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18th Space Generation Congress
70th International Astronautical Congress
Move an Asteroid Competition 2019 Page 1 of 10
Move an Asteroid Competition 2019
Asteroid Control through Surface Restructuring
Manfred Ehresmanna,*
a Institute of Space Systems, University of Stuttgart, Pfaffenwaldring 29, 70569 Stuttgart, Germany,
ehresmann@irs.uni-stuttgart.de
* Corresponding Author
Abstract
A novel concept of asteroid orbit control by restructuring asteroid surfaces to manipulate albedo and respective
radiation pressure effects is introduced. The method itself is propellant less allowing for prolonged operation and
permitting adaption and even reversing introduced reflection effects. Microscopic restructuring of asteroid surface
material allows for the manipulation of reflective properties, which can be exploited for influencing orbit and attitude
parameters. Asymmetric radiation pressures are well known for their ability to change the orbit of an asteroid through
the Yarkovsky effect or rotational parameters by the YORP effect. In the simplest form albedo manipulation of an
asteroid with a solid surface can be achieved with a single spacecraft mission. This spacecraft will locally focus energy
from a very low (pseudo-)orbit onto the asteroids surface. The candidates for utilisation are CO2 laser systems. First,
conventionally laser engravers to brighten mineralic and metallic surfaces. Second, CO2 laser cleaning systems often
used to remove silicate residue of industrial processes.
It is calculated that an asteroid with a high albedo will experience significantly less Yarkovsky effect, resulting in
reduced orbit drift and improved future predictability.
Laser technology can further be exploited to create surface structures that represent an asymmetric saw tooth
pattern (i.e. repeating sharp right triangles) by using femto second laser pulses or by an angled focal point. This
asymmetric surface pattern leads to an angular dependent reflectivity, which can be exploited to create radiation
pressure differences. When properly applied, countering spin-rate changes and rotation axis drift of the YORP effect
is possible. Preliminary analysis indicates feasibility for probes equipped for laser treatment of Near Earth Objects.
Keywords: Asteroid, Planetary defense, Laser application, Yarkovsky effect
Nomenclature
A – area
A – albedo
– asteroid physical parameter
a – acceleration
a – semi-major axis
– vacuum light speed
– effective (exhaust) velocity
– thermal inertia
– obliquity
d – model exponent
D – diameter
E – energy
– emissivity
F – force
– thermal parameter
G – gravity constant
– solar constant
– mass
– mass flow
n – multiplication factor
P – power
P – rotation period
p – semi latus rectum
– mass density
r – (radial) distance
– mean distance of Earth
– projected area of sphere
– Stefan-Boltzmann constant
t – time
– sub solar temperature
v – velocity
– standard radiation force factor
Acronyms/Abbreviations
AU – Astronomical Unit
IRS – Institute of Space Systems
LASER – Light Amplification by Stimulated
Emission of Radiation
NASA – National Aeronautics and Space
Administration
NEO – Near Earth-Object
US – United States
YORP – Yarkovsky-O’Keefe-Radzievskii-
Paddack
1. Introduction
Planetary defence is literally a vital challenge for
humankind. An impact with an asteroid of sufficient size
has the capability for civilisation or world ending
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scenarios. Destruction of an impact event is mainly
caused by shock of wind, pressure, thermal radiation or
tsunamis [1]. The primary hazards capable to trigger
secondary effects like large-scale fires or secondary
earthquakes, hindering emergency response efforts. The
scale of destruction can very likely be beyond any
national or even international relief efforts.
The current strategy for the threat of asteroids is therefore
not focused on disaster response but on impact
mitigation. The US ‘Nation near-Earth Object
preparedness strategy and action plan’ summarizes five
goals [2]. Four of these goals consider mitigation of an
impact through enhanced observation, prediction, data
exchange and development of appropriate mitigation and
deflection technologies. While only the fifth goal
considers the development and training with emergency
protocols for minimizing direct harm.
The key to impact mitigation are technologies that enable
the redirection or deflection of a large asteroid.
Realistically the timespan for operating such a
technology can be considered to be lengthy in
application. As NASA states that the undertaking of an
intercept mission, will require at least five years of
preparation [3].
