attachment:ss.tex of Brown2013

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  11 
  12 \begin{document}
  13 \conference{}
  14 
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  17 
  18 \begin{figure}\begin{center}
  19    {\resizebox{\wsize}{!}{\includegraphics{A0_title.jpg}}}
  20 \end{center}\end{figure}
  21 % ------------------------------------------------------------------------
  22 % abstract 
  23 % ------------------------------------------------------------------------
  24 
  25 {\large Paper thin satellites, precisely positioned by light
  26 pressure on switchable mirrors,  self-assemble into megawatt arrays. 
  27 Solid state technology advances permit robust
  28 survivability in high radiation.
  29 Applications include internet for the developing world,
  30 and centimeter-accurate space debris tracking. \par}
  31 
  32 {\large Stable operation in earth orbit limits the area to mass ratio.
  33 Ballast mass, scavenged from derelict rocket tanks, can minimize launch
  34 weight while reducing space debris.  \par}
  35 
  36 % ------------------------------------------------------------------------
  37 \begin{multicols}{2}
  38 % ------------------------------------------------------------------------
  39 \section{Introduction}
  40 % ------------------------------------------------------------------------
  41 
  42 \PARstart{M}{ost satellites} convert \textbf{solar power} and information
  43 into \textbf{signals} transmitted to receivers on earth.   
  44 
  45 In essence, a satellite is a surface that collects solar energy,
  46 connected by sensors and computation to another surface directing
  47 radio energy into a narrow beam.  Efficient satellites do this
  48 with the minimum possible mass.\par
  49 
  50 Currently, satellites are built like aircraft, manually, from "proven"
  51 (obsolete) components in small batches.  Consumer electronics are mass
  52 produced on automated manufacturing lines, packing bleeding edge
  53 technology into smaller and cheaper packages.  Careful design and
  54 quality materials produce high reliability, feature-rich products
  55 more quickly and cheaply than satellite avionics. \par
  56 
  57 Small transistors and wires save power.  Billions of transistors
  58 replace software algorithms with optimized special purpose hardware,
  59 more immune to errors and radiation upsets.\par
  60 
  61 Low cost mass produced semiconductors permit vast distributed systems
  62 of cooperative objects, working together like mesh Wi-Fi or cell phone
  63 networks, replacing the centralized resources of the past. \par
  64 
  65 \textbf{What if satellites got a solid state makeover, mass produced
  66 and networked like cell phones, optimized for the space environment?}\par
  67 
  68 % ------------------------------------------------------------------------
  69 \section{Space Power for Computation and Radio}
  70 % ------------------------------------------------------------------------
  71 \begin{figure}\begin{center}
  72    {\resizebox{\imsize}{!}{\includegraphics{C0_world_marble.png}}}
  73 \end{center}\end{figure}
  74 
  75 As poverty diminishes worldwide, world power demand skyrockets. 
  76 The earth intercepts 170,000 terawatts. Nature evolved to use
  77 most of the terawatts reaching land.\par
  78 
  79 The sun emits \textbf{380 trillion TW} into empty space.  If
  80 170,000 TW was proportional to a marble, the sun's total output
  81 is proportional to 212 acres (50\% larger than the Brown University
  82 campus) compared to that small marble.  With all that high quality,
  83 continuous power going to waste, why should we diminish nature's
  84 share of that tiny marble?
  85 
  86 Data centers consume 3\% of US base load generation, and the
  87 fraction grows rapidly, in spite of efficiency improvements.
  88 \textbf{What if we power future data center growth with space solar
  89 energy, \textsl{in space?}}\par
  90 
  91 % ------------------------------------------------------------------------
  92 \begin{figure}\begin{center}
  93    {\resizebox{\imsize}{!}{\includegraphics{C3_energy.png}}}
  94 \end{center}\end{figure}
  95 
  96 Terrestrial data centers require cases, racks, cabling, power
  97 conversion, cooling, buildings, land, transmission lines, power
  98 plants, fuel,  and continental-scale optical fiber networks. 
