Planet Disassembly
As has been pointed out by Freeman
Dyson and others, planets are not a particularly useful form for the
matter in the universe. The gravity imposes travel costs for people
or machines who would like to travel over a wider range than the planet
on which they originated. Perhaps the only benefit we may see in
gravity is that in sufficient quantity it causes the retention of an atmosphere
which allows the evolution of life. In the form of planets, a significant
majority of the matter is unavailable for useful purposes. Planets
sequester materials which may be valuable and useful in the construction
of machines or structures which have a concrete benefit to intelligent
pursuits.
It would be much better if the barriers to travel were reduced and heretofore
unusable matter were made available for the construction of biological
or non-biological machines. To achieve this result we must discuss
the disassembly or dismantlement of the planets.
One of the earliest references to this idea is the paper Search
for Artificial Stellar Sources of Infrared Radiation by Freeman
Dyson in Science in 1960.
In that paper Dyson documented that the mass of Jupiter (2 x
1027 kg) could be disassembled and put to useful
purposes using the energy generated by the sun in 800 years (1044
ergs). The purpose of this discussion is to update the ideas promoted
by Dyson in light of more recent engineering concepts such as Solar Cells,
Solar Power Satellites, Mass Drivers and Nanotechnology.
The simplest calculations of the energy required to disassemble a planet
relate to the energy required to gravitationally disrupt the body by accelerating
each particle of matter to its escape velocity. This is the energy
required is known as the gravitational
binding energy and is given by the formula:
where G is Newton's Gravitational constant,
m is the mass of the planet, r
is the radius and U is the gravitational
binding energy. If we can develop a scheme to deliver the energy, U,
to each particle of the planet we will have effectively disassembled (or
destroyed) it.
Planet Vaporization
Future technologies might produce giant reflectors to focus IR, visible
and UV photons produced by the sun onto the planet. Materials making
up the surface of solid planets have boiling points from 2500 to 3800oK.
Applying sufficient energy would heat the surface material of the planet
to the boiling point. If enough energy were applied, a significant
fraction of the gas molecules would achieve escape velocity and the planet
would literally evaporate. The efficiencies of this process are high,
perhaps 90% of the energy released by the sun could be utilized in this
process. However, the resulting gas would have to be captured and
put through successive cooling phases in order to separate out useful materials.
Since, these methods are not typically used in materials processing due
to the high energy costs, there is little research on the mass requirements
and techniques that could utilize this process. As a result it is
difficult to make estimates of the time scales involved.
Mechanical Disassembly
An alternate approach is to convert solar energy to electricity and use
the electricity to do mechanical disassembly of the planet. Since
this approach has precedents in our current material processing industries,
e.g. the aluminium and steel industries, there is much more information
available on the energy costs and production methods.
The Sun produces 3.82x1026 W of energy. The highest
efficiency solar cells can achieve a conversion efficiency of 30%.
Solar cells currently in mass production have lower efficiencies in the
12-20% range. Assuming high efficiency conversion of sunlight to electricity,
the energy available for the disassembly of planets in our solar system
would be ~1.15*1026 W. Table 1
provides a list of bodies in the solar system, their gravitational binding
energy and disassembly times using estimated available power.
Table 1. Gravitational Binding
Energy and Dissassembly Time
Body
|
Mass
|
Radius
|
Gravitational
Binding Energy
|
Total Solar Output
Disassembly Time |
(kg)
|
(km)
|
(W)
|
Mercury |
3.3 x 1023
|
2,440
|
1.80 x 1030
|
5 hours
|
Venus |
4.9 x 1024
|
6,052
|
1.58 x 1032
|
16 days
|
Earth |
5.9 x 1024
|
6,378
|
2.18 x 1032
|
22 days
|
Mars |
6.4 x 1023
|
3,397
|
4.90 x 1030
|
12 hours
|
Jupiter |
1.9 x 1027
|
71,492
|
2.04 x 1036
|
563 years*
|
Saturn |
5.7 x 1026
|
60,268
|
2.16 x 1035
|
60 years
|
Uranus |
8.7 x 1025
|
25,559
|
1.19 x 1034
|
3.3 years
|
Neptune |
1.0 x 1026
|
24,766
|
1.72 x 1034
|
8.2 years
|
Pluto |
1.3 x 1022
|
1,137
|
5.91 x 1027
|
2 minutes
|
Moon |
7.4 x 1022
|
1,738
|
1.25 x 1029
|
19 minutes
|
Asteroid (1km) |
1.6 x 1012
|
0.5
|
1.98 x 1011
|
<< 1 microsecond
|
It is worth noting that the 563 year
disassembly time for Jupiter, does not differ significantly from Dyson's
estimate
of 800 years.
