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\begin{document}
\conference{}

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\begin{figure}\begin{center}
   {\resizebox{\wsize}{!}{\includegraphics{A0_title.jpg}}}
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% ------------------------------------------------------------------------
% abstract 
% ------------------------------------------------------------------------

{\large Paper thin satellites, precisely positioned by light
pressure on switchable mirrors,  self-assemble into megawatt arrays. 
Solid state technology advances permit robust
survivability in high radiation.
Applications include internet for the developing world,
and centimeter-accurate space debris tracking. \par}

{\large Stable operation in earth orbit limits the area to mass ratio.
Ballast mass, scavenged from derelict rocket tanks, can minimize launch
weight while reducing space debris.  \par}

% ------------------------------------------------------------------------
\begin{multicols}{2}
% ------------------------------------------------------------------------
\section{Introduction}
% ------------------------------------------------------------------------

\PARstart{M}{ost satellites} convert \textbf{solar power} and information
into \textbf{signals} transmitted to receivers on earth.   

In essence, a satellite is a surface that collects solar energy,
connected by sensors and computation to another surface directing
radio energy into a narrow beam.  Efficient satellites do this
with the minimum possible mass.\par

Currently, satellites are built like aircraft, manually, from "proven"
(obsolete) components in small batches.  Consumer electronics are mass
produced on automated manufacturing lines, packing bleeding edge
technology into smaller and cheaper packages.  Careful design and
quality materials produce high reliability, feature-rich products
more quickly and cheaply than satellite avionics. \par

Small transistors and wires save power.  Billions of transistors
replace software algorithms with optimized special purpose hardware,
more immune to errors and radiation upsets.\par

Low cost mass produced semiconductors permit vast distributed systems
of cooperative objects, working together like mesh Wi-Fi or cell phone
networks, replacing the centralized resources of the past. \par

\textbf{What if satellites got a solid state makeover, mass produced
and networked like cell phones, optimized for the space environment?}\par

% ------------------------------------------------------------------------
\section{Space Power for Computation and Radio}
% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{C0_world_marble.png}}}
\end{center}\end{figure}

As poverty diminishes worldwide, world power demand skyrockets. 
The earth intercepts 170,000 terawatts. Nature evolved to use
most of the terawatts reaching land.\par

The sun emits \textbf{380 trillion TW} into empty space.  If
170,000 TW was proportional to a marble, the sun's total output
is proportional to 212 acres (50\% larger than the Brown University
campus) compared to that small marble.  With all that high quality,
continuous power going to waste, why should we diminish nature's
share of that tiny marble?

Data centers consume 3\% of US base load generation, and the
fraction grows rapidly, in spite of efficiency improvements.
\textbf{What if we power future data center growth with space solar
energy, \textsl{in space?}}\par

% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{C3_energy.png}}}
\end{center}\end{figure}

Terrestrial data centers require cases, racks, cabling, power
conversion, cooling, buildings, land, transmission lines, power
plants, fuel,  and continental-scale optical fiber networks. 
If we deliver space solar power to the terrestrial grid,
we add huge transmitters and rectennas.\par

\textbf{Computers in space don't need all that.}  With reliable
sunlight and a deep space heat sink, they need little more than
solar cells, silicon chips, circuit board runs, and gossamer
structure to hold them together in microgravity.  Data from space
can be delivered \textbf{anywhere on earth}:  ships, aircraft,
remote sensors, temporary outposts and remote villages, and
also to other satellites in orbit.\par

% ------------------------------------------------------------------------
\section{Thinsats}
% ------------------------------------------------------------------------

\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{B0_serversatV3a.png}}}
\end{center}\end{figure}

Very thin satellites ("thinsats") maximize power with minimal launch
weight.  Large area thinsats can share resources such as time references
and maneuvering, and use narrow-beam phased-array techniques.\par
Too light, and orbit eccentricity must be high to compensate for light
pressure, interfering with other orbits.  Too wide, and pitch/yaw turns
are slow, and gravity gradient torques are difficult to correct. 
Reasonable dimensions are 20 centimeters across, and 8 m$^2$/kg.\par

One thinsat is almost useless, but large arrays can out-perform
multi-ton satellites.  Server sky thinsats weigh three grams,
so an array of 33,000 thinsats weighs 99 kilograms, and makes 100kW
of power from sunlight, 100 times the power to weight ratio of a big
comsat.  Thinsats deploy into constellations 100 meters across or
larger.  Over time, arrays can grow or shrink, change shape, or be
reprogrammed for different functions.  There is no upper limit
on array size, though large arrays must be sparse so radio signals 
and sunlight can penetrate them.