  99 If we deliver space solar power to the terrestrial grid,
 100 we add huge transmitters and rectennas.\par
 101 
 102 \textbf{Computers in space don't need all that.}  With reliable
 103 sunlight and a deep space heat sink, they need little more than
 104 solar cells, silicon chips, circuit board runs, and gossamer
 105 structure to hold them together in microgravity.  Data from space
 106 can be delivered \textbf{anywhere on earth}:  ships, aircraft,
 107 remote sensors, temporary outposts and remote villages, and
 108 also to other satellites in orbit.\par
 109 
 110 % ------------------------------------------------------------------------
 111 \section{Thinsats}
 112 % ------------------------------------------------------------------------
 113 
 114 \begin{figure}\begin{center}
 115    {\resizebox{\imsize}{!}{\includegraphics{B0_serversatV3a.png}}}
 116 \end{center}\end{figure}
 117 
 118 Very thin satellites ("thinsats") maximize power with minimal launch
 119 weight.  Large area thinsats can share resources such as time references
 120 and maneuvering, and use narrow-beam phased-array techniques.\par
 121 Too light, and orbit eccentricity must be high to compensate for light
 122 pressure, interfering with other orbits.  Too wide, and pitch/yaw turns
 123 are slow, and gravity gradient torques are difficult to correct. 
 124 Reasonable dimensions are 20 centimeters across, and 8 m$^2$/kg.\par
 125 
 126 One thinsat is almost useless, but large arrays can out-perform
 127 multi-ton satellites.  Server sky thinsats weigh three grams,
 128 so an array of 33,000 thinsats weighs 99 kilograms, and makes 100kW
 129 of power from sunlight, 100 times the power to weight ratio of a big
 130 comsat.  Thinsats deploy into constellations 100 meters across or
 131 larger.  Over time, arrays can grow or shrink, change shape, or be
 132 reprogrammed for different functions.  There is no upper limit
 133 on array size, though large arrays must be sparse so radio signals 
 134 and sunlight can penetrate them.
 135 
 136 Thinsat substrates are circuit boards made from triangular sheets of glass,
 137 with shaped surface cavities holding strips of indium phosphide solar cells
 138 and silicon integrated circuits such as processors, memories, and radios. 
 139 The ground plane on the back side will have arrays of hundreds of radio
 140 chips, each surrounded by slotted antennas.  Multilayer circuit board
 141 traces thread between the slots.\par
 142 
 143 Glass is inexpensive, transparent, insulating,
 144 radiation and UV resistant, and moldable into complex shapes. 
 145 Thinsat fragility is unimportant in microgravity.
 146 
 147 Launch is stressful, so thinsats are densely stacked for launch,
 148 as strong as a cylinder of glass.  Thinsats are formed with slight
 149 curvatures, actually two different curvatures that alternate in the
 150 stack like Belleville springs.  This creates a small force that
 151 gently pushes them apart when they deploy from the stack in orbit.\par
 152 
 153 \begin{figure}\begin{center}
 154    {\resizebox{\imsize}{!}{\includegraphics{M3_deploy.png}}}
 155 \end{center}\end{figure}
 156 
 157 % ------------------------------------------------------------------------
 158 \section{Light Pressure}
 159 % ------------------------------------------------------------------------
 160 
 161 The thinsat corners are three large switchable mirrors acting as thrusters.
 162 The mirrors are thin films of electrochromic material,
 163 which switch between transparent and reflective in fractions of a second,
 164 using a solid-solution electroplating process.  
 165 Light pressure is 4.56 \textmu N/m$^2$.
 166 Pass-through light creates no force, reflected light creates double the force. 
 167 Thinsats are mostly opaque, with constant thrust, but the thrusters allow
 168 individual thinsats to maneuver \textbf{relative} to their neighbors,
 169 and turn sideways to the sun, changing incoming light pressure,
 170 and creating sideways forces.
