The idea of putting solar converters in space, and beaming the power to reception areas on earth, by microwaves or by lasers has been discussed [58] for decades. One possible scheme, based on concentrating mirrors, a "heliostat” in space, is sketched in Figure 5.7 [59].

The conceptual heliostat design of Figure 5.7 (one ofthe five designs proposed in the cited report) is envisioned to be stationary at 22 700 miles above a location on earth. Tilting ofthe primary and secondary mirrors optimizes power collected bythe energy converter during the 24h cycle. The size of this system is large: to make a suitably collimated beam at 5.8 GHz, the satellite transmitting antenna would have to be about 500 m in diameter, powered by a phased array transmitter, and would require a7.5 km diameter rectifying antenna "rectenna” on earth. The power density at this receiving antenna would not be dangerous, but this expensive system would provide only 1.2 GW on earth. The system would have to be assembled in space, as was the International Space Station (ISS), which, in a Low Earth Orbit, LEO, cost $130 billion. This would suggest more than $100/W cost, 100 times larger than on-earth solar or wind installations. Electric power usage in America is on the order of500 GW, so the Heliostat Power Satellite device indicated in Figure 5.7 would be a relatively

rectifying antenna of 7.5 km diameter on earth, assuming a 500m phased array transmitting antenna on the satellite, and delivering 1.2GW on earth. The cost ofthis system is likely to be more than $100 billion, corresponding to$100/ W. The transmission frequency is 5.8GHz, correspondingto wavelength 5.2 cm. This band transmits well through clouds and even light rain.

small contribution. A prior power satellite design of a generally similar nature [60] called for a 15 km linear array of344 combined solar collectors/converters, including power cables up to 15 km in length. The power satellite was to be launched in 340 segments, each containing rotatable solar arrays and part of the transmitter, which would be assembled in orbit using on-segment electrical propulsion. Economical earth to orbit transportation capable of30 ton payloads would be needed to assemble one such satellite. A set of smaller geosynchronous satellites, adding up to 1.2 GW would be possible with laser transmission of energy to earth, avoiding the large transmitting antenna (http://science. nasa. gov/science-news/science-at-nasa/2001/ ast13nov_1/.). It appears that the reception area for each laser-based satellite, a field of solar cells, would require the same area, 7.5 km in diameter. This hypothetical laser version has the further drawback that clouds would block the power, unlike the microwave version that will operate in cloudy weather. It is clear that these designs are all extremely expensive, and likely unsuitable for an urban power supply, on the basis of the 7.5 km diameter receiving space requirement.

The reports cited are nearly a decade old and do not reflect experience from the International Space Station (http://en. wikipedia. org/wiki/International_Space_Sta- tion.). ISS is at altitude varying from 400 to 335 km, maintained by onboard power, and has been manned since the late 2000s and projected to extend at least to 2020. It has 262 400 solar cells (http://science. nasa. gov/science-news/science-at-nasa/2001/ ast13nov_1/.) located on 8 arrays of dimension 34 m x 11m, cell area about 2500 m2, and delivers about 110 kW. NiH batteries are charged during illumination to provide power during the 36 min of each 92 min orbit in which the sun is obscured by the earth. The cost of the ISS space station has been estimated as $130 billion over 30 years.

The cited studies generally consider neither thin-film solar cells nor the possibility of unfurling thin aluminized mylar mirror surfaces, such as the 10 m2 “nanosail” (http://science. nasa. gov/science-news/science-at-nasa/2011/24jan_so- larsail/.), which might be the basis for a less massive structure along the lines of Figure 5.7.

Progress has been made in the private space industry over the past decade. A recent event is the award, in June 2010, of a $492 million contract (http://www. freerepublic .com/focus/f-chat/2537487/posts.) to SpaceX, by Iridium Communications, to launch tens of communications satellites at 666 km altitude, as part of Iridium’s $2.9 billion plan for its upgraded communication satellite network, called NEXT (http://en. wikipedia. org/wiki/Iridium_satellite_constellation.). This work will in part use the SpaceX Falcon 9 launch vehicle, capable of putting 11 tons in low earth orbit.

The Iridium NEXT network to be launched starting in 2015 will deploy 66 communications satellites at 666 km altitude, plus 6 in-orbit and 6 on-ground spare satellites, approximately 1000 kg in mass. The price $2.9 billion for an in-orbit fleet of 66 low earth orbit satellites is much below the ISS cost estimated as $130 billion. We can think of adapting satellites of this type, perhaps outfitted with parabolic mirrors to be unfurled in space, concentrating solar cells, and phased array microwave transmitters to send power to earth.

For a solar power satellite in 666 km orbit, if we accept the 7.5 km needed rectenna size from 36 000 km, one can estimate the required rectenna size by linear scaling. Using the same 500 m diameter phased array antenna, described for the power satellite of Figure 5.7, one would need a (666 km/36 000 km) x 7.5 km = 139 m diameter dedicated ground “rectenna.” This area is equivalent to 1.89 football fields or 3.75 acres, a reasonable size for urban satellite power system, small enough to be cordoned off to allow a higher microwave power density. A rectenna is an array of dipole antennas with diodes mounted to produce direct current. The spacing of the many elements would be on the order of the wavelength,

5.2 cm. This array could be elevated above ground so that the ground beneath would receive sunlight (possibly could have solar cells) with near-zero microwave power density at ground level. Admissible legal occupational 5.8 GHz power density is 50 W/m2, while the power density to deliver 1 GW to the proposed area is 66 kW/m2. As we know, full sunlight is about 1 kW/m2 and full power inside a typical microwave oven is 10 kW/m2. The envisioned beam would be deadly, 6.6 times more intense than a microwave oven.

On this basis, it seems unlikely that such a satellite power system could be implemented near New York, although the receiver area would be more dangerous but cover less area than tolerated hazards of miles subway tracks, heliports, airport runways, and freeways. A reasonable microwave power density, equivalent to full sunlight, 1 kW/m2, would deliver only 15.2 MW, which seems not enough to be useful. (The Indian Point Nuclear Reactor 40 miles north of New York has three reactors totaling 1.9 GW.) From the solar power satellite, one GW could be delivered at the 1 kW/m2 intensity level if the beam were split equally onto 66 areas of the 3.75 acre size. A phased array antenna on the solar power satellite could, in principle, address 66 separate rectennas in rapid sequence. This might offer also a solution to the problem of building more power lines, as part of the distribution can be done directly from the satellite.

We can make a more detailed model for a power satellite “constellation” in sun – synchronous orbit, extrapolating from the Radarsat-1 and -2 satellites developed