The good news is that planet disassembly using available energy seems
feasible in reasonable time scales. Particularly important is the
observation that a total of only 12 years of available solar power is required
to push all of the matter out of the gravitational wells of all of the
planets and asteroids with the exception of Jupiter and Saturn. Less
than 100 years is required if we include Saturn but not Jupiter .
The bad news is that we do not have even a small fraction of the Sun's
power output at our disposal. We must develop an approach which would
make available a large amount of power if planet disassembly is to be a
realistic discussion.
Obviously we need to leverage our efforts to get us to the point where
we have a significant fraction of the solar power available for construction
work. There are two possible approaches to this, leverage with asteroid(s)
or leverage with Mercury. In either of these approaches the basic
job is to disassemble a smaller body to provide the surface area required
to collect a significantly larger amount of energy than is available to
the body itself.
Solar Collectors
Solar power converter systems (collectors) generally consist of solar concentrators
(either reflectors or lenses) and solar cells. This is because the
solar cell conversion efficiencies are achieved at solar flux concentrations
greater than 100x the normal Earth orbit solar flux levels. To get
the highest conversion efficiencies, the sunlight must be concentrated.
On Mercury the solar flux is very high (9214 W/m2) while
at the asteroid belt it is rather low (~ 200-500
W/m2). The choice of whether to use asteroids or Mercury
as a base for solar collection has significant effects on the architecture
of the solar collectors and solar cells. On Mercury a concentration
of ~10x would produce the highest power conversion efficiencies.
The high temperatures and radiation levels near Mercury would however require
significant attention to keeping the solar cells cool and shielding them
from excessive radiation. In contrast in the asteroid belt, solar
concentrations of 1000x might be required to produce the highest efficiencies.
Cooling and radiation on the other hand are much smaller problems in the
asteroid belt. Collectors on or near Mercury will have small reflectors
or concentrators and careful attention to the rejection of infrared radiation
and shielding from solar radiation. Collectors in the asteroid belt
will require very large reflectors or concentrators and have minimal cooling
and shielding requirements. Lacking specific designs, it is difficult
to say in which location the element availability best matches the solar
collector designs. We must assume that there should be material in
both locations in significant excess of the actual collector design requirements.
Since there are a variety of collector architectures it is distinctly possible
that their designs would be tailored to match the element availabilities
of the two locations.
Solar Collectors from Asteroids
The asteroid approach has some advantages. Asteroids may pass relatively
close to the Earth and so travel time to them may be minimal and the work
could be supported from Earth. Solar system evolutionary theory would
predict that because many asteroids evolved in the middle regions of the
solar system, they are likely to contain higher percentages of the lighter
elements such as carbon and aluminium compared with bodies formed in the
inner regions of the Solar System such as Mercury. This is reflected
in the lower density of asteroids, averaging 3.0 g/cm3
compared to Mercury's 5.43 g/cm3. The lighter elements
are the preferred materials for solar collector construction for reasons
of weight and strength. Asteroids have disadvantages as well.
The development of multiple asteroids may be required to provide all of
the material necessary for Sun-surrounding solar collectors. Significant
orbital corrections would be required to reposition solar collectors produced
from asteroid material in more optimal locations closer to the sun where
the solar power flux is greater. Orbital corrections usually require
the expenditure of mass which might be better utilized in the construction
of the collectors themselves.
Solar Collectors from Mercury
The Mercury approach has the key advantage of a very high solar flux.
So at least an order of magnitude less material is required for collectors
in an orbit near Mercury, compared with orbits near the asteroid belt for
the same amount of solar energy harvested. A disadvantage may be
that the heat and radiation levels as so high in the vicinity of Mercury
may shorten the life of the solar collectors. An orbit between Mercury
and Venus may be more suitable for longer lived solar collectors.
Even in an orbit near Venus, the solar flux (2660 W/m2) is still
much higher than the asteroid belt. The mass of Mercury is 3.3x
1023 kg, the estimated mass of the asteroids is
5.9 x 1021
kg, so even if the fraction of ideal elements for solar collectors is lower
in Mercury than it is in the asteroids, it provides much more material
to work with.