Thinsat substrates are circuit boards made from triangular sheets of glass,
with shaped surface cavities holding strips of indium phosphide solar cells
and silicon integrated circuits such as processors, memories, and radios. 
The ground plane on the back side will have arrays of hundreds of radio
chips, each surrounded by slotted antennas.  Multilayer circuit board
traces thread between the slots.\par

Glass is inexpensive, transparent, insulating,
radiation and UV resistant, and moldable into complex shapes. 
Thinsat fragility is unimportant in microgravity.

Launch is stressful, so thinsats are densely stacked for launch,
as strong as a cylinder of glass.  Thinsats are formed with slight
curvatures, actually two different curvatures that alternate in the
stack like Belleville springs.  This creates a small force that
gently pushes them apart when they deploy from the stack in orbit.\par

\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{M3_deploy.png}}}
\end{center}\end{figure}

% ------------------------------------------------------------------------
\section{Light Pressure}
% ------------------------------------------------------------------------

The thinsat corners are three large switchable mirrors acting as thrusters.
The mirrors are thin films of electrochromic material,
which switch between transparent and reflective in fractions of a second,
using a solid-solution electroplating process.  
Light pressure is 4.56 \textmu N/m$^2$.
Pass-through light creates no force, reflected light creates double the force. 
Thinsats are mostly opaque, with constant thrust, but the thrusters allow
individual thinsats to maneuver \textbf{relative} to their neighbors,
and turn sideways to the sun, changing incoming light pressure,
and creating sideways forces.

\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{I0_echrome.png}}}
\end{center}\end{figure}

Three 5cm corner thrusters on a 3 gram thinsat weigh 600mg and
deliver $ \approx $ 20 nanonewtons of average thrust, throttleable
to a fraction of a nanonewton over a fraction of a second.  The
thruster $ I_{SP} $ is 10,000 seconds for 10 years in orbit.\par

Thrusters are segmented, allowing fine tuning of the thrust,
and increasing survivability to micrometeoroid punctures.\par

The thruster acceleration for a sun-oriented 3 gram thinsat averages
7 \textmu m/s$^2$. 
Turns between sun-oriented and {60\textdegree} sideways can produce
an additional 6 \textmu m/s$^2$ of acceleration over an orbit for
long distance maneuvers. \par

% ------------------------------------------------------------------------
\begin{center}
\begin{tabular}{|l|l|lr|} \hline
Start and  & Thrust  &  Distance     &                            \\
stop time & fraction &  moved        &                            \\ \hline
0.2 sec    & 0.1     &    7 nm       & optical position tweak     \\ \hline
1.0 sec    & 1.0     & 1.7 \textmu m & microwave position tweak   \\ \hline
6 min      & 1.0     &   20 cm       & occultation avoidance      \\ \hline
30 min     & 1.0     &    5 m        & precision debris avoidance \\ \hline
7 hours    & 1.0     &   1 km        & crude debris avoidance     \\ \hline
6 days     & 1.0     &  444 km       & 1 degree around m288 orbit \\ \hline
41 days    & 1.8  & 40,000 km  & {180\textdegree} around m288 orbit \\ \hline
\end{tabular}
\end{center}
% ------------------------------------------------------------------------

Thinsats are torqued and turned with differences between thrusters, 
accelerating one side of the thinsat differently than the other side.
A 20 cm thinsat can make a {45\textdegree} turn and stop in 6 minutes.\par

\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{J3_turn_tidal.png}}}
\end{center}\end{figure}

Continuous torque is required to counteract tidal forces.  The only
stable position for a thinsat is edge-on to the center of the earth. 
Continuous sun orientation requires torques at the 3 o'clock and
9 o'clock positions of the orbit.
\textbf{ Light pressure cannot correct the gravitational torque
of thick and heavy thinsats.}\par

% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{K0_lighteccentric.png}}}
\end{center}\end{figure}

\textbf{Light pressure can destabilize orbits.} 
Light pressure subtracts $ \Delta V $ from the sunbound side of the
orbit, and adds $ \Delta V $ to the the outbound side. 
This modifies a circular orbit into an ellipse,
driving apogee and perigee perpendicular to the sun.
If this change in eccentricity is added to an ellipse with a
\textbf{sunwards perigee},
the eccentricity and the orbit will precess eastward. 
A properly chosen elliptical orbit precesses {360\textdegree} per year, 
with perigee following the sun through the sky.\par

The oblate earth adds a $J_2/R^3$ term to the gravity field, also
precessing perigee eastward, {360\textdegree} per year at 15000km
radius.  Below this altitude, the precession is too fast, so
light pressure precession is subtracted using a \textbf{sunwards apogee}. 
Above 15000km, light pressure precession dominates,
and a sunward perigee orbit should be chosen. 
Higher orbits have lower orbital speeds,
so light pressure has a greater effect,
and the orbit must be more elliptical to compensate. \par

