒ resonant return to hit the Earth in 2036

• 2. At 01 Jan 2020, a solar sail KEI is launched from Earth

◮ 160 m × 160 m, 168 kg solar sail assembly ◮ 150 kg impactor ◮ ac = 0.5 mm/s2 ◮ Tlim = 240◦C ◮ C3 = 0 km2/s2

• 3. After having attained a trajectory that is retrograde to Apophis’
• rbit, the solar sail KEI is brought onto a collision trajectory, from

where it can impact Apophis in 2026 in the case that Apophis is still likely to fly through the keyhole Two kinds of collision trajectories are investigated:

◮ A trajectory that maximizes vimp ◮ An exactly retrograde orbit (ERO) that encounters

Apophis at every perihelion and aphelion passage

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Orbit Cranking Phase

Trajectory, ∆i

T -(r, a)-t-diagram, and solar sail control angles

x [AU] y [AU]

• 1
• 1

1 1

• 1
• 1
• 0.5
• 0.5

0.5 0.5 1 1 1.5 1.5

520 500 450 400 350 300

Retrograde orbit (∆iT = 10 deg) attained on 20 May 2024

Sail Temp. [K]

Solar sail KEI mission (orbit cranking phase) Launch at Earth

• n 01 Jan 2020

C3=0km

2/s 2

Nonperfectly reflecting solar sail with ac=0.5mm/s

2 and Tmax=240°C

Duration of this phase: 4.38 years

Apophis orbit Earth orbit

x [AU] z [AU]

• 0.2
• 0.2

0.2 0.2

• 0.2
• 0.2

0.2 0.2

520 500 450 400 350 300

Retrograde orbit (∆iT = 10 deg) attained on 20 May 2024

Sail Temp. [K]

Solar sail KEI mission (orbit cranking phase) Launch at Earth

• n 01 Jan 2020

C3=0km

2/s 2

Nonperfectly reflecting solar sail with ac=0.5mm/s

2 and Tmax=240°C

Duration of this phase: 4.38 years

0.5 1 50 100 150 500 1000 1500 r [AU] (blue), a [AU] (red) ∆ iT [deg] t [days]

200 400 600 800 1000 1200 1400 1600 20 40 60 80 pitch angle [deg] t [days] 200 400 600 800 1000 1200 1400 1600 90 180 270 360 clock angle [deg] t [days]

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Targeting Phase

Trajectory that maximizes vimp vs. exactly retrograde orbit

x [AU] y [AU]

• 1
• 1
• 0.5
• 0.5

0.5 0.5 1 1

• 0.5
• 0.5

0.5 0.5 1 1

520 500 450 400 350 300

Sail Temp. [K]

Solar sail KEI mission (targeting phase) Nonperfectly reflecting solar sail with ac=0.5mm/s

2 and Tmax=240°C

Duration of this phase: 1.62 years

Apophis’ orbit Impact on 02 Jan 2026 Head-on impact velocity: 75.38 km/s

Trajectory that maximizes vimp

x [AU] y [AU]

• 1
• 1
• 0.5
• 0.5

0.5 0.5 1 1

• 0.5
• 0.5

0.5 0.5 1 1

520 500 450 400 350 300

Sail Temp. [K]

Solar sail KEI mission (transfer phase to exactly retrograde orbit) Nonperfectly reflecting solar sail with ac=0.5mm/s

2 and Tmax=240°C

Duration of this phase: 1.60 years

Apophis’ orbit Exactly retrograde orbit attained on 26 Dec 2025 Impact possiblility at every perihelion passage of Apophis’ with a head-on impact velocity of 75.26 km/s

Transfer trajectory to exactly retrograde orbit (ERO)