The basic strategy for mining operations would be relatively simple.
First deliver to Mercury a von Neumann automated factory (or nanoassembler
factory) which is designed to replicate itself. Available power is
used to process sufficient materials to replicate solar cells over much
of the surface of the planet. Mining machines then burrow into
the planet, cutting planetary materials into convenient blocks which are
delivered to rail guns which accelerate the materials into space at escape
velocity. The factories have to produce four basic machine types:
solar collectors, mining machines, transportation machines and rail guns.
Primitive forms of all of these machines have been previously designed
and built. Only large scale mining machines and rail guns remain
untested in space conditions. The requirement for transportation
machines could be minimized by positioning the rail guns at the bottom
of ever deepening craters and allowing the mining machines to cut away
blocks that fall down the slopes into the rail gun intakes.
The surface of Mercury could provide approximately ~3.4 x
1017 W of power, which would allow planet disassembly
in ~550,000 years. However, if the material blocks which are lifted
into space are reprocessed by space factories into large thin solar collectors,
an exponential growth in the amount of power available is possible.
If the power is delivered back to the planet and used to accelerate disassembly
operations then the time drops considerably. A fully efficient cycle
would allow the disassembly of Mercury in less than month! The factors
affecting the disassembly time the most would be the fraction of material
in the planet useful for collector construction, the solar collectors mass
per area (areal mass) and the transport time for the material to the final
collector positions.
Collector Composition
Table 2 details the composition of the Earth, some
reasonable adjustments for Mercury and an estimate of the quantity of materials
available.
Table 2. Composition
of Earth and Mercury
Element |
Earth's Mass % |
Mercury (est.) |
Crust
|
Core
|
Whole Planet |
Mass %
|
kg |
Oxygen (O) |
46.6%
|
5.18%
|
31.7%
|
25%
|
8.2 x 1022
|
Iron (Fe) |
5.00%
|
85.55%
|
32.0%
|
36%
|
1.2 x 1023
|
Magnesium (Mg) |
2.09%
|
0.35%
|
14.9%
|
14%
|
4.6 x 1022
|
Silicon (Si) |
27.7%
|
?
|
14.6%
|
16%
|
5.2 x 1022
|
Nickel (Ni) |
|
2.69%
|
1.7%
|
2%
|
6.6 x 1021
|
Calcium (Ca) |
3.63%
|
~0%
|
1.7%
|
2%
|
6.6 x 1021
|
Aluminium (Al) |
8.13%
|
~0%
|
1.4%
|
1%
|
3.3 x 1021
|
Sulfur (S) |
|
0.45%
|
0.9%
|
1.1%
|
3.6 x 1021
|
Chromium (Cr) |
|
0.41%
|
0.3%
|
0.5%
|
1.6 x 1021
|
Sodium (Na) |
2.83%
|
0.01%
|
0.2%
|
0.1%
|
3.3 x 1021
|
Manganese (Mn) |
0.10%
|
0.41%
|
0.2%
|
0.4%
|
1.3 x 1021
|
Phosphorus (P) |
0.12%
|
0.35%
|
0.1%
|
0.1%
|
3.3 x 1021
|
Cobolt (Co) |
|
0.22%
|
0.1%
|
0.2%
|
6.6 x 1021
|
Titanium (Ti) |
0.44%
|
0.08%
|
0.07%
|
0.2%
|
6.6 x 1021
|
Potassium (K) |
2.59%
|
0.02%
|
0.02%
|
0.01%
|
3.3 x 1020
|
Other nonmetals
(excluding nobel gases) |
0.01-0.0001% each
|
|
|
Other metals (nonradioactive) |
0.01-10-7% each
|
|
|
Source: Earth composition adapted from Kargel
& Lewis (1993)
A sphere surrounding the sun in Mercury's orbit has an area of 4.2x
1022 m2, while at the orbit of Venus it must
have an area of 1.5 x1023
m2. Mercury (at 7.8 kg/m2) and Venus (at 33
kg/m2) both provide sufficient structural material to
envision constructing structures in their respective orbits that would
be capable of gathering the entire energy output of the sun. Making use
of the most abundant materials, it would appear that the solar cells should
be constructed from hematite (Fe2O3) with a silicon
surface on the sun side. These structures could be reinforced with
sapphire (Al2O3) or diamond whiskers, or buckytubes.