The NASA report “Near-Earth Object Survey and
Deflection Analysis of Alternatives” [4] make the
following assessments:
Nuclear standoff explosions are most likely highly
effective in altering the trajectory and properties of a
targeted - potentially harmful - asteroid but carry high
development and operations risks. Especially the risk of
fracturing an asteroid can lead to a hazardous cloud of
asteroids fragments, which more likely of hitting Earth.
Non-nuclear kinetic impactors are mature, but have a
limited use-case against single small, solid asteroids. The
alternative are “slow push” techniques, which are
generally less mature and require long preparation times.
1.1. Slow Push Asteroid deflection techniques
A few examples of slow push techniques are given and
briefly discussed:
1. The gravity tractor [5]:
The gravity interaction between an actively
propelled spacecraft and the target asteroid is
exploited for trajectory alteration. The applied
force can directly be calculated with Newton’s
law of universal gravitation [6]:
, (1)
Indicated by the universal gravitational constant
of [7], the
resulting net force F between the two attracting
masses and, with the distance, will be
very small for small celestial bodies and an
orbiting space probe.
In principle, any probe with active propulsion
can be utilized as gravity tractor and should be
utilized in combination with other concepts
given in the following.
2. Ion beam shepherd [8,9]:
An asteroid is exposed to a quasi-neutral
plasma, which is then pushed into a desired
direction. The generated force F upon the
asteroid can then be calculated by:
, (2)
Where the mass flow and the effective
velocity of the plasma and the coefficient
for adjusting between the cases of full
absorption and total reflection of
the impinging plasma particles.
Conventionally, electric propulsion systems
require large power plants and have a very low
mass flow producing very low thrust. While
system with high mass flow have very high
propellant consumption. Thus, applicability is
very limited.
3. Laser ablation [10]:
Nearly indefinite operation can be achieved by
using a high-power laser or other directed
energy beam source to locally heat asteroid
surface material above 3000 K for vaporization.
Thus, an artificial thruster operated with ablated
asteroid material is effectively created. The
thrust can be calculated by Eqn. 2 with n=1,
while the estimation of the thrust vector can be
challenging, as laser ablation is not guaranteed
to be uniform. Overall energy demand is high as
mineral has to be heated above the required
vaporization temperature.
4. White Painting [11,12]:
Changing the albedo of an asteroid allows for
momentum exchange by photons of the sun.
Thus, it has been proposed to whiten an asteroid
through the application of white powders [11] or
paint balls [12]. The main challenge here is, that
the whitening agent has to be carried to the
asteroid, budgeting the mass of a spacecraft.
Thus, these concepts are likely to be bound for
a single attempt due to mass constraints of the
asteroid deflection space probe. The application
of the agent might lead to stir up of dark surface
dusts potentially negating or reducing the
albedo enhancing effect.
In this paper, another concept is introduced
combining the use of lasers for albedo changes.
The use of a laser system does not require
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additional mass that is consumed during
operation. While laser operation can be quasi
indefinite, allowing for more operational
flexibility in terms of repeated irradiation and
adapted patterns of surface (albedo)
manipulation.
The power demand for such a system will be
well below the power demand of a laser ablation
system as no vaporization is required.
2. Assessment of radiation pressure effects
Photons have a mass through the fact that they store
energy and can therefore exchange momentum when
emitted, absorbed or reflected by or from an object.
Although the generated force by these effects is small, it
is a continuous force on celestial bodies perturbing their
orbits.
The effect can be quickly estimated by considering the
mass-energy equivalence:
(3)
and dividing by the time t to obtain a formulation for the
radiation power yields:
, (4)
which can be rearranged with to obtain
(5)
When considering a single watt of absorbed radiation
power the resulting force is and
for full reflection .
When considering full absorption on a square meter
material and the solar constant of is
given by Eqn. 5 the resulting force can be calculated. The
result is with a vector radially outward
from the Sun, fully agreeing with literature values using
alternative derivations [13].
Asteroid trajectories are affected by radiation pressure of
different origin. These effects and relevant equations are
to be discussed in the following.