◮ From an ERO, the solar sail KEI encounters the target at every

perihelion and aphelion passage

◮ The slightly lower achievable impact velocity from an ERO is

compensated by the flexibility in choosing the impact date

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Targeting Phase

Trajectory that maximizes vimp vs. exactly retrograde orbit

Days KEI head-on Worst case Deflection Impact before impact velocity change from a Date 2029- velocity from a single single KEI encounter [km/s] KEI [mm/s] [km] From trajectory that maximizes the impact velocity: 02 Jan 2026 1198.0 75.38 0.2811 93.2 22 Nov 2026 874.4 77.91 0.2905 71.6 11 Oct 2027 550.8 80.28 0.2993 48.7 30 Aug 2028 227.2 80.95 0.3018 23.3 From exactly retrograde orbit: 02 Jan 2026 1198.0 75.26 0.2806 93.2 22 Nov 2026 874.4 75.26 0.2806 69.5 11 Oct 2027 550.8 75.26 0.2806 45.8 30 Aug 2028 227.2 75.26 0.2806 21.9 Parabolic limit case: 02 Jan 2026 1198.0 86.39 0.3221 107.0 22 Nov 2026 874.4 86.39 0.3221 79.8 11 Oct 2027 550.8 86.39 0.3221 52.5 30 Aug 2028 227.2 86.39 0.3221 25.1

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Scenario II

(fictional) 4.

◮ Impact is aborted before 2029-encounter because it is

found that Apophis is not likely anymore to fly through the keyhole

◮ Impact on 02 Jan 2026 is changed into a close flyby ◮ Instead of aborting the mission, however, the solar sail

KEI is brought to a trajectory that maximizes the deflection for a post-2029-encounter impact, for the case that this might be necessary

• 5. After close Earth-encounter on 13 Apr 2029 it is found that

Apophis really flew through the 2036-keyhole ⇒ resonant return to hit the Earth on 13 Apr 2036.

• 6. The solar sail KEI impacts the asteroid shortly after the

2029-encounter on 11 Jun 2029

• 6b. Alternatively, for comparison, after launch on 01 Jan 2020, the

solar sail KEI is directly sent onto a collision trajectory that maximizes vimp on 11 Jun 2029

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Scenario II

(fictional) 4.

◮ Impact is aborted before 2029-encounter because it is

found that Apophis is not likely anymore to fly through the keyhole

◮ Impact on 02 Jan 2026 is changed into a close flyby ◮ Instead of aborting the mission, however, the solar sail

KEI is brought to a trajectory that maximizes the deflection for a post-2029-encounter impact, for the case that this might be necessary

• 5. After close Earth-encounter on 13 Apr 2029 it is found that

Apophis really flew through the 2036-keyhole ⇒ resonant return to hit the Earth on 13 Apr 2036.

• 6. The solar sail KEI impacts the asteroid shortly after the

2029-encounter on 11 Jun 2029

• 6b. Alternatively, for comparison, after launch on 01 Jan 2020, the

solar sail KEI is directly sent onto a collision trajectory that maximizes vimp on 11 Jun 2029

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Scenario II

(fictional) 4.

◮ Impact is aborted before 2029-encounter because it is

found that Apophis is not likely anymore to fly through the keyhole

◮ Impact on 02 Jan 2026 is changed into a close flyby ◮ Instead of aborting the mission, however, the solar sail

KEI is brought to a trajectory that maximizes the deflection for a post-2029-encounter impact, for the case that this might be necessary

• 5. After close Earth-encounter on 13 Apr 2029 it is found that

Apophis really flew through the 2036-keyhole ⇒ resonant return to hit the Earth on 13 Apr 2036.

• 6. The solar sail KEI impacts the asteroid shortly after the

2029-encounter on 11 Jun 2029

• 6b. Alternatively, for comparison, after launch on 01 Jan 2020, the

solar sail KEI is directly sent onto a collision trajectory that maximizes vimp on 11 Jun 2029

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Scenario II

(fictional) 4.

◮ Impact is aborted before 2029-encounter because it is

found that Apophis is not likely anymore to fly through the keyhole

◮ Impact on 02 Jan 2026 is changed into a close flyby ◮ Instead of aborting the mission, however, the solar sail

KEI is brought to a trajectory that maximizes the deflection for a post-2029-encounter impact, for the case that this might be necessary

• 5. After close Earth-encounter on 13 Apr 2029 it is found that

Apophis really flew through the 2036-keyhole ⇒ resonant return to hit the Earth on 13 Apr 2036.