% ------------------------------------------------------------------------
\section{The M288 orbit}
% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{E0_m288xx.png}}}
\end{center}\end{figure}

The 12789 km radius M288 orbit makes exactly 5 orbits per day relative
to the ground, for a 288 minute ground repeat time.
 M288 is a compromise between northern latitude visibility
({55\textdegree}) and round trip ping time. 
Most of the world's population is south of {55\textdegree} N .\par

The M480 orbit (three repeats per day) is visible farther north,
but ping time is slower and launch $ \Delta V $ is higher. 
The M720 orbit is occupied by GPS and Glosnass, 
and the M360 orbit is slated for the O3B satellites.  
Both M360 and M480 are close to the 15000km light pressure instability.\par

%------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{E3_crosser.png}}}
\end{center}\end{figure}

The NORAD spacewatch database lists about 13000 tracked objects.
The population of tracked objects drops rapidly with altitude.
The flux rate drops faster, as equatorial plane crossings are
spread out over a larger orbital radius and longer orbital periods.

Equatorial orbits have lower average closing velocities with objects
in inclined orbits.  Objects in opposing polar orbits can close with
each other at twice orbital velocity.

% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{H0_toroid.png}}}
\end{center}\end{figure}

The sidereal period of an Earth orbit is $ T = 2 \pi \sqrt{ a^3 / \mu } $, where $ a $ is the semimajor
axis and $ \mu $ is the Earth's gravitational parameter. 
\textbf{The period is the same for all orbits with the same
semimajor axis.}\par

We can map many elliptical orbits with identical periods onto a toroid
around a central orbit, packing them closely with no chance of high speed
collisions between them.\par

3 dimensional arrays mapped onto these orbits will skew towards
apogee as they move around the orbit, and also make one rotation
around their center orbit axis as they make one orbit.\par

% ------------------------------------------------------------------------
\section{Cooling and Temperature stress}
% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{M0_temperature.png}}}
\end{center}\end{figure}

M288 objects spend 40 minutes per orbit in solar eclipse, without
power.  Their high surface-to-volume ratio makes them cool rapidly
by black body radiation, reaching equilibrium with deep space and
Earth's night sky infrared emissions.\par

Since the materials have different thermal expansion properties,
there will be thermal stresses between objects and on wiring and
connections.  Differences between average front and back side 
expansion can cause curling and warping of thinsats.  

% ------------------------------------------------------------------------
\section{Radiation}
% ------------------------------------------------------------------------
The M288 orbit is in the van Allen belt.  Thinsats are unshielded,
so electronics and solar cells get huge radiation doses. 
Recent semiconductor advances provide solutions. \par

\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{R0_radiation.png}}}
\end{center}\end{figure}

Ionizing particles can cause latch-up, but not at modern power
supply voltages below 1 volt.  Particle hits can flip bits,
but RAZOR "detect error and recompute" techniques
can compensate, while increasing power performance.\par

% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{R3_radiation.png}}}
\end{center}\end{figure}

Annealing, briefly cooking the semiconductor lattice,
can heal displacement damage caused by high energy particles. 
Lateral thermal conductivity through the very thin substrate
does not spread heat,
so all 4 watts of a chipsat can be redirected to heat one small
region above 400C.
The figure shows the heating of one of the solid state memory chips. \par

Gate charge trap effects can be almost eliminated by the new Intel
hafnium oxide process.  Particle tracks leave a trail of trapped
electrons in the HfO film, and a compensating track of trapped
holes in the SiO$_2$ beneath it.  Such transistors withstand doses
of many megarads without noticable voltage threshold shifts.\par

Thin, graded junction indium phosphide solar cells are rad hard,
as are highly-doped deep submicron transistors. 
Thinsats contain no radiation-and-UV-sensitive plastics. 
Other materials will need evaluation. \par

% ------------------------------------------------------------------------
\section{Phased Array Radio}
% ------------------------------------------------------------------------

\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{Q0_phasedarray.png}}}
\end{center}\end{figure}

Phased array transmitters sum the signals from many precisely timed
emitters to form a beam.  Electronically changing the phase of the
emitters steers the beam in nanoseconds.  A 100 kg array with 
\textbf{ 33,000 3 gram thinsats } and spread out over 100 meters
can focus kilowatt pulses onto a ground spot 1 km wide and 10,000 km
distant.  Thousands of different pulses in different directions
can be emitted simultaneously, by superposition.\par

% ------------------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{Q3_arrayspace.png}}}
\end{center}\end{figure}

Averaging over thousands of emitters results in tight and accurate
power beams. 
However, a regular array that is widely spread out sprays 99\% of
the energy in all directions,
and focuses some of it into \textbf{grating lobes},
making high power interference in the wrong places.
Intentionally dithering thinsat positions into a non-uniform
grid smears out interference, reducing peaks to acceptable levels.\par