2.1. Solar radiation pressure
The solar radiation pressure results in a respective
acceleration acting upon an asteroid. This force is
calculated by the following equation [14, 15]:
. (6)
Here the effectively radiated area , the mass of the
asteroid and the albedo of the asteroid are
Figure 1: Radiation acceleration acting on asteroid
Bennu in dependence of the distance from the sun
for cases of varying albedo.
Figure 2: Radiation force acting on asteroid Bennu
in dependence of the distance of the sun for cases of
varying albedo.
Figure 3: Relative radiation force acting on asteroid
Bennu in dependence of the distance of the sun for
cases of varying albedo. Comparing the force as a
percentage difference from the force acting on
Bennu with natural albedo of 0.017.
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required as physical parameters. While the total received
power is estimated through the distance square law, that
considers the solar constant, the mean distance of
Earth to the sun to the actual distance of the asteroid.
Table 1. Selected parameters of 101955 Bennu relevant
for the estimation of solar radiation pressure [14].
101955 Bennu
/ -
0.017
/ kg
/ m
510
/ AU
0.89674
/ AU
/ AU
1.126
* AU = Astronomical Unit = 149597900 km
2.1.1. Case Study: Asteroid 101955 Bennu
To evaluate the effect of albedo change in the asteroid
Bennu the parameters in Table 1 are used.
The results are given in Fig. 1. to Fig. 3. The total solar
radiation pressure is small, as it is on the order of
m/s², while the total force acting on the asteroid is
estimated at approximately 1 N. Changing the albedo
from the initial 0.017 of Bennu allows for allows for a
maximum increase of generated force by 41.2 % at an
albedo of 95 % as shown in Fig. 3.
Simulations indicate that a maximum displacement of
18.2 km and reduction in the semi-major axis of 34 m is
produced by this [14]. When naively assuming a linear
correlation between acceleration and displacement a
maximum position displacement of 25.7 km and a change
of 48.11 m in the semi-major axis is achieved through
solar radiation pressure, when increasing albedo. Thus,
the overall effect in trajectory drift by solar radiation
pressure in relation to albedo can be considered small.
2.2. Yarkovsky-effect
The Yarkovsky-effect describes asymmetric radiation of
energy by a heated rotating body. A hot side emits more
heat energy than a cold side; the total forces can be
calculated by Eqn. 5, when respective emitted radiation
powers are known.
For asteroids with spin-axis obliquity of near ±180° to the
orbital plane, the hot side is rotated either into the
direction of travel or behind it. Exerting a net force in
prograde or retrograde direction, which is capable to
significantly alter trajectories over time.
For simplicity reasons only a transversal Yarkovsky
effect is considered in this paper, based on the model of
[14]. Tranversal Yarkovsky means that the force is
generated in or against direction of travel.
For computing the transversal Yarkovsky acceleration,
the following expression used [17]:
Figure 5: Yarkovsky force acting transversal on
asteroid Bennu in dependence of the distance from
the sun for cases of varying albedo.
Figure 6: Relative Yarkovsky force acting
transversal on asteroid Bennu in dependence of the
distance of the sun for cases of varying albedo.
Comparing the force as a percentage difference from
the force acting on Bennu with natural albedo of
0.017.
Figure 4: Yarkovsky acceleration acting transversal
on asteroid Bennu in dependence of the distance
from the sun for cases of varying albedo.
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, (7)
The constant is utilized, which is 2-3 for most
NEOs [18], resembling now the distance square law, with
the reference distance of Earth and the current distance
of the asteroid.
The asteroid specific parameter is correlated to other
physical parameters by [18, 19]:
, (8)
where is the asteroid bond albedo, which is the sum of
reflection of all electromagnetic waves. The obliquity
is the angle between the orbital plane normal axis and the
rotation axis.
The standard radiation force factor at one astronomical
unit is given by:
, (9)
where the solar constant at at 1 AU is correlated to the
asteroid density, the mean asteroid diameter and the
vacuum light speed.
The function of the thermal parameter is simply a product
of linear heat theory and given as:
. (10)
The thermal parameter itself is defined as:
. (11)
With the thermal emissivity , the Stefan-Boltzmann
constant , the thermal inertia and the rotational period
of the asteroid .