• 6. The solar sail KEI impacts the asteroid shortly after the

2029-encounter on 11 Jun 2029

• 6b. Alternatively, for comparison, after launch on 01 Jan 2020, the

solar sail KEI is directly sent onto a collision trajectory that maximizes vimp on 11 Jun 2029

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Earth-Impacting Apophis Variations

◮ Kahle has generated 20 000 potential Apophis orbits by random

variation of the orbital elements within the 3σ-accuracy

◮ Two of them have been found to collide with Earth, both during a

7:6 resonant return on 13 Apr 2036 (Ap1 and Ap2)

◮ We have used them as potential impact-trajectories

x [AU] y [AU]

• 1

1

• 1
• 0.5

0.5 1 1.5

Apophis’ post-2029- encounter orbit Earth impact

• n 13 Apr 2036

Apophis’ pre-2029- encounter orbit Earth orbit Close Earth-encounter

• n 13 Apr 2029

Comparison of Ap1’s pre- and post-2029-encounter orbit

−1.5 −1.0 −0.5 0.5 −1.0 −0.5 0.5 1.0 x [105 km] y [105 km] Ap1 Ap2

Closeup of the 2029-encounter and the im- pact (geocentric reference frame)

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Scenario Step 6

Targeting trajectory for an impact on 11 Jun 2029 (impact from a pre-2029-encounter impact trajectory, i.e. 02 Jan 2026 flyby)

x [AU] y [AU]

• 2
• 2
• 1
• 1

1 1

• 1
• 1
• 0.5
• 0.5

0.5 0.5 1 1 1.5 1.5 2 2 2.5 2.5

520 500 450 400 350 300

Sail Temp. [K]

Solar sail KEI mission (2nd targeting phase)

Flyby on 02 Jan 2026

Nonperfectly reflecting solar sail with ac=0.5mm/s

2 and Tmax=240°C

Duration of this phase: 3.44 years

Apophis’ orbit before 2029-encounter Apophis’ orbit after 2029-encounter Impact on 11 Jun 2029 Head-on impact velocity: 71.44 km/s

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Post-2029-Encounter Deflection

Required velocity change and optimal deflection angle for Ap1 and Ap2

2020 2022 2024 2026 2028 2030 2032 2034 2036 10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

10

3

10

4

1 KEI 10 KEIs 100 KEIs 1000 KEIs Close Earth−encounter Earth−impact Required ∆v for deflection [mm/s] 2020 2022 2024 2026 2028 2030 2032 2034 2036 −180 −90 90 180 Time of deflection Optimal deflection angle [deg] Ap1 Ap2

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design

Pre-2029-Encounter Impact Scenario (II) Post-2029-Encounter Impact

Variation of Mission Design Parameters Summary and Conclusions

Scenario Step 6b

Maximizing vimp right after launch (Scenario 6b)

x [AU] y [AU]

• 2
• 2
• 1
• 1

1 1

• 1
• 1
• 0.5
• 0.5

0.5 0.5 1 1 1.5 1.5 2 2 2.5 2.5

520 500 450 400 350 300

Sail Temp. [K]

Solar sail KEI mission (targeting phase) Nonperfectly reflecting solar sail with ac=0.5mm/s

2 and Tmax=240°C

Duration of this phase: 5.06 years

Apophis’ orbit (after 2029-encounter) Impact on 11 Jun 2029 Head-on impact velocity: 72.32 km/s

Impact from trajectory that maximizes the impact velocity

−1.5 −1.0 −0.5 0.5 −1 −0.5 0.5 1 x [105 km] y [105 km] 1 KEI 50 KEIs 75 KEIs 100 KEIs

Deflection for different numbers of KEIs (Ap1, geocentric reference frame)