 171 
 172 \begin{figure}\begin{center}
 173    {\resizebox{\imsize}{!}{\includegraphics{I0_echrome.png}}}
 174 \end{center}\end{figure}
 175 
 176 Three 5cm corner thrusters on a 3 gram thinsat weigh 600mg and
 177 deliver $ \approx $ 20 nanonewtons of average thrust, throttleable
 178 to a fraction of a nanonewton over a fraction of a second.  The
 179 thruster $ I_{SP} $ is 10,000 seconds for 10 years in orbit.\par
 180 
 181 Thrusters are segmented, allowing fine tuning of the thrust,
 182 and increasing survivability to micrometeoroid punctures.\par
 183 
 184 The thruster acceleration for a sun-oriented 3 gram thinsat averages
 185 7 \textmu m/s$^2$. 
 186 Turns between sun-oriented and {60\textdegree} sideways can produce
 187 an additional 6 \textmu m/s$^2$ of acceleration over an orbit for
 188 long distance maneuvers. \par
 189 
 190 % ------------------------------------------------------------------------
 191 \begin{center}
 192 \begin{tabular}{|l|l|lr|} \hline
 193 Start and  & Thrust  &  Distance     &                            \\
 194 stop time & fraction &  moved        &                            \\ \hline
 195 0.2 sec    & 0.1     &    7 nm       & optical position tweak     \\ \hline
 196 1.0 sec    & 1.0     & 1.7 \textmu m & microwave position tweak   \\ \hline
 197 6 min      & 1.0     &   20 cm       & occultation avoidance      \\ \hline
 198 30 min     & 1.0     &    5 m        & precision debris avoidance \\ \hline
 199 7 hours    & 1.0     &   1 km        & crude debris avoidance     \\ \hline
 200 6 days     & 1.0     &  444 km       & 1 degree around m288 orbit \\ \hline
 201 41 days    & 1.8  & 40,000 km  & {180\textdegree} around m288 orbit \\ \hline
 202 \end{tabular}
 203 \end{center}
 204 % ------------------------------------------------------------------------
 205 
 206 Thinsats are torqued and turned with differences between thrusters, 
 207 accelerating one side of the thinsat differently than the other side.
 208 A 20 cm thinsat can make a {45\textdegree} turn and stop in 6 minutes.\par
 209 
 210 \begin{figure}\begin{center}
 211    {\resizebox{\imsize}{!}{\includegraphics{J3_turn_tidal.png}}}
 212 \end{center}\end{figure}
 213 
 214 Continuous torque is required to counteract tidal forces.  The only
 215 stable position for a thinsat is edge-on to the center of the earth. 
 216 Continuous sun orientation requires torques at the 3 o'clock and
 217 9 o'clock positions of the orbit.
 218 \textbf{ Light pressure cannot correct the gravitational torque
 219 of thick and heavy thinsats.}\par
 220 
 221 % ------------------------------------------------------------------------
 222 \begin{figure}\begin{center}
 223    {\resizebox{\imsize}{!}{\includegraphics{K0_lighteccentric.png}}}
 224 \end{center}\end{figure}
 225 
 226 \textbf{Light pressure can destabilize orbits.} 
 227 Light pressure subtracts $ \Delta V $ from the sunbound side of the
 228 orbit, and adds $ \Delta V $ to the the outbound side. 
 229 This modifies a circular orbit into an ellipse,
 230 driving apogee and perigee perpendicular to the sun.
 231 If this change in eccentricity is added to an ellipse with a
 232 \textbf{sunwards perigee},
 233 the eccentricity and the orbit will precess eastward. 
 234 A properly chosen elliptical orbit precesses {360\textdegree} per year, 
 235 with perigee following the sun through the sky.\par
 236 
 237 The oblate earth adds a $J_2/R^3$ term to the gravity field, also
 238 precessing perigee eastward, {360\textdegree} per year at 15000km
 239 radius.  Below this altitude, the precession is too fast, so
 240 light pressure precession is subtracted using a \textbf{sunwards apogee}. 
 241 Above 15000km, light pressure precession dominates,
 242 and a sunward perigee orbit should be chosen. 
 243 Higher orbits have lower orbital speeds,
 244 so light pressure has a greater effect,
 245 and the orbit must be more elliptical to compensate. \par
 246 
 247 % ------------------------------------------------------------------------
 248 \section{The M288 orbit}
 249 % ------------------------------------------------------------------------
 250 \begin{figure}\begin{center}
 251    {\resizebox{\imsize}{!}{\includegraphics{E0_m288xx.png}}}
 252 \end{center}\end{figure}
 253 
 254 The 12789 km radius M288 orbit makes exactly 5 orbits per day relative
 255 to the ground, for a 288 minute ground repeat time.
