Analysis of Proportional Navigation Guidance Algorithms in the Context of a Near-Earth Object Intercept Mission

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Guidance Algorithms in the Context of a Near-Earth Object Intercept Mission

Clark Matteo

Space Engineering, master's level (120 credits) 2018

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

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SCHOOL OF AEROSPACE, TRANSPORT AND MANUFACTURING

Astronautics and Space Engineering

MSc

Academic Year: 2017–2018

MATTEO A. CLARK

Analysis of Proportional Navigation Guidance Algorithms in the Context of a Near-Earth Object Intercept Mission

Supervisor: Dr Changhun Lee October 2018

This thesis is submitted in partial fulfilment of the requirements for the degree of MSc.

permission of the copyright owner.

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Abstract

An impact of a Near-Earth Object with the Earth is rare but possible, and can have negative consequences ranging from localized annoyance and injury to global devastation and the end of the world as we know it. Considering the magnitude of the consequences and the lack of an ability to respond to such a threat, it is important that these Planetary Defense capabilities are developed.

The research conducted for this project analyzes the spacecraft design trade-space in the context of a conceptual kinetic impact mission with Asteroid 101955 Bennu. To accomplish the research objectives, an orbit propagator was developed, proportional navigation guidance algorithms were implemented and simulations were run with difference combinations of design parameters.

It was found that both studied guidance algorithms performed very similarly in most regards, yet the augmented three-plane proportional guidance algorithm appeared to achieve impact more efficiently. There is uncertainty as to whether this is a characteristic of the algorithm or a consequence of the initial conditions.

Additionally, it was seen that the more significant performance enhancements for the kinetic impact mission were more significantly influenced by the design of a spacecraft as opposed to the selection of a guidance algorithm over another.

Keywords

Planetary Defense; Guidance Algorithms; Spacecraft Design.

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List of Figures

2.1 Artist’s depiction of the a fragment of Comet Shoemaker-Levy 9 and Jupiter showing part of the impact event. (Davis, 1994) . . . . 7 2.2 Artist’s depiction of the asteroid that caused the Cretaceous-Tertiary ex-

tinction. (Davis, n.d.) . . . . 8 2.3 Planetesimal Orbital Classification Flowchart. . . 12 2.4 Basic geometrical parameters for elliptical orbits. . . 13 2.5 Representative orbits of Near-Earth Asteroids (viewpoint is perpendicular

to the orbital plane of the Earth). . . 14 2.6 Discoveries of Near Earth Asteroids since the 1980s (as of September 18,

2018). (Jet Propulsion Laboratory, 2018a) . . . 18 2.7 Estimated diameters of the NEAs that have been discovered (as of Septem-

ber 18, 2018). (Jet Propulsion Laboratory, 2018b) . . . 18 2.8 Comparison between the NEA population estimate and the number of

NEAs discovered (as of August 2014) by their absolute magnitude (and diameter). (Harris and DAbramo, 2015) . . . 19 2.9 A representation of the Tunguska airburst event. (Davis, 2008) . . . 24 2.10 A representation of the Chelyabinsk airburst event that occurred on Febru-

ary 15, 2013. (Davis, 2013) . . . 25 2.11 Torino Impact Hazard Scale. (Wikimedia Commons, 2007) . . . 26 2.12 Figure depicting the kind of strategy to employ relative to the diameter of

the threat and warning time. (National Research Council, 2010) . . . 30 2.13 Artist’s representation of the triumphant destruction / vaporization of a

significant threat. (Conceptual space vehicle shown in the foreground) (Marquand, 1983) . . . 31 2.14 Two-dimensional version of the cartesian reference system within which

the spacecraft and target exist. . . 45 2.15 Diagram of the Lambert problem geometry. . . 46 3.1 Diagram showing a representative 2D impact geometry between target

and spacecraft. . . 56 3.2 Example of an impact threshold for a spacecraft traveling towards Aster-

oid 101955 Bennu at relative velocity of 1.0 km per second and a time step duration of 1.0 second. . . 58 3.3 Simplistic notional structure of a Guidance, Navigation and Control (GN&C)

system. . . 59 3.4 Pseudo-code for control of the spacecraft’s propulsion unit. . . 61

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4.1 Asteroid 101955 Bennu Position Propagation Error for a range of time- steps sizes. . . 65 4.2 Asteroid 101955 Bennu Velocity Propagation Error for a range of time-

steps sizes. . . 65 4.3 Asteroid 101955 Bennu Position Propagation Error over a longer period

for a range of time-steps sizes. . . 67 4.4 Asteroid 101955 Bennu Velocity Propagation Error over a longer period

for a range of time-steps sizes. . . 67 4.5 Asteroid 101955 Bennu reference and propagated trajectories for a range

of time-step sizes. . . 68 4.6 Asteroid 101955 Bennu reference and propagated trajectories for a range

of time-step sizes (enlarged view). . . 68 4.7 Trajectories of each spacecraft relative to Asteroid 101955 Bennu. . . 71 4.8 Closing trajectories of each spacecraft relative to Asteroid 101955 Bennu

(enlarged view). . . 71 4.9 Comparison of relative target-spacecraft magnitude of position for both

spacecrafts. . . 72 4.10 Comparison of relative target-spacecraft velocity magnitudes for both space-

crafts. . . 72 4.11 Comparison of variation in mass throughout the simulation for both space-

crafts. . . 73 4.12 Difference in position between asteroid reference orbit and deflected orbit

after impact. . . 76 4.13 Difference in velocity between asteroid reference orbit and deflected orbit

after impact. . . 76 4.14 Impact to Miss Ratio relationship between the selected simulation time-

step and the guidance algorithm. . . 79 4.15 The effect of the time-step selection on the mean (left) and median (right)

DV imparted on the target at impact for both guidance algorithms. . . 80 4.16 The effect of the time-step selection on the minimum (left) and maximum

(right)DV imparted on the target at impact for both guidance algorithms. 81 4.17 The effect of the time-step selection on the mean (left) and median (right)

mean normalized spacecraft mass at impact for both guidance algorithms. 82 4.18 The effect of the time-step selection on the minimum (left) and maximum