The remaining parameter in Eqn. 11 is the subsolar
Temperature defined as:
, (12)
with already defined parameters except for the semi latus
rectum p, given by:
, (13)
with the orbital eccentricity of the asteroid.
Table 2. Selected parameters of 101955 Bennu relevant
for the estimation of the Yarkovsky effect. [14]
101955 Bennu
/ -
2
/ °
/ kg/m³
1260
/ -
0.9
/ -
/ J
310
P / h
4.29746
2.2.1. Case Study: Asteroid 101955 Bennu
The data of Table 1 and Table 2 is used to assess the
effects on asteroid Bennu with varying Albedo. It is
assumed that a change in bond albedo does not affect
the emissivity . The results of the respective transversal
Yarkovsky acceleration, force and percentage deviation
from the natural albedo are given in Fig. 4-6.
The total effect of force or acceleration shown in Fig. 4
and 5 vary by a factor of 2.28, achieving largest value
closes to the sun and lowest values farthest from the sun.
The total Yarkovsky acceleration and force of the
asteroid Bennu is smaller by two orders of magnitude, as
for the case of natural bond albedo of 0.017 the
acceleration is ~ and ~ 0.06 N.
This might appear to be a lower order effect than solar
radiation pressure, but the transversal nature of the
Yarkovsky effect does perturb the asteroid trajectory
more severely.
Literature values for a 12-year propagation indicate that
Yarkovsky forces produce a maximum displacement
position of 185.20 km and a change in semi-major axis
of 3.485 km [14]. Which is significantly more than the
18.2 km displacement and 0.034 change in semi-major
axis for solar radiation pressure effects alone [14].
Figure 6 clearly shows that Yarkovsky forces and albedo
have direct linear correlation, indicating that an increase
in Albedo will at least linearly, more likely quadratic,
reduce the perturbations caused of the Yarkovsky effect.
2.3. YORP-effect
The YORP-effect is a second order anisotropic radiation
emission effect; it can be caused through asymmetric
surface geometries or material properties [20]. The
emission of a photon with a path deviating from the
centre of gravity of the celestial body, causes either a
torque or a force due to the momentum it carries with
itself.
This change is small, as for example the observation of
the asteroid 54509 YORP yielded that the spin rate will
double in 600,000 years [21]. This drift varies the spin
rate parameter in Eqn. 11, ultimately changing the
magnitude of the resulting Yarkovsky effect. The other
perturbation produced by the YORP-effect is the spin-
axis orientation changes by produced torques, changing
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the obliquity parameter in Eqn. 8. Making the order of
magnitude and direction of the occurring Yarkovsky
effect a prediction uncertainty. Modelling the magnitude
of the YORP effect is unfortunately beyond the scope of
this work.
Selective albedo adaption of the asteroid surface is likely
to mitigate the YORP effect, as here only minor changes
of local albedo is required for more uniform radiation.
2.4. Conclusions on radiation effects.
The major radiation based orbit perturbation for most
asteroids is the Yarkovsky effect. The considered
example asteroid 101955 Bennu is representative of most
asteroids with overall low bond albedo. Nonetheless,
similar magnitudes of orbit perturbations are expected by
other NEOs.
A reduction of the Yarkovsky effect by increasing the
asteroid albedo allows for reducing orbit perturbation and
improved predictability.
Localized albedo increase has the potential to minimize
the YORP effect and therefore the drift of the Yarkovsky
effect.
2.5. Potential mission scenario
A potential mission scenario with the aim of asteroid
orbit stabilisation and potential deflection will follow two
main operational phases:
1. Minimize YORP effect
a. Selectively albedo increase irregular
surface geometries to obtain a quasi-
uniform radiation pattern
b. Use incidence angle dependent reflectivity
adaption by surface restructuring
2. Minimize Yarkovsky effect
a. Increase overall global albedo uniformly
An additional benefit of a mission scenario that overall
increases bond albedo is the enhancement of remote
observation of the treated asteroid.
3. Technology Assessment
The technology for manipulating asteroid albedo does
already exist in multiple forms, while the quantitative
analysis for this particular is not yet fully developed.