◮ 70-75 KEIs are required for a successful deflection of Ap1 ◮ 130-140 KEIs are required for a successful deflection of Ap2 ◮ Assuming the worst case, 200 KEIs (63.2 mt) should be launched ◮ This would require 7 Delta IV Heavy, 10 Atlas 5, or 6 Ariane 5 ESC-B

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Variation of the Sail Temperature Limit

0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 acr [AU] ∆i / ∆t [deg/day] Tlim = 220°C Tlim = 240°C Tlim = 260°C

◮ The optimal orbit-cranking semi-major axis can be approximated with an error of less than 2% by ˜ acr,opt ≈ 1.4805 − 0.23 · ln( ˜ Tlim) ◮ The maximum inclination change rate can be approximated with an error of less than 2% by ( ∆i/∆t)max ≈ 0.0224 · ˜ a−1.32

cr,opt

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Variation of the Sail Temperature Limit

0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 acr [AU] ∆i / ∆t [deg/day] Tlim = 220°C Tlim = 240°C Tlim = 260°C

◮ The optimal orbit-cranking semi-major axis can be approximated with an error of less than 2% by ˜ acr,opt ≈ 1.4805 − 0.23 · ln( ˜ Tlim) ◮ The maximum inclination change rate can be approximated with an error of less than 2% by ( ∆i/∆t)max ≈ 0.0224 · ˜ a−1.32

cr,opt

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Variation of the Sail Temperature Limit

0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 acr [AU] ∆i / ∆t [deg/day] Tlim = 220°C Tlim = 240°C Tlim = 260°C

◮ The optimal orbit-cranking semi-major axis can be approximated with an error of less than 2% by ˜ acr,opt ≈ 1.4805 − 0.23 · ln( ˜ Tlim) ◮ The maximum inclination change rate can be approximated with an error of less than 2% by ( ∆i/∆t)max ≈ 0.0224 · ˜ a−1.32

cr,opt

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Variation of the Sail Temperature Limit

200 400 600 800 1000 1200 1400 1600 20 40 60 80 100 120 140 160 180 t [days] i [deg] Tlim = 220°C Tlim = 240°C Tlim = 260°C

Inclination over flight time, i(t)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 20 40 60 80 100 120 140 160 180 a [AU] i [deg] Tlim = 220°C Tlim = 240°C Tlim = 260°C

Inclination over semi-major axis, i(a)

The InTrance-trajectories match the determined optimal

• rbit-cranking semi-major axes very closely.

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Variation of the Sail Temperature Limit

200 400 600 800 1000 1200 1400 1600 20 40 60 80 100 120 140 160 180 t [days] i [deg] Tlim = 220°C Tlim = 240°C Tlim = 260°C

Inclination over flight time, i(t)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 20 40 60 80 100 120 140 160 180 a [AU] i [deg] Tlim = 220°C Tlim = 240°C Tlim = 260°C

Inclination over semi-major axis, i(a)

The InTrance-trajectories match the determined optimal

• rbit-cranking semi-major axes very closely.

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Variation of the Sail Temperature Limit

Tlim acr,opt (∆i/∆t)max ∆toc [◦C] [AU] [deg/day] [days] 220 0.236 0.1461 1722 240 0.220 0.1648 1604 260 0.205 0.1838 1513 The time required for the orbit-cranking phase can be approximated with an error of less than 1% by

• ∆toc ≈ 765(1 − ˜

acr,opt) + 166.7 ( ∆i/∆t)max Note that 166.7 is the required inclination change in degrees and 1 − ˜ acr,opt is the spiralling-in distance in astronomical units

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Solar Sail Degradation Model

(by Dachwald et al.)