(right) mean normalized spacecraft mass at impact for both guidance algorithms. . . 82 4.19 The effect of the time-step selection on the mean (left) and median (right)

relative terminal/impact velocity for both guidance algorithms. . . 83 4.20 The effect of the time-step selection on the minimum (left) and maximum

(right) relative terminal/impact velocity for both guidance algorithms. . . 83 4.21 The effect of the time-step selection on the mean (left) and median (right)

impact offset angle for both guidance algorithms. . . 84 4.22 The effect of the time-step selection on the minimum (left) and maximum

(right) impact offset angle for both guidance algorithms. . . 84 4.23 Histogram showing impact offset angle range and number of occurrences. 85

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4.24 The effect of the gain factor on the total impact fraction for both guidance algorithms. . . 86 4.25 The effect of the gain factor on the mean (left) and median (right) DV

imparted on the target at impact for both guidance algorithms. . . 87 4.26 The effect of the gain factor on the minimum (left) and maximum (right)

DV imparted on the target at impact for both guidance algorithms. . . 87 4.27 The effect of the gain factor on the mean (left) and median (right) mean

normalized spacecraft mass at impact for both guidance algorithms. . . . 88 4.28 The effect of the gain factor on the minimum (left) and maximum (right)

mean normalized spacecraft mass at impact for both guidance algorithms. 88 4.29 The effect of the gain factor on the mean (left) and median (right) relative

terminal/impact velocity for both guidance algorithms. . . 89 4.30 The effect of the gain factor on the minimum (left) and maximum (right)

relative terminal/impact velocity for both guidance algorithms. . . 90 4.31 The effect of the gain factor on the mean (left) and median (right) impact

offset angle for both guidance algorithms. . . 90 4.32 The effect of the gain factor on the minimum (left) and maximum (right)

impact offset angle for both guidance algorithms. . . 91 4.33 The effect of the initial spacecraft mass on the total impact fraction for

both guidance algorithms. . . 92 4.34 The effect of the initial spacecraft mass on the mean (left) and median

(right)DV imparted on the target at impact for both guidance algorithms. 93 4.35 The effect of the initial spacecraft mass on the minimum (left) and maxi-

mum (right)DV imparted on the target at impact for both guidance algorithms. . . 93 4.36 The effect of the initial spacecraft mass on the mean (left) and median

(right) normalized spacecraft mass at impact for both guidance algorithms. 94 4.37 The effect of the initial spacecraft mass on the minimum (left) and max-

imum (right) normalized spacecraft mass at impact for both guidance algorithms. . . 94 4.38 The effect of the initial spacecraft mass on the mean (left) and median

(right) relative terminal/impact velocity for both guidance algorithms. . . 95 4.39 The effect of the initial spacecraft mass on the minimum (left) and maxi-

mum (right) relative terminal/impact velocity for both guidance algorithms. 95 4.40 The effect of the initial spacecraft mass on the mean (left) and median

(right) impact offset angle for both guidance algorithms. . . 96 4.41 The effect of the initial spacecraft mass on the minimum (left) and maxi-

mum (right) impact offset angle for both guidance algorithms. . . 96 4.42 The effect of the initial spacecraft mass on the total impact fraction for

both guidance algorithms. . . 97 4.43 The effect of the initial propellant mass ratio on the mean (left) and me-

dian (right)DV imparted on the target at impact for both guidance algorithms. . . 98 4.44 The effect of the initial propellant mass ratio on the minimum (left) and

maximum (right)DV imparted on the target at impact for both guidance algorithms. . . 98

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4.45 The effect of the initial propellant mass ratio on the mean (left) and median (right) normalized spacecraft mass at impact for both guidance algorithms. . . 99 4.46 The effect of the initial propellant mass ratio on the minimum (left) and

maximum (right) normalized spacecraft mass at impact for both guidance algorithms. . . 99 4.47 The effect of the initial propellant mass ratio on the mean (left) and me-

dian (right) relative terminal/impact velocity for both guidance algorithms. 100 4.48 The effect of the initial propellant mass ratio on the minimum (left) and

maximum (right) relative terminal/impact velocity for both guidance algorithms. . . 100 4.49 The effect of the initial propellant mass ratio on the mean (left) and me-

dian (right) impact offset angle for both guidance algorithms. . . 101 4.50 The effect of the initial propellant mass ratio on the minimum (left) and

maximum (right) impact offset angle for both guidance algorithms. . . 101 4.51 The effect of the specific impulse on the total impact fraction for both

guidance algorithms. . . 102 4.52 The effect of the specific impulse on the mean (left) and median (right)

DV imparted on the target at impact for both guidance algorithms. . . 103 4.53 The effect of the specific impulse on the minimum (left) and maximum

(right)DV imparted on the target at impact for both guidance algorithms. 103 4.54 The effect of the specific impulse on the mean (left) and median (right)

normalized spacecraft mass at impact for both guidance algorithms. . . . 104 4.55 The effect of the specific impulse on the minimum (left) and maximum

(right) normalized spacecraft mass at impact for both guidance algorithms. 105 4.56 The effect of the specific impulse on the mean (left) and median (right)

relative terminal/impact velocity for both guidance algorithms. . . 106 4.57 The effect of the specific impulse on the minimum (left) and maximum

(right) relative terminal/impact velocity for both guidance algorithms. . . 106 4.58 The effect of the specific impulse on the mean (left) and median (right)

impact offset angle for both guidance algorithms. . . 107 4.59 The effect of the specific impulse on the minimum (left) and maximum

(right) impact offset angle for both guidance algorithms. . . 107 4.60 The effect of the maximum propellant flow rate on the total impact frac-

tion for both guidance algorithms. . . 108 4.61 The effect of the maximum propellant flow rate on the mean (left) and

median (right) DV imparted on the target at impact for both guidance algorithms. . . 109 4.62 The effect of the maximum propellant flow rate on the minimum (left) and

maximum (right)DV imparted on the target at impact for both guidance algorithms. . . 109 4.63 The effect of the maximum propellant flow rate on the mean (left) and

median (right) normalized spacecraft mass at impact for both guidance algorithms. . . 110