%------------------------------------------------------------
\end{multicols}
%------------------------------------------------------------
\section {Tracking space debris, recycling rocket tanks}
%------------------------------------------------------------

\begin{figure}\begin{center}
   {\resizebox{\wsize}{!}{\includegraphics{U0_radar.png}}}
\end{center}\end{figure}
%------------------------------------------------------------
\begin{multicols}{2}
%------------------------------------------------------------
Modern radars emit chirps, complex pulses spread in time and frequency,
with receivers correlating the return energy to the chirps.  This
detects much lower amplitude signals with high timing accuracy.\par

Many server sky arrays can be synchronized and focus narrow-band
continuous microwave energy on a small volume of near-earth space,
creating three dimensional interference patterns, standing waves in
space.  As an object orbits through that volume, the energy it reflects
will be modulated by the changing field, creating a time-varying return
similar to a radar chirp.  Different objects in different orbits will
emit different signatures, and a powerful parallel computation engine
can correlate for all the expected signatures simultaneously.\par

The drawing above shows seven widely separated arrays looking at a
half-kilometer region of space with centimeter resolution. 
Compacting the arrays expands the search region,
and closing the orbital separation between arrays looks for
larger objects. 
Once objects are identified and their rough orbital parameters tracked,
we can use other array configurations to characterize object
position and velocity to centimeter accuracy,
measuring tumble and estimating mass from the long term response to
drag and light pressure.\par

Server sky can use this expanded collider database to plan maneuvers 
long in advance.   But a large database will also protect big
satellites with limited maneuvering fuel.  When we can precisely
predict where billions of large and small colliders will be, we
can make tiny micrometer-per-second thrusts on the big birds, 
confident of a 10 meter miss six months in the future.  Today,
NORAD tracks larger objects with kilometer short-term
accuracy, only marginally useful for avoidance maneuvers.\par

%------------------------------------------------------------
\section{Capturing ballast mass}
%------------------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{U3_rocketbody.png}}}
\end{center}\end{figure}

Instead of mere avoidance, we can collect the derelict objects,
then recycle or re-enter them.  NORAD tracks 1500+ spent upper
stages, with acres of aluminum tank.\par

Specialized satellites with high $I_{SP}$ VASIMR thrusters and
powerful lasers can cut the skins and tanks into penny-sized
ballast mass for future ultra-thinsats. 
The ballasts are ferried to M288 to attach to new ultralight thinsats. 
Every kilogram delivered to M288 with fuel-efficient space tugs
enables an extra kilowatt of ultra-thinsat.\par

Many of those rocket bodies are far from M288, in LEO and MEO
orbits accessible to electrodynamic tether EDDE capture systems.
Those objects can be collected into "junkyards" in low orbit
for other re-uses, or de-orbited and re-entered. 
Accurate server sky radar will help mission planning for EDDE
as well as detect and characterize potential tether-cutting
colliders.\par

%------------------------------------------------------------
\section{Conclusion}
%------------------------------------------------------------
\begin{figure}\begin{center}
{\resizebox{\imsize}{!}{\includegraphics{S0_costdrop.png}}}
\end{center}\end{figure}

The spectacular transistor density increases driving Moore's
Law are slowing; computing cost is now driven by energy costs,
not transistor cost. 
The spirit of Moore's law, providing exponentially increasing
computing value per dollar, can continue in space for decades. 
Space energy is unbounded, and the cost of collecting it will drop with
efficiency improvements, mass reductions, and launch cost reductions.\par

Rocket designs are already optimized.  Most re-use proposals are
misconceived, trading expensive payload mass fraction and complicated
logistics for cheap tank aluminum. 
Logistic improvements from scheduled high traffic expendable
launches will reduce launch costs, but Tsiolkovsky's exponential
law will always make fuel-carrying launchers more expensive than
the resulting payload energy.\par

Server sky greatly increases the productivity of a kilogram in orbit,
making hundreds of launches a day economically attractive.
That creates a market for electrically powered alternatives to
rockets, such as the coilgun launcher prototypes built by
E. F. Northrup in the 1930's, or more recent proposals such
as the space cable and the launch loop.  When space solar power
provides terrestrial grid power to launch more space solar power
collection systems, power costs will drop and launch capability
will grow exponentially, while reducing the environmental costs
of global abundance.\par

%------------------------------------------------------------
\section{References}
%------------------------------------------------------------
References and errata: http://server-sky.com/Brown2013

%------------------------------------------------------------
\end{multicols}
% test ruler ------------------------------------------------
\begin{figure}\begin{center}
   {\resizebox{\imsize}{!}{\includegraphics{ruler.png}}}
\end{center}\end{figure}
\end{document}