 256  M288 is a compromise between northern latitude visibility
 257 ({55\textdegree}) and round trip ping time. 
 258 Most of the world's population is south of {55\textdegree} N .\par
 259 
 260 The M480 orbit (three repeats per day) is visible farther north,
 261 but ping time is slower and launch $ \Delta V $ is higher. 
 262 The M720 orbit is occupied by GPS and Glosnass, 
 263 and the M360 orbit is slated for the O3B satellites.  
 264 Both M360 and M480 are close to the 15000km light pressure instability.\par
 265 
 266 %------------------------------------------------------------
 267 \begin{figure}\begin{center}
 268    {\resizebox{\imsize}{!}{\includegraphics{E3_crosser.png}}}
 269 \end{center}\end{figure}
 270 
 271 The NORAD spacewatch database lists about 13000 tracked objects.
 272 The population of tracked objects drops rapidly with altitude.
 273 The flux rate drops faster, as equatorial plane crossings are
 274 spread out over a larger orbital radius and longer orbital periods.
 275 
 276 Equatorial orbits have lower average closing velocities with objects
 277 in inclined orbits.  Objects in opposing polar orbits can close with
 278 each other at twice orbital velocity.
 279 
 280 % ------------------------------------------------------------------------
 281 \begin{figure}\begin{center}
 282    {\resizebox{\imsize}{!}{\includegraphics{H0_toroid.png}}}
 283 \end{center}\end{figure}
 284 
 285 The sidereal period of an Earth orbit is $ T = 2 \pi \sqrt{ a^3 / \mu } $, where $ a $ is the semimajor
 286 axis and $ \mu $ is the Earth's gravitational parameter. 
 287 \textbf{The period is the same for all orbits with the same
 288 semimajor axis.}\par
 289 
 290 We can map many elliptical orbits with identical periods onto a toroid
 291 around a central orbit, packing them closely with no chance of high speed
 292 collisions between them.\par
 293 
 294 3 dimensional arrays mapped onto these orbits will skew towards
 295 apogee as they move around the orbit, and also make one rotation
 296 around their center orbit axis as they make one orbit.\par
 297 
 298 % ------------------------------------------------------------------------
 299 \section{Cooling and Temperature stress}
 300 % ------------------------------------------------------------------------
 301 \begin{figure}\begin{center}
 302    {\resizebox{\imsize}{!}{\includegraphics{M0_temperature.png}}}
 303 \end{center}\end{figure}
 304 
 305 M288 objects spend 40 minutes per orbit in solar eclipse, without
 306 power.  Their high surface-to-volume ratio makes them cool rapidly
 307 by black body radiation, reaching equilibrium with deep space and
 308 Earth's night sky infrared emissions.\par
 309 
 310 Since the materials have different thermal expansion properties,
 311 there will be thermal stresses between objects and on wiring and
 312 connections.  Differences between average front and back side 
 313 expansion can cause curling and warping of thinsats.  
 314 
 315 % ------------------------------------------------------------------------
 316 \section{Radiation}
 317 % ------------------------------------------------------------------------
 318 The M288 orbit is in the van Allen belt.  Thinsats are unshielded,
 319 so electronics and solar cells get huge radiation doses. 
 320 Recent semiconductor advances provide solutions. \par
 321 
 322 \begin{figure}\begin{center}
 323    {\resizebox{\imsize}{!}{\includegraphics{R0_radiation.png}}}
 324 \end{center}\end{figure}
 325 
 326 Ionizing particles can cause latch-up, but not at modern power
 327 supply voltages below 1 volt.  Particle hits can flip bits,
 328 but RAZOR "detect error and recompute" techniques
 329 can compensate, while increasing power performance.\par
 330 
 331 % ------------------------------------------------------------------------
 332 \begin{figure}\begin{center}
 333    {\resizebox{\imsize}{!}{\includegraphics{R3_radiation.png}}}
 334 \end{center}\end{figure}
 335 
 336 Annealing, briefly cooking the semiconductor lattice,
 337 can heal displacement damage caused by high energy particles. 