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4.64 The effect of the maximum propellant flow rate on the minimum (left) and maximum (right) normalized spacecraft mass at impact for both guidance algorithms. . . 111 4.65 The effect of the maximum propellant flow rate on the mean (left) and

median (right) relative terminal/impact velocity for both guidance algorithms. . . 111 4.66 The effect of the maximum propellant flow rate on the minimum (left)

and maximum (right) relative terminal/impact velocity for both guidance algorithms. . . 112 4.67 The effect of the maximum propellant flow rate on the mean (left) and

median (right) impact offset angle for both guidance algorithms. . . 112 4.68 The effect of the maximum propellant flow rate on the minimum (left)

and maximum (right) impact offset angle for both guidance algorithms. . 113 4.69 The effect of the minimum propellant flow rate on the total impact fraction

for both guidance algorithms. . . 114 4.70 The effect of the minimum propellant flow rate on the mean (left) and

median (right) DV imparted on the target at impact for both guidance algorithms. . . 115 4.71 The effect of the minimum propellant flow rate on the minimum (left) and

maximum (right)DV imparted on the target at impact for both guidance algorithms. . . 115 4.72 The effect of the minimum propellant flow rate on the mean (left) and

median (right) normalized spacecraft mass at impact for both guidance algorithms. . . 116 4.73 The effect of the minimum propellant flow rate on the minimum (left) and

maximum (right) normalized spacecraft mass at impact for both guidance algorithms. . . 116 4.74 The effect of the minimum propellant flow rate on the mean (left) and me-

dian (right) relative terminal/impact velocity for both guidance algorithms. 117 4.75 The effect of the minimum propellant flow rate on the minimum (left)

and maximum (right) relative terminal/impact velocity for both guidance algorithms. . . 117 4.76 The effect of the minimum propellant flow rate on the mean (left) and

median (right) impact offset angle for both guidance algorithms. . . 118 4.77 The effect of the minimum propellant flow rate on the minimum (left) and

maximum (right) impact offset angle for both guidance algorithms. . . 118 5.1 The effect of the time-step selection and gain factor on the mean nor-

malized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 123 5.2 The effect of the time-step selection and gain factor on the median nor-

malized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 124 5.3 The effect of the time-step selection and gain factor on the impact frac-

tion for the ATPPN (left) and TPPN (right) guidance algorithms over a different range of time-steps. . . 124

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5.4 The effect of the gain factor and initial spacecraft mass on the mean normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 125 5.5 The effect of the gain factor and initial spacecraft mass on the median

normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 125 5.6 The effect of the initial spacecraft mass and the specific impulse on the

mean normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 126 5.7 The effect of the initial spacecraft mass and the specific impulse on the

median normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 127 5.8 The effect of the specific impulse and maximum propellant flow rate on

the mean normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 127 5.9 The effect of the specific impulse and maximum propellant flow rate

on the median normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 128 5.10 The effect of the specific impulse and maximum propellant flow rate se-

lection on the mean normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 128 5.11 The effect of the specific impulse and maximum propellant flow rate se-

lection on the median normalized performance for the ATPPN (left) and TPPN (right) guidance algorithms. . . 129 5.12 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the guidance algorithms. . 130 5.13 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the gain factor. . . 131 5.14 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the initial spacecraft mass. 131 5.15 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the initial propellant mass ratio. . . 132 5.16 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the specific impulse. . . 132 5.17 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the maximum propellant mass flow rate. . . 133 5.18 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the minimum propellant mass flow rate. . . 134 5.19 The number of missions resulting in at least a 95.0% (left) and 99.0%

(right) match to the mission values in terms of the time-step. . . 134 A.1 Torino Impact Hazard Scale (Jet Propulsion Laboratory, 2018d) . . . 142

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List of Tables

4.1 The physical properties of asteroid 101955 Bennu (Lauretta et al., 2015) . 63

4.2 NEO Intercept Simulation Settings . . . 69

4.3 Interception Spacecraft Properties (both the initial position and velocity are relative to the target initial conditions) . . . 70

4.4 Initial conditions of Interception Spacecrafts (both are relative to the target initial conditions, which are taken from NASA JPL Horizons data for the start time) . . . 70

4.5 Kinetic energy of interception between the two spacecrafts and the target asteroid. . . 74

4.6 Various impact simulation properties updated for this simulation relative to that of Table 4.3. . . 75

4.7 Input parameters for simulations. . . 78

4.8 Initial conditions of Interception Spacecraft (both are relative to the target initial conditions) . . . 78

5.1 Mission Designer Values, including weight factors and relative ranking (where the smallest number indicates highest importance). . . 122

5.2 Mean parameter values likely to result in a successful mission. . . 130

B.1 Derivation of mission value weightings. . . 143

B.2 Mission value indices for Table B.1. . . 144

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List of Abbreviations

AIAA American Institute of Aeronautics and Astronautics AIDA Asteroid Impact and Deflection Assessment

ARM Asteroid Redirect Mission

ATPPN Augmented Three-Plane Proportional Navigation

AU Astronomical Units

DART Double Asteroid Redirection Test ESA European Space Agency

FB Free Body

FOB Fixed Orbit Body

GN&C Guidance, Navigation and Control IAA International Academy of Astronautics ISRU In-Situ Resource Utilization

JPL Jet Propulsion Laboratory

LOS Line-of-sight

NASA National Aeronautics and Space Administration NEA Near-Earth Asteroid

NEC Near-Earth Comet

NEO Near-Earth Object

NRC National Research Council NSS National Space Society

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OSIRIS- REx

Origins, Spectral Interpretation, Resource Identification, and SecurityRe- golith Explorer

PHO Potentially Hazardous Object TNT Trinitrotoluene

TPPN Three-Plane Proportional Navigation

UNOOSA United Nations Office for Outer Space Affairs

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Acknowledgements

I would like to thank Don Davis for most of the artwork included in this thesis. I would like to thank my supervisor for his guidance. I would like to thank my parents, my brother, and my extended family for their support.