Carbon constitutes 27% of the 5 x 1020
kg atmosphere of Venus. Mining operations using rotating sky hooks
with large scoops or upper atmosphere ram-jet mining ships could easily
provide ~1.4 x 1020
kg of carbon between the orbits of Mercury and Venus. Dismantlement
of Venus itself would be most efficient after first removing the atmosphere
to eliminate drag losses on planetary materials accelerated into space..
Collector Areal Mass
The collector areal mass is a key determinant of the disassembly time.
The lower the areal density, the greater the energy which can be collected
from eack kg of material delivered from the planet into space and the faster
the exponential growth. Extensive material exists on studies of light-weight
solar cells, solar collectors, solar sails, solar power satellites and
space-based telescopes. Table 3 lists some
of these designs and areal densities.
Obviously if the collectors are made too thin they become solar sails and
would require significant engineering of positioning technologies such
as rockets, ion jets, tether cables, etc. to be kept in a proper orbit.
So a balance must be created between the goal of accelerating energy collection
by decreased areal density and the additional engineering problems created
by excessively thin cells. Ideally the mass should be such that the
photon radiation pressure and solar wind ion pressure significantly balances
the gravitational attraction of the sun.
Transport Time
There is a tradeoff regarding the problem of doing material refining on-planet
or off-planet. Doing the material refining on-planet reduces the
energy required to transport the material into space because only those
materials best suited for solar collector construction are accelerated
to escape velocity. Waste materials remain behind in the planet's
gravity well. Because some of the available energy is being diverted
into refining operations, the amount of energy available for material transport
(rail-gun power) would be diminished. Whether this approach
would accelerate or decelerate the construction process depends primarily
on the fraction of material from the planet which can be effiently used
in the construction of space based factories and collectors. If the
space-usable raw materials percentage is high, then the optimal approach
is to send everything into space. If the space-usable fraction is
low, then the optimal approach is to refine on the planet and send only
the usable materials into space. As the amount of power available
in space increases and the surface area of the planet which can receive
that power decreases, shifts must occur in the process. If the mining
operations create cones with steep side walls, the effective surface area
of the planet may be increased to extend the period during which energy
transmission from space based solar collectors to the planet surface is
possible.
At some point, the amount of power available in space, significantly
exceeds the power which can be delivered to the planet in a useful form
(raw reflected light or microwave or laser energy).
When the limits of power which can be delivered to the planet are reached
and alternate processing method must be implemented. There are three
possible solutions at this point.
-
Planetary vaporization would be possible because there would be ample material
in space to capture the escaping gases and factories which could process
that material effectively.
-
The planet could be cut into smaller planetesimals that could be separated
to make more surface area available for power reception.
-
The planet surface could be grown. Collector surfaces are placed
on supporting columns which vertically grow to place the collectors at
an ever increasing altitude where an increased surface for power collection
is available. Small holes in the collectors would provide exit paths
for high velocity projectiles from the rail guns.
Further studies are needed to determine the most efficient method or combination
of methods is best for the utilization of the exponential growth in available
power.
Energy Required to Break Bonds
The binding strength of a solid is molar enthalpy change required to completely
separate the entities (ions or molecules) that compose the solid and is
known as its Lattice Enthalpy (DHL).
Expressed as chemical equations this would be:
LiCl (s) ® Li+ (g) +
Cl- (g)
or
H2O (s) ® H2O
(g)
The Born-Meyer equation provides the theoretical basis for the lattice
enthalpy:
DHL
= |z1z2|
NAe2 /
(4p e0d)
(1 - d* / d)
A
Where z1 and z2
are the charges on the cations and anions, NA
is Avagadro's constant (6.02214 x 1023),
e is the elementray charge (1.602177x
10-19 C), e0
is the vacuum permittivity (8.85419 x
10-12 J-1C2m-1),
d is the distance between the ions,
d* is an emperical parameter taken
to be 34.5 pm, and A is the Madelung
Constant which varies in a range from ~1.7 to 2.4 depending on the
material. The most important aspect of the equation is that DHL
is proportional to z1z2/d
meaning that the largest lattice enthalpies will be in solids with large
charges and small ions. This can be seen in the following table.