 338 Lateral thermal conductivity through the very thin substrate
 339 does not spread heat,
 340 so all 4 watts of a chipsat can be redirected to heat one small
 341 region above 400C.
 342 The figure shows the heating of one of the solid state memory chips. \par
 343 
 344 Gate charge trap effects can be almost eliminated by the new Intel
 345 hafnium oxide process.  Particle tracks leave a trail of trapped
 346 electrons in the HfO film, and a compensating track of trapped
 347 holes in the SiO$_2$ beneath it.  Such transistors withstand doses
 348 of many megarads without noticable voltage threshold shifts.\par
 349 
 350 Thin, graded junction indium phosphide solar cells are rad hard,
 351 as are highly-doped deep submicron transistors. 
 352 Thinsats contain no radiation-and-UV-sensitive plastics. 
 353 Other materials will need evaluation. \par
 354 
 355 % ------------------------------------------------------------------------
 356 \section{Phased Array Radio}
 357 % ------------------------------------------------------------------------
 358 
 359 \begin{figure}\begin{center}
 360    {\resizebox{\imsize}{!}{\includegraphics{Q0_phasedarray.png}}}
 361 \end{center}\end{figure}
 362 
 363 Phased array transmitters sum the signals from many precisely timed
 364 emitters to form a beam.  Electronically changing the phase of the
 365 emitters steers the beam in nanoseconds.  A 100 kg array with 
 366 \textbf{ 33,000 3 gram thinsats } and spread out over 100 meters
 367 can focus kilowatt pulses onto a ground spot 1 km wide and 10,000 km
 368 distant.  Thousands of different pulses in different directions
 369 can be emitted simultaneously, by superposition.\par
 370 
 371 % ------------------------------------------------------------------------
 372 \begin{figure}\begin{center}
 373    {\resizebox{\imsize}{!}{\includegraphics{Q3_arrayspace.png}}}
 374 \end{center}\end{figure}
 375 
 376 Averaging over thousands of emitters results in tight and accurate
 377 power beams. 
 378 However, a regular array that is widely spread out sprays 99\% of
 379 the energy in all directions,
 380 and focuses some of it into \textbf{grating lobes},
 381 making high power interference in the wrong places.
 382 Intentionally dithering thinsat positions into a non-uniform
 383 grid smears out interference, reducing peaks to acceptable levels.\par
 384 
 385 %------------------------------------------------------------
 386 \end{multicols}
 387 %------------------------------------------------------------
 388 \section {Tracking space debris, recycling rocket tanks}
 389 %------------------------------------------------------------
 390 
 391 \begin{figure}\begin{center}
 392    {\resizebox{\wsize}{!}{\includegraphics{U0_radar.png}}}
 393 \end{center}\end{figure}
 394 %------------------------------------------------------------
 395 \begin{multicols}{2}
 396 %------------------------------------------------------------
 397 Modern radars emit chirps, complex pulses spread in time and frequency,
 398 with receivers correlating the return energy to the chirps.  This
 399 detects much lower amplitude signals with high timing accuracy.\par
 400 
 401 Many server sky arrays can be synchronized and focus narrow-band
 402 continuous microwave energy on a small volume of near-earth space,
 403 creating three dimensional interference patterns, standing waves in
 404 space.  As an object orbits through that volume, the energy it reflects
 405 will be modulated by the changing field, creating a time-varying return
 406 similar to a radar chirp.  Different objects in different orbits will
 407 emit different signatures, and a powerful parallel computation engine
 408 can correlate for all the expected signatures simultaneously.\par
 409 
 410 The drawing above shows seven widely separated arrays looking at a
 411 half-kilometer region of space with centimeter resolution. 
 412 Compacting the arrays expands the search region,
 413 and closing the orbital separation between arrays looks for
 414 larger objects. 