0.02 0.02 0.04 0.04 0.06 . 6 0.08 0.08 0.1 . 1 0.12 . 1 2 0.14 0.14 0.16 . 1 6 0.18 0.18 0.2 0.2

Σ ρ/ρ0 , s/s0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.8 0.85 0.9 0.95 1

0.02 0.02 0.04 0.04 0.06 . 6 0.08 0.08 0.1 0.1 0.12 0.12 0.14 0.14 0.16 0.16 0.18 0.18 0.2 0.2

Σ εf /εf0

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 1.05 1.1 1.15 1.2

d d

“degradation” of optical coefficients

. = Σ 5 . = Σ . 1 = Σ . 5 = Σ

r

e

t

e

“degradation” of SRP force bubble

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters

Sail Temperature Limit Solar Sail Degradation

Summary and Conclusions

Solar Sail Degradation

“Half life” solar radiation dose ˆ Σ = 25 S0·yr = 394 TJ/m2

200 400 600 800 1000 1200 1400 1600 1800 2000 20 40 60 80 100 120 140 160 180 t [days] i [deg] d = 0.0 d = 0.05 d = 0.1 d = 0.2

Inclination over flight time

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 20 40 60 80 100 120 140 160 180 a [AU] i [deg] d = 0.0 d = 0.05 d = 0.1 d = 0.2

Inclination over semi-major axis

Transfer Earliest Calculated Degradation time to Attainment possible deflection factor ERO

• f ERO

Apophis impact from a single [days] Date KEI [km] 0.0 2186 26 Dec 2025 02 Jan 2026 93.2 0.05 2395 23 Jul 2026 22 Nov 2026 69.5 0.1 2574 18 Jan 2027 11 Oct 2027 45.8 0.2 2816 17 Sep 2027 11 Oct 2027 45.8

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters Summary and Conclusions

Summary and Conclusions

◮ A single solar sail (160 m × 160 m, 168 kg plus 150 kg

impactor, ac = 0.5 mm/s2 and Tlim = 240◦C) is a realistic option to deflect Apophis with a kinetic impact before its 2029-Earth-encounter with very high velocity from a retrograde orbit

◮ Only a small and thus cheap launch vehicle is required ◮ Conventional KEI spacecraft (chemical, electrical) is

also able to prevent Apophis from flying through a 600-m keyhole in 2029

◮ Our solar sail KEI mission concept, however, is also able

to deflect larger asteroids out of a keyhole

◮ Using solar sail KEIs, it is still feasible to deflect

asteroids that do not pass through a keyhole before impacting Earth

◮ In the latter case, however, a short lead time requires

many KEIs

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters Summary and Conclusions

KEI Mission Challenges

◮ The mission performance might be seriously affected by

• ptical degradation of the sail surface, as it is expected

in the extreme space environment close to the sun

◮ Ground and in-space tests are required due to the

unknown degradation behavior of solar sails in the space environment

◮ Extreme requirements for terminal guidance prior to

impact (accuracy much better than 100 m at a relative velocity of ≈ 75 km/s)

◮ Extreme requirements for thermal control that has to

withstand very close solar distances (0.2 − 0.25 AU)

Solar Sailing KEI Apophis Deflection Mission Bernd Dachwald Ralph Kahle Bong Wie Outline Introduction Mission Design Variation of Mission Design Parameters Summary and Conclusions

Solar Sailing Kinetic Energy Impactor (KEI) Mission Design Tradeoffs for Impacting and Deflecting Asteroid 99942 Apophis

Bernd Dachwald

German Aerospace Center (DLR) Mission Operations Section Oberpfaffenhofen, 82234 Wessling, Germany bernd.dachwald@dlr.de

Ralph Kahle

German Aerospace Center (DLR) Space Flight Technology Section Oberpfaffenhofen, 82234 Wessling, Germany ralph.kahle@dlr.de

Bong Wie

Arizona State University Department of Mechanical & Aerospace Engineering Tempe, AZ 85287, USA bong.wie@asu.edu

Acknowledgements: The work described in this paper was funded in part by the In-Space Propulsion Technology Program, managed by NASA’s Science Mission Directorate in Washington, D.C., and implemented by the In-Space Propulsion Technology Office at Marshall Space Flight Center in Huntsville, Alabama