Lattice Enthalpies of common solids
Compound
|
DHL
kJ/mol
|
Lattice Spacing
A
|
Madelung
Constant
|
Al2O3
|
15916
|
|
4.1719
|
Mn2O3
|
15146
|
|
|
Fe203
|
14774
|
|
|
SiO2
|
15135
|
|
2.2197 (b)
|
TiO2
|
12150
|
|
2.408
|
Mn(OH)4
|
10933
|
|
|
CeB6
|
10083
|
|
|
VN
|
8283
|
|
|
TiN
|
8130
|
|
|
MgO
|
3850
|
|
|
CaO
|
3461
|
|
|
MgS
|
3406
|
|
|
SrO
|
3283
|
|
|
CaS
|
3119
|
|
|
BaO
|
3114
|
|
|
SrS
|
2974
|
|
|
BaS
|
2832
|
|
|
LiF
|
1037
|
2.014 (200)
1.424 (220)
|
|
NaF
|
926
|
|
|
LiCl
|
852
|
|
|
KF
|
821
|
|
|
LiBr
|
815
|
|
|
NaCl
|
786
|
2.820
|
1.74756
|
LiI
|
761
|
|
|
NaBr
|
752
|
|
|
KCl
|
717
|
3.14
|
|
NaI
|
705
|
|
|
KBr
|
689
|
3.29
|
|
KI
|
649
|
|
|
Sources: Atkins, P. (1997), pg 366-370;
Lide, D. R. (1992), Chp. 12..
For our purposes, we will use a generous 20,000 kJ / mol as the energy
requiremed to break the chemical bonds binding together the elements of
the planets.
References
-
Solar Cells and Their Applications,
Partain, L. D. (ed.), Wiley (1995).
-
Ultralight
Optics Page at NASA Gordon
Space Flight Center, 1998.
-
The Elements of Physical Chemistry, P.
Atkins, W. H. Freeman & Co., 1993, 1997.
-
Kargel, J. S. and J. S. Lewis, "The Composition
and Early Evolution of Earth", Icarus 105:1-25 (1993).
-
Lide, D. R., "Handbook of Chemistry and Physics",
CRC Press (1992).
-
Drexler,
K. E.,
"Molecular Manufacturing for Space Systems: An Overview," J.
British Interplanetary Society, 45:401-405 (1992).
Other Notes:
From: Solar Cells and Their Applications, Chapter 13, pp 285-299.
Solar Cells for space usage have parameters as follows:
Si: 2.40 g/cm3, GaAs/Ge, 5.46 g/cm3 (from 50-200
mm thick)
Coverglass 2.2-2.6 g/cm3 (from 75-700 mm
thick)
Coverglass is necessary to protect the cells from radiation.
A concentration to 10,000 suns and produces 3,300 K and is equivalent in
power to a megawatt.
Solar absorbers, such as the porcupine
can work up to 5,000 suns
WWW Sources:
-
Photovoltaic Information
-
Solar Furnace Information (1 sun = 1 kw/m2)
-
NREL and Sandia
collaborate on EREN's SunLab
. Sandia hosts National
Solar Thermal Test Facility with a peak power of 5 MW (~50,000 suns)
at a flux density of 2,600,000 W/m2 providing 2480o
K peak temperatures. NREL hosts the 10 kW High-Flux Solar Furnace
which typically achieves 2000 suns (~20,000-50,000?). NREL pages document
their Solar
Industrial Research and Solar
powered laser. Research is conducted with the Univ.
of Chicago High Energy PhysicsNonimaging
Optics group.
-
OIT High-Flux
Solar Furnace
-
Polytechnical College
of Esslingen, Germany: High-Flux
Solar Furnace
-
University of Minnesota Dept.
of M.E. has a Solar
Furnace that can achieve 7,000 suns and temperatures from 1,000-3,000
K.
-
Paul Scherrer Institut has a 70
kW parabolic concentrator which produces 4,000 suns
-
ANUTECH has produced 400
m2 350 kW parabolic concentrators
-
Plataforma Solar de Almería
-
Red Rock Energy: Heliostats & Links
-
Circa 1960 photo
of Dr. Pol Duwez Solar Furnace at Caltech
-
STL Solar
Energy Units
-
Lattice Energy Information
-
Gravitational Binding Energy Information
Comments or Suggestions? Click here.
Created: May 4, 1998
Last Modified: May 22, 1999
Author: Robert Bradbury