Thus, indications for applicability and estimates for
capabilities will be given in the following.
First, laser etching is commercially utilized technology to
etch and mark a vast multitude of materials [22, 23]. Here
the laser radiation causes the etched material to respond
in a way to molecularly restructure its surface in a way
that the incoming radiation is scattered more efficiently.
Laser etching allows for effectively brightening the
targeted material and increasing at least its geometric
albedo, i.e. the diffuse reflection of incoming visible
light.
The company Trotec gives the following list of etchable
minerals: Granite, Marble, Slate, Basalt, Salt Crystals,
Pebbles, Garden Stones, Stone Tiles, Natural Stone,
Ceramic / Porcelain [22]. These materials can be etched,
i.e. brightened, with the use of CO2 laser with output
power of 12-120 W [23]. The list of laser treatable
minerals can be extended by the large mineral group of
silicates, as CO2 lasers are used for laser cleaning of
silicates [24, 25], indicating a strong susceptibility of this
mineral group to CO2 laser treatment.
It is further stated that:
“in general dark, regular stones are very well suited for
engraving […]. The surface of the stones does not have
to be polished, natural stone structures are also well-
suited to laser processing”. [26]
A sample of laser engraved slate is given in Fig. 7. Due
to the lack of direct samples public available online
imagery is used to albedo change estimation [22]. By
using commercially available photo editing software it
can be assessed that the brightness and therefore
geometric albedo can be increased from at least 34 % up
to 75 %, indicating a significant change in geometric
albedo, which has to increase the bond albedo likewise.
If a new bond albedo of 50 % is assumed it can be
compared to the data of relative Yarkovsky forces shown
in Fig. 6. The result is that a relative reduction of
Yarkovsky forces of 60 % is achieved; leading to
significantly reduced orbital drift.
The second interesting technology is the utilisation of
femto second laser pulses to generate micro structures
that are capable to produce anisotropic reflectivity
properties [27]. A simple geometric example of such a
structure is given in Fig. 8.
Figure 7: Sample of laser etched slate [22]. Significant
change in albedo is evident, while digital measurement
yield a maximum difference of 34 % to 75 % in
brightness.
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Here it is shown that anisotropic reflective geometric
structures can be designed, where the angle of specular
reflection is different for differing incidence angles of
incoming radiation.
The master thesis given in [27] was able to produce such
microstructures with the use of femto second laser pulses
and appropriate irradiation strategies as seen in Fig. 9.
Such microstructures can be produced at least for the
materials aluminium and titanium [27]. The brittle nature
of minerals and behaviour of minerals when under the
influence of laser cleaning devices indicates that
microscopic chipping processes are likely to be achieved
with femto second laser pulses as well.
Another key point of this technique is the reversibility of
the applied surface effects, as by using the correct pulsing
and overlap strategies of multiple passes, repeated
whitening and darkening of surfaces is possible [27].
An extreme application of using incidence angle
dependent reflectivity is given in Fig. 10. Here a
maximum reflectivity or albedo is assumed for structures
moving into the direction of the viewer, while structures
moving away from the viewer have minimal reflectivity.
This is an intended YORP effect, as this asymmetric
reflectivity is a torque inducing asymmetry in radiation
pressure. Over time, the rotation of the model object
would slow down, stop and reverse – although such
processes can take several hundreds to thousand years
[21].
For a practical application, it can be expected that only
localized micro restructuring is required to counter the
YORP effect, as YORP torques and forces are caused by
random structures and irregularities and are in total small.
3.1. Feasibility Analysis
For a preliminary feasibility assessment the asteroid
Bennu is used again as a representative example, with a
diameter of , we can estimate a surface area
of for a spherical shape.
Thus, an additional 20 % margin is added to obtain the
total area that is to be laser treated to be
.
Public sources indicate that commercially available CO2
Laser can be operated for more than 50,000 h [25],
allowing cumulative system operation for at least 5.7
years.
To allow for sufficient margin, the operative mission
time is arbitrarily set to 3 years. Thus, the requirement for
laser treating velocity per area becomes
. Such a velocity might achieved by adapting
currently available systems, for example the Trotec
Speedy series is qualified for movement speeds of up to
, when operating a CO2 laser of at least
12 to 120 W [23]. As precision is not required for this
application, a maximum diameter focal point or wide
beam concept for effective engraving is desired.
The required beam width is simply calculated by
dividing the area treatment speed by the movement speed
and yields a required etching laser beam width of 2.8 mm
to achieve the mission within the given 3-year range.
Realizing such a laser is possible, when considering the
wide beam laser cleaning systems with focal beams of
100 - 120 mm width that operate at a maximum of 1000
W of laser power [25].
A realistic estimate for the system can be produced by
considering the minimal resolution of a speedy CO2
engraving laser of 125 dpi [23]. This corresponds to a
pixel size or beam width of 0.2 mm.
Figure 10: Example schematic of anisotropic
reflectivity on a sphere to reduce rotation speed. Light
source from the point of viewer. High reflectivity for
incidence angle of 180° and low reflectivity for
incidence angle of -180°
Figure 8: Example of an anisotropic reflection
geometry [27].
Figure 9: Example of laser treated aluminium, with
anisotropic reflection microstructure [27].
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This laser beam diameter requires the stacking of 14
laser units to generate the respective line width. A single
unit requiring each [23]. This
results in total laser output power of the modified system
to be .
When considering a highly efficient system a CO2
laser can have an efficiency of up to 20 % [29]. Thus, the
resulting electric power system demand is 840 - 8400 W,
while 672 - 6720 W of excess heat is generated, which
has to be ultimately radiated away. Although these
numbers are significant, they do indicate an overall
technical feasibility.
A power demand for a worst-case assumption of 8.4
kW and a worst-case distance of the asteroid Bennu of
1.36 AU corresponds to an effective area of 9.2 m² of
solar arrays, when considering 30 % efficiency for
commercially available space grade photovoltaic cells
[30]. This a feasible size for a solar array of an
interplanetary probe. As a comparison, the Rosetta probe
features 64 m² of solar panels [31].
Auxiliary systems for assessing and controlling the
process should be based on the design of OSIRIS-Rex
mission [32].
The following instruments are required for the
success of the mission. A laser altimeter is required to
determine the distance to the surface and adjust the laser
focal beam accordingly. The bond albedo will be
assessed by a sensor suite that records reflectivity on
visible and infrared spectra as well as thermal emissions
and adjusts irradiation strategies accordingly.
4. Conclusions & Outlook
This paper discussed whether it is possible to control
an asteroid orbit by adjusting its albedo through surface
restructuring. For this, the dependency of radiation
driven orbit perturbations has been analysed. The
considered effects are the solar radiation pressure and the
Yarkovsky effect, while forces and accelerations for
differing bond albedos have been calculated and resulting
perturbations estimated. It was possible to show, that an
increase in bond albedo allows for a significant reduction
in orbit perturbation by the Yarkovsky effect, while a
moderate perturbation by increased solar radiation
pressure is generated.
Further, it was demonstrated that currently available
laser etching technology is capable to produce the desired
effect through the utilization of CO2 laser systems.
Sources indicate that laser etching technique is highly
likely to be applicable to asteroid minerals of various
nature.
An estimation was used to shown that it is possible
that the full surface of the asteroid Bennu could be laser
treated for albedo increase within 3 years of continuous
operation within conventional mission design
limitations. Faster mission times are possible; feasibility
is directly correlated to the available electric power.
For further assessment of the presented concept, the
following steps are recommended to further the maturity
of the technology:
1. Higher order orbit perturbation assessment
for a detailed quantitative analysis of orbit
changes through albedo changes.
2. Experimental testing of achievable albedo
change by laser etching of real or simulated
asteroid material.
3. System analysis of laser etching devices in
terms of mass, volume, heat, power and
cost budgets.
4. Development of a designated laser-etching
device for asteroid material for energy
efficient area wide surface etching.
5. Preparation of a respective
preparation/pathfinder mission.
5. Acknowledgement
The support of the interns Madlen Zipper and Jonathan
Kurth, who aided in literature research and the
implementation of relevant physical functions for the
system design, is greatly acknowledged.
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