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Chapter 1 Introduction

A common theme in science-fiction is the human (or other sentient and intelligent species’) struggle against an existential threat. In some cases, this threat can take the form of a Near-Earth Object (NEO) on an Earth-bound collision trajectory. While the science in these stories can be questionable at times, the level of global devastation and loss of life that an impact could cause is plausible in our reality. Thus, it is important for humanity to find a way to ensure our survival on this planet, if not the survival of the Earth.

Planetary Defense is an area of science and engineering focused on studying and mitigating the threat of impact of NEOs with the Earth. The four key technical areas of study and/or action within the discipline are: the identification of NEOs, estimation of their orbital trajectories, characterization of their physical properties, and threat reduction or elimination by deflection/fragmentation/destruction.

As a discipline, Planetary Defense is still young. Current capabilities allow us to identify, track and somewhat characterize NEOs and other celestial bodies, yet many improvements can still be made in these areas. On the other hand, our capability of dealing with a NEO on a collision trajectory with the Earth is inexistent (in public knowledge), and this must be changed.

Science has shown us that the Earth has been hit by many foreign objects of varying sizes in the past. Some of these impacts have gone unnoticed, whereas others have had

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significant ramifications throughout the history of the Earth. Assuming that the universe and time are infinite and that any possible event (that is a function of time) can occur and will occur. It is imperative that we prepare against a potential threat by developing technologies and mitigation strategies in the four technical areas of Planetary Defense. At some point in the future, the need for Planetary Defense will be tangible and humanity may not have the luxury of time to respond as it seems to have now.

1.1 Aims and Objectives

The aim of this thesis is to better understand the effects of Proportional Navigation Guid- ance Algorithms and other related design parameters on the success of simulated kinetic impactor Planetary Defense missions.

Several objectives were established to accomplish this aim:

• Develop an orbit propagator in Python capable of modeling the momentum transfer between bodies.

• Implement guidance algorithms to study the spacecraft’s performance in the terminal mission phase prior to interception/impact.

• Analyze the simulation results to determine what variables that influence the success of the mission.

1.2 Thesis Layout

The thesis is structured the following way:

• Chapter 1 introduced the subject-area as well as the aims and objectives of the thesis project undertaken.

• Chapter 2 will present a literature review including some historical background on Planetary Defense, an overview of Near-Earth Objects, the consequences of a

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NEO impacts with the Earth, the defense and mitigation strategies and methods that have been studied in literature. Chapter 2 will also include an overview and some mathematical background on Guidance Laws for spacecrafts.

• Chapter 3 will present an overview of the work that was done to develop the capabilities that were used to simulate the kinetic impactor mitigation method on an asteroid.

• Chapter 4 will present the results of various simulations in the scope of validating the propagator and impact mechanics, the guidance algorithms, as well as the simulation results for an investigation into the effects of spacecraft design parameters.

• Chapter 5 will discuss the results presented in Chapter 4 in the context of Planetary Defense mission design.

• The conclusions drawn from this work will be presented in Chapter 6.

• Chapter 7 will provide recommendations for future work.

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Chapter 2 Literature Review

2.1 Historical Background of Planetary Defense

Although it has long been recognized that Asteroids and Comets alike can pose a threat to the Earth (Chapman, 2004), Planetary Defense didn’t take shape until the late 1980s (Mellor, 2007), primarily in response to a few key events.

The event that really put things in motion for the field of Planetary Defense was the discovery of Asteroid 1989FC (4581 Asclepius) on March 31, 1989 by Holt and Thomas at the Palomar Observatory in California (Jet Propulsion Laboratory, 2003). The discovery of an asteroid normally isn’t that noteworthy, however, this case was different.

Asteroid 1989FC had just made an undetected close encounter with the Earth on March 23, 1989, which prompted a response from the scientific community (Tagliaferri, 1996) and subsequently media (Asimov, 1989, Leary, 1989).

Apollo Asteroid 1989FC (4581 Asclepius) had passed within 400,000 miles (650,000 km) of the Earth (Tagliaferri, 1996). To put this in perspective, that distance is roughly 1.6 times the mean distance between the Earth and the Moon (Yaplee et al., 1965). This may at first seem to be a large distance from a human perspective, but to an asteroid traveling at approximately 67,100 MPH (30.0 km/s), this distance can be covered in just under 6 hours. A short and sweet commute to devastation on the Earth.

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Many factors influence the magnitude of the damage caused by the impact of an asteroid or a comet with the Earth (or any other celestial body for that matter). In the case of Asteroid 1989FC, if it had collided with the Earth an estimate of its destructive energy would be equivalent to between 1 · 10³ and 20 · 10³ megatons of TNT. All three sources agree that if a city were struck, the damage would be widespread (Leary, 1989) and the number of fatalities would be significant.

In April of 1990, the American Institute of Astronautics and Aeronautics (AIAA) published a position paper recommending that the scientific community address the hazard of asteroids and develop strategies to better prepare the Earth for future events (American Institute of Aeronautics and Astronautics, 1990). Since then, other similar professional societies have published their own position papers on the matter. These societies include:

the International Academy of Astronautics (IAA) (International Academy of Astronau- tics, 2009), the National Space Society (NSS) (National Space Society, 2014), and the United Nations Office for Outer Space Affairs (United Nations Office for Outer Space Affairs, 2018).

A few years after the publication of AIAA’s position paper (American Institute of Aeronautics and Astronautics, 1990) on the threat of NEOs, Comet Shoemaker-Levy 9 was discovered by David H. Levy, Eugene M. Shoemaker, and Carolyn S. Shoemaker at the Palomar Observatory (March 23, 1993). Analysis of the comet’s trajectory by Marsden, and later Yeomans and Chodas would predict with almost certainty that all 21 fragments of the comet would collide with Jupiter the following year. Between July 16 and 22, 1994, comet Shoemaker-Levy 9 struck Jupiter as predicted. This was most likely the first time that an impact had been witnessed since the invention of the telescope, which provided an unprecedented opportunity for scientific discovery as well as a tangible case to validate the need for Planetary Defense. (Levy, 1998) Shown in Figure 2.1 is a representation of some of the Jovian impacts as viewed by one of the fragments of Comet Shoemaker-Levy 9. (Davis, 1994)

As previously mentioned, the fact that asteroids and comets can pose a threat to the

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Figure 2.1: Artist’s depiction of the a fragment of Comet Shoemaker-Levy 9 and Jupiter showing part of the impact event. (Davis, 1994)

Earth was already known, yet any organized efforts to study the hazard were short-lived and their credibility was negatively affected by what some have referred to as the ‘giggle factor’ (Tagliaferri, 1996, Mellor, 2007). These earlier efforts may still have helped the formation of Planetary Defense by providing a precedent or increasing awareness.

In 1967, ‘Project Icarus’ was initiated at MIT by Professor Paul Sandorff. The students selected for the project were tasked with mitigating the threat of impact of Asteroid 1566 Icarus in a hypothetical collision scenario. This academic project later inspired the 1979 movie ‘Meteor’, in which the USA and the USSR had to join forces to eradicate a threat to humanity. (Neame, 1979)

In this same decade, Arthur C. Clarke published a novel called ‘Rendezvous with Rama’ (1973), and later, Larry Niven and Jerry Pournelle published ‘Lucifer’s Hammer’

(1977). Both of these novels featured an asteroid that would impact the Earth, and both

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novels had an influence on the scientists working on the issue of Planetary Defense in the form of citations in peer-reviewed papers and policy. (Mellor, 2007)

In 1980, evidence in support of the theory that the Cretaceous-Tertiary extinction was caused by an extraterrestrial impact was published. This paper supports the view-point that the impact of an asteroid with the Yucat´an peninsula (creating what is known today as the Chicxulub crater) destroyed the natural environment required to sustain most life forms on Earth (Alvarez et al., 1980). Shown in Figure 2.2 is a representation of what the Cretaceous-Tertiary extinction event may have looked like. (Davis, n.d.)

Figure 2.2: Artist’s depiction of the asteroid that caused the Cretaceous-Tertiary extinction. (Davis, n.d.)

Between the late 1980s and the early 2000s, the threat of an object impacting the Earth had permeated through the scientific community to the general public. It is suggested that the scientists involved in the field took on both the role of the prophet and the hero, spreading the notion that the Earth would only be saved by scientists and the technological means that they developed (if they had enough funding). (Mellor, 2007)

Planetary Defense has since grown (with support by the progressive increase in the number of governmental and non-governmental organizations that have published a stance

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on the issue or discipline) and progress towards building earth defense capabilities con- tinues slowly but surely. There are currently a range of governmental, academic, private and non-profit organizations globally that are involved in studying the threat of NEOs and potential mitigation strategies.

NASA, the independent aeronautics and space agency of the United States, in 1992 initiated what is known as the ‘Spaceguard Survey’ (in honor of science fiction writer Arthur C. Clarke) whose objective was to locate 90% of the Near Earth Asteroids (NEAs) with a diameter larger than 1 km. (Chapman, 2004) This led to the creation of the Space- guard Foundation in 1996, and other Near-Earth Object observation programs across the world.

More recently, a non-profit organization, called The B612 Foundation, has entered the Planetary Defense space. Founded in 2002 (and named after the asteroid in ‘The Little Prince’), their mission is to protect the Earth from asteroid impacts by advocating for Planetary Defense strategies and technologies through research and communication with international scientists and policy-makers. They were almost able to develop and launch a satellite to detect potentially hazardous NEOs. This foundation is an interesting example of how the space industry has evolved over the last few decades (from being primarily run by governments, to now having a significant private industry presence or interest) and how the public can have an impact on science and the space industry.

Other similar efforts to develop and validate Planetary Defense technologies have failed due to lack of funding or interest, and possibly also political factors. Notable ex- amples are the European Space Agency’s (ESA) Don Quijote spacecraft and mission, and NASA’s Asteroid Redirect Mission (ARM). Both of these missions were promising and would have tested different Planetary Defense methods. However, one of these has been replaced by a joint NASA-ESA mission planned for the coming decade, which is set to become the first ever validation of a mitigation method for Planetary Defense.

Unlike two decades ago, the NEO threat is taken much more seriously. Governments and organizations around the world have acknowledged this threat and have taken action

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to become more prepared for potential impacts. However, there is still much research and development and validation that needs to be done in terms of the capabilities required to mitigate against a hazardous object if it were on a collision course with the Earth.

By no means is the account provided in Section 2.1 above a complete history of the origins and development of Planetary Defense; the events mentioned were deemed to have a significant role in shaping the environment and perception of NEO threats, and creating what Planetary Defense has become.

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2.2 Near-Earth Objects: Categorization and Detection

The universe is ‘full’ of planetesimals of various shapes, sizes and compositions. Most of these objects are located outside of our solar system, however, the ones we are most interested in for the context of this project are commonly referred to as Near-Earth Objects (NEOs) for their relative proximity to the Earth.

Section 2.2.1 will cover the primary way in which NEOs are categorized, and subsequently, Section 2.2.2 will present some of the ways in which NEOs (and other bodies) are detected.

2.2.1 Categorization

Near-Earth Objects (NEOs) are bodies whose orbits around the Sun have a perihelion of less than 1.3 Astronomical Units (AU) and orbital time periods less than 200.0 years, and thus can exist in the Earth’s vicinity. (Bottke et al., 2002)

Further classifications of these bodies can be made based on their composition and origin, but more importantly, based on the level of threat that they pose to the Earth within a certain timeframe. Figure 2.3 shows a breakdown of how NEOs can be further classified. (Bottke et al., 2002, Jet Propulsion Laboratory, 2018c) Some of the additional detail shown in the Figure 2.3 will be presented in the following subsections.