 415 Once objects are identified and their rough orbital parameters tracked,
 416 we can use other array configurations to characterize object
 417 position and velocity to centimeter accuracy,
 418 measuring tumble and estimating mass from the long term response to
 419 drag and light pressure.\par
 420 
 421 Server sky can use this expanded collider database to plan maneuvers 
 422 long in advance.   But a large database will also protect big
 423 satellites with limited maneuvering fuel.  When we can precisely
 424 predict where billions of large and small colliders will be, we
 425 can make tiny micrometer-per-second thrusts on the big birds, 
 426 confident of a 10 meter miss six months in the future.  Today,
 427 NORAD tracks larger objects with kilometer short-term
 428 accuracy, only marginally useful for avoidance maneuvers.\par
 429 
 430 %------------------------------------------------------------
 431 \section{Capturing ballast mass}
 432 %------------------------------------------------------------
 433 \begin{figure}\begin{center}
 434    {\resizebox{\imsize}{!}{\includegraphics{U3_rocketbody.png}}}
 435 \end{center}\end{figure}
 436 
 437 Instead of mere avoidance, we can collect the derelict objects,
 438 then recycle or re-enter them.  NORAD tracks 1500+ spent upper
 439 stages, with acres of aluminum tank.\par
 440 
 441 Specialized satellites with high $I_{SP}$ VASIMR thrusters and
 442 powerful lasers can cut the skins and tanks into penny-sized
 443 ballast mass for future ultra-thinsats. 
 444 The ballasts are ferried to M288 to attach to new ultralight thinsats. 
 445 Every kilogram delivered to M288 with fuel-efficient space tugs
 446 enables an extra kilowatt of ultra-thinsat.\par
 447 
 448 Many of those rocket bodies are far from M288, in LEO and MEO
 449 orbits accessible to electrodynamic tether EDDE capture systems.
 450 Those objects can be collected into "junkyards" in low orbit
 451 for other re-uses, or de-orbited and re-entered. 
 452 Accurate server sky radar will help mission planning for EDDE
 453 as well as detect and characterize potential tether-cutting
 454 colliders.\par
 455 
 456 %------------------------------------------------------------
 457 \section{Conclusion}
 458 %------------------------------------------------------------
 459 \begin{figure}\begin{center}
 460 {\resizebox{\imsize}{!}{\includegraphics{S0_costdrop.png}}}
 461 \end{center}\end{figure}
 462 
 463 The spectacular transistor density increases driving Moore's
 464 Law are slowing; computing cost is now driven by energy costs,
 465 not transistor cost. 
 466 The spirit of Moore's law, providing exponentially increasing
 467 computing value per dollar, can continue in space for decades. 
 468 Space energy is unbounded, and the cost of collecting it will drop with
 469 efficiency improvements, mass reductions, and launch cost reductions.\par
 470 
 471 Rocket designs are already optimized.  Most re-use proposals are
 472 misconceived, trading expensive payload mass fraction and complicated
 473 logistics for cheap tank aluminum. 
 474 Logistic improvements from scheduled high traffic expendable
 475 launches will reduce launch costs, but Tsiolkovsky's exponential
 476 law will always make fuel-carrying launchers more expensive than
 477 the resulting payload energy.\par
 478 
 479 Server sky greatly increases the productivity of a kilogram in orbit,
 480 making hundreds of launches a day economically attractive.
 481 That creates a market for electrically powered alternatives to
 482 rockets, such as the coilgun launcher prototypes built by
 483 E. F. Northrup in the 1930's, or more recent proposals such
 484 as the space cable and the launch loop.  When space solar power
 485 provides terrestrial grid power to launch more space solar power
 486 collection systems, power costs will drop and launch capability
 487 will grow exponentially, while reducing the environmental costs
 488 of global abundance.\par
 489 
 490 %------------------------------------------------------------
 491 \section{References}
 492 %------------------------------------------------------------
 493 References and errata: http://server-sky.com/Brown2013
 494 
 495 %------------------------------------------------------------
 496 \end{multicols}
 497 % test ruler ------------------------------------------------
 498 \begin{figure}\begin{center}
 499    {\resizebox{\imsize}{!}{\includegraphics{ruler.png}}}
 500 \end{center}\end{figure}
 501 \end{document}