Note that an orbit’s semi-major axis is defined to be the half of the distance between the apogee (furthest point from the orbit’s focus) and the perigee (closest point to the orbit’s focus). The radius of perigee (or the perigee distance) is the distance between the perigee and the orbit’s focal point. Similarly, the radius of apogee is the distance between the apogee and the orbit’s focal point. The perihelion and aphelion distances are equivalent to the perigee and apogee distance, respectively, if the focal point of the orbit is a sun. See Figure 2.4 for a visual representation of these orbital parameters.

Additionally, the minimum orbit intersection distance is equivalent to the minimum separation distance that exists between the Earth and the NEO throughout an orbit.

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Figure 2.3: Planetesimal Orbital Classification Flowchart.

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Figure 2.4: Basic geometrical parameters for elliptical orbits.

Near-Earth Asteroids

As defined in Asteroids III, an asteroid is an interplanetary body formed without significant ice content, and thus incapable of displaying cometary activity. It is however thought that Asteroids and Comets are part of the same continuum that have had different evolu- tionary paths. (Weissman et al., 2002)

Asteroids can be further categorized by their compositions (spectral signature), and Near-Earth Asteroids (NEAs) specifically can be categorized into one of four classes de- pending on the semi-major axis and aphelion or perihelion distances of their orbits.

As shown in Figure 2.3, if an NEA’s orbit has a semi-major axis distance of less than 1.0 AU it is either classed as an Atiras or Atens asteroid, based on whether its aphelion distance is less than or more than 0.983 AU respectively. On the other hand, if an NEA’s semi-major axis distance is greater than 1.0 AU, it is classed as an Apollo or Amors asteroid, if its perihelion distance is either less than or greater than 1.017 AU respectively.

(Bottke et al., 2002, Jet Propulsion Laboratory, 2018c)

It important to note that NEAs in the Apollo and Atens classes have orbits that in- tersect that of the Earth, meaning that they are more likely to be Potentially Hazardous Asteroids (PHAs). A representation of what NEA orbits might look like with respect to

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Figure 2.5: Representative orbits of Near-Earth Asteroids (viewpoint is perpendicular to the orbital plane of the Earth).

the Earth’s orbit is shown in Figure 2.5.

Asteroids are typically classified by their spectral signature, which can be sensed by spacecrafts and observatories when the asteroid is illuminated by electromagnetic waves.

This signature in turn is used to understand what that composition of the asteroid is and identify what some key features including but not limited to grain size, space weathering, and albedo. (DeMeo et al., 2015)

Asteroids can traditionally be classed into three primary groups: S-Complex, C- Complex, and X-Complex. There are also outliers to these three classifications. S- Complex asteroids are categorized together for a spectral signature that suggests that they are composed of silicates. C-Complex asteroids were named such based on their similar- ities with carbonaceous chondrites meteorites. X-Complex asteroids, on the other hand, categorize a wide range of objects that have a similar and subtle spectral signature while not necessarily having similar compositions. (DeMeo et al., 2015)

In terms of the threat to Earth, some of the more important characteristics are the asteroid’s density, volume, porosity, coherence, surface features, and geometry. Using these parameters it is possible to model the asteroid and the required energy to mitigate against it. (Barbee, 2005)

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The density and volume define the overall geometrical dimensions and mass of the object. These two parameters can be used to create a rudimentary point mass model of an asteroid or other object (as was implemented in this research).

The porosity defines the proportion of voids that exist within the asteroid’s internal structure, and the coherence defines whether the structure is a single coherent object or possibly made up of multiple smaller objects. Both of these parameters have an influence on the strength, stress propagation, and fracture mechanics of the asteroid structure, which plays an important role in the selection of a mitigation method.

An asteroid’s surface features include evidence of cratering, regolith composition and albedo, all of which can be used to pinpoint potential target areas on the surface for mitigation efforts or scientific exploration.

Near-Earth Comets

A comet (or a cometary nucleus) is a body formed in the outer planets region (or beyond) containing a significant fraction of volatiles in the form of ices and capable of developing a coma if its orbit brings it close enough to the Sun. (Weissman et al., 2002)

Although more modern classification systems have been proposed, the traditional method classifies comets based on their orbital period, specifically whether the orbital period is over or under 200 years (Levison, 1996). Based on JPL’s definitions of NECs, only short period comets (orbital period less than 200 years) are considered to be Near- Earth Comets. (Jet Propulsion Laboratory, 2018c)

Based on the constituents of the sublimated nucleus in the coma, it was found that chemical compositions of comets are relatively similar to each other, the main difference are the comparative sublimation rates. Thus, two cometary classes (‘typical’ or

‘depleted’) have been identified based on the normalized rate of production of radicals.

(A’Hearn et al., 1995)

Near-Earth Comets (NECs) are expected to constitute roughly 1% of the risk of an earth impact (Chapman, 2004). This has made them the secondary focus relative to NEAs

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for Planetary Defense.

Potentially Hazardous Objects

Potentially Hazardous Objects (PHOs) are NEOs whose Minimum Orbit Intersection Dis- tance (MOID) relative to the Earth is less than or equal to 0.05 AU, and whose absolute magnitude (H) is less than or equal to 22.0. The only other difference relative to NEOs is the amount of attention given to studying these objects in their orbits.

2.2.2 Detection

The ability to detect NEOs is of crucial importance for several reasons: it allows us to understand what a realistic impact risk might be, it helps us understand our solar system and universe better, and it also helps improve our trajectory estimation technology and build a database for potential NEO rendezvous and/or intercept missions.

As previously mentioned, during the 1990s there was a push towards detecting 90%

of all NEOs with a diameter larger than 1.0 km. This effort has taken multiple extended duration NEO surveys such as ATLAS (Asteroid Terrestrial-impact Last Alert System), the Catalina Sky Survey (CSS), the LINEAR (Lincoln Near-Earth Asteroid Research), LONEOS (Lowell Observatory Near-Earth-Object Search), NEAT (Near-Earth Asteroid Tracking), NEOWISE (Near-Earth Object Wide-Field Infrared Survey Explorer), Pans- STARRS1 (Panoramic Survey Telescope and Rapid Response System), and the Space- watch project in the United States. Internationally, NEO search efforts include the Ar- magh Observatory, the Japanese Spaceguard Association (JSGA), NEODyS (Near-Earth Object Dynamics Site), NEOSSat (Near-Earth Object Surveillance Satellite), and the near-future SSA-NEO System. New programs will most likely continue to be established around the planet, improving the capabilities of SpaceGuard Survey and the odds of detecting objects prior to impact or a close approach.

Most of these search surveys employ ground based approaches to monitor the skies in the visible light and infra-red spectra. Some of the efforts have involved space-based tele-

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scopes. It is likely that the future will see more space-based telescopes for their improved resolution and lack of an electromagnetic spectrum attenuating atmosphere.

As of September 18, 2018, nearly 20,000 NEAs have been discovered (as shown in Figure 2.6). Based on the absolute magnitude of these discovered asteroids, an estimate of the diameter can be made. Of the asteroids discovered, 894 are larger than 1.0 km in diameter, and 8,326 are larger than 0.14 km in diameter. It is estimated that the population size for asteroids with diameters larger than 1.0 km is 1,227⁺¹⁷⁰₉₀ (Stuart, 2001) or 990 ± 20 (Harris and DAbramo, 2015). A histogram of the estimated diameters for the NEAs discovered is shown in Figure 2.7.

Figure 2.8 presents a comparison of the number of asteroids discovered relative to the estimated population size as a function of absolute magnitude (H). It can be clearly seen that a larger proportion of the larger asteroids have been discovered.

2.2.3 Conclusion

Knowledge of the NEO population and representative properties is useful for calculating the potential risks that they may cause on the planetary surface in the event that an impact occurs. From a Planetary Defense perspective, this knowledge also allows for narrowing down the list of mitigation strategies and methods to be further developed.

Chapman refers to objects larger than 100.0 km in diameter as having the potential to be ‘extremely destructive’ (Chapman, 2004). The ability to detect and proactively mitigate the extent of the consequences of a potential impact is important for these objects, which the Spaceguard initiative has enabled.

While smaller diameter objects can have significant, localized consequences but are more difficult to detect. There was no warning prior to the Chelyabinsk impact in 2013 as none of the surveys had detected it. Many more asteroids make undetected close approaches with the Earth.

The search for Near-Earth Objects is still incomplete; it is in the best interest of the Planetary Defense community and the stakeholders of a potential impact to continue sur-

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Discovery Date

Cumulative Number Discovered

https://cneos.jpl.nasa.gov/stats/ Alan Chamberlin (JPL/Caltech)

Near-Earth Asteroids Discovered

Most recent discovery: 2018-Sep-17

All 140m+

1km+

1980 1990 2000 2010

0 5 000 10 000 15 000 20 000

Figure 2.6: Discoveries of Near Earth Asteroids since the 1980s (as of September 18, 2018). (Jet Propulsion Laboratory, 2018a)

Estimated Diameter (m)

Total Discovered

https://cneos.jpl.nasa.gov/stats/ Alan Chamberlin (JPL/Caltech)

Near-Earth Asteroids Discovered

Total per Size Bin (as of 2018-Sep-18)

3 683

5 421

4 658

4 055

894

0-30 30-100 100-300 300-1000 1000+

0 1 000 2 000 3 000 4 000 5 000 6 000

Figure 2.7: Estimated diameters of the NEAs that have been discovered (as of September 18, 2018). (Jet Propulsion Laboratory, 2018b)

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Figure 2.8: Comparison between the NEA population estimate and the number of NEAs discovered (as of August 2014) by their absolute magnitude (and diameter). (Harris and DAbramo, 2015)

veying the skies for potentially hazardous asteroids and comets, as well as developing more effective and less costly technologies capable of detecting smaller diameter NEOs.

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2.3 Impact Consequences

It is important to understand and be capable of predicting what the consequences of an impact could be. This information is vital for informing the appropriate decision analysis framework that would result in a selected mitigation strategy. The decision metrics might vary, however, a good decision might result in a strategy that maximizes the probability of success of the enacted mitigation mission while also minimizing the consequences.

This section will present a few significant impacts in history, provide an overview of the theoretical consequences and impact mechanisms. Additionally, the impact risk scales that are used to communicate threat levels related to particular NEOs will be presented.

2.3.1 Theoretical Consequences

Over the Earth’s existence, it is likely to have been impacted by dozens of K-T level (if not more consequential) celestial bodies, resulting in multiple mass extinctions. Chap- man argues that NEO or other impacts with the Earth are the most likely cause of global extinction level events for two primary reasons. (Chapman, 2004)

The first is that the environmental effects that arise as a consequence of an impact occur on a time scale too short for life to have the opportunity to evolve or migrate.

The second reason is simply the magnitude of the effects and their duration: the impact winter, caused by the darkening of the atmosphere from ejecta and other substances; long lasting firestorms, tsunamis, and earthquakes; pollution of the atmosphere and oceans;

and the potential for centuries of unfavorably altered climates. (Chapman, 2004) There are even theories describing the existence of a sub-glaciated Earth (Hoffman et al., 1998) that Chapman argues could have been a consequence of an impact, but also that an impact could have also assisted in warming the planet (from a sub-glaciated state). (Chapman, 2004)

In his paper, Chapman describes some scenarios of the potential consequences of impacts on humanity. Consider the scenario of a 1 · 10⁶MT impact and the near-immediate

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global cooling (lasting on the order of months) caused by impact ejecta and other matter in the atmosphere, along with some or all of the previously mentioned disastrous effects (firestorms, tsunamis, earthquakes, pollution). This situation would most likely lead to the global loss of that year’s harvest, and starvation and ultimately the collapse of the socio- economic structure that we live in, and the loss of many lives world-wide. (Chapman, 2004)

In the same paper, Chapman describes a more likely and more frequent airburst event similar to that of the Tunguska event in 1908, which would almost certainly have less severe consequences than the 1 · 10⁶ MT impact. As this impact would not have global catastrophic effects, its consequences would be highly dependent on location but the potential for loss of life still exists. The danger of these types of threats is that the hazardous object may go unnoticed by the NEO search programs due to their smaller size (Chap- man, 2004), so the entire event might come as a horrible surprise. Additionally, one of the associated risks of airbursts is the potential for them to be misinterpreted as hostile military activity. (Chapman, 2004, Boslough, 2015)

2.3.2 Impact Types

For the potential of an impact with the Earth’s surface, a threatening NEO will travel through the atmosphere and will deplete some or all of its mass or energy in doing so.

NEO impacts can thus be classified into two major categories: surface impacts and airburst.

A body traveling at hypervelocity in a gas phase medium will experience significant external forces acting on it and within it. Aerodynamic forces have a decelerating and thermal effect on the body; the bow shock dramatically compresses the atmospheric medium upstream of the body, which increases its temperature and ionizes the atmospheric particles. In addition to the drag energy loss, the body also loses kinetic energy through self-ablation and the creation of a tail due to the plasmic thermal radiation. These processes occur for any hypervelocity entry of an atmosphere, but the magnitude of these

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effects is dependent on the atmospheric conditions. (Boslough, 2015)

With a reduction in altitude there is an increase in the atmospheric density and pres- sure, leading to increased surface stresses on the body which can cause it to deform and fragment. Due to the rate of radiative heat transfer from the plasma to the body being faster than the vapor expansion rate, internal pressures can increase rapidly. This, in addition to internally generated shock waves, can lead to an explosion as the high pressures expand outwards. This is what is known as an ‘airburst’. (Boslough, 2015)

Whether the body has entirely been vaporized on atmospheric entry or it is still a surface impact threat depends highly on the dimensions and properties of the body (which define its integrity and susceptibility to explosive fragmentation) and its entry trajectory (which defines the amount of atmosphere it will travel through). (Boslough, 2015)

With airbursts defined above, a land impact occurs if and when a coherent body pass- ing through the atmosphere results in a collision with a terrestrial surface. Analogously, an ocean impact is one which results in a collision with an aquatic surface.

2.3.3 Notable Impacts in History

Of the many impacts there have been to the Earth throughout the ages, a few notable ones are the K-T extinction event impact (approximately 65 million years ago), the Tun- guska airburst (1908), the Comet Shoemaker-Levy impact (1993) and the Chelyabinsk airburst (2013). The consequences of these impacts range from somewhat destructive but no known human casualties to long-lasting atmospheric consequences, or to catastrophic destruction and the extinction of many species.

K-T Extinction Event Impact

The K-T extinction event 65 million years ago is likely to have been caused by a NEO, whose diameter was 10±4 km and impact energy estimated to be equivalent to 10⁸mega-

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tons of TNT.¹(Alvarez et al., 1980)

The K-T asteroid struck the Earth’s surface near the Yucat´an peninsula and created what is known today as the Chicxulub crater. The asteroid had significant effects on biological life; the amount of particulate shot into the sky would have reduced the solar radiation available for photosynthesis, leading to the collapse of major land- and ocean- based food chains. While the vegetation would eventually regenerate from seedlings or root structures, most of the animal life forms directly and indirectly dependent on the flora would not have survived. (Alvarez et al., 1980)

Shown previously in Figure 2.2 is a depiction of what this impact event might have looked like shortly after collision. (Davis, n.d.)

The Tunguska Impact

The Tunguska airburst event occurred on June 30, 1908, over the Central Siberian Plateau.

Recent scientific analyses claim that the most likely cause for this event is either a 50 to 60 m diameter asteroid or a 80 to 100 m diameter comet. (Napier and Asher, 2009)

The energy of the explosion, although uncertain, has been estimated to be as little as 3 megatons (Napier and Asher, 2009) or as energetic as 15 megatons of TNT²(Lyne et al., 1998). The energy of the explosion was enough to destroy a 2,000 square km region of Russian coniferous forests. The localized devastation of such an event over a more populated area would be significant. (Napier and Asher, 2009)

Comet Shoemaker-Levy 9 Impact

The airburst impact of Comet Shoemaker-Levy 9 with Jupiter occurred between July 16 and 22, 1994, as the fragments of the comet entered the Jovian atmosphere. It has been estimated that the total impact energy of all 21 fragments of the Shoemaker-Levy 9 comet

1Referring back to Section 2.1, the K-T extinction event impact would be approximately 5,000 times more energetic than that if Asteroid 1989FC had collided with the Earth.

2The Tunguska event would be 1,300 times less energetic than an Earth-Asteroid 1989FC collision.

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Figure 2.9: A representation of the Tunguska airburst event. (Davis, 2008)

imparted an energy equivalent to 300 · 10³ megatons of TNT ³ and the probable initial diameter of a coherent comet was of 1.4 km. (Crawford, 1997)

The effects the comet had on Jupiter were significant. Fireballs and plumes were witnessed on a shorter time scale, but the comet had long term effects on the composition and dynamics of the atmosphere. (Crawford, 1997, Levy, 1998). As devastating as this impact was, it was a rare opportunity to study Jupiter, the Jovian atmosphere and planetesimal airburst mechanics on a scale that is still unparalleled today (Boslough, 2015), as well as being a good opportunity for the scientific community to learn how to communicate and engage with a global public (Levy, 1998).

3Alternately, the SL-9 event with Jupiter would only be 15 times more energetic than an Earth-Asteroid 1989FC collision.

Analysis of Proportional Navigation Guidance Algorithms in the Context of a Near-Earth Object Intercept Mission

Guidance Algorithms in the Context of a Near-Earth Object Intercept Mission

Abstract

Contents

List of Figures

List of Tables

List of Abbreviations

Acknowledgements

Chapter 1 Introduction

Chapter 2

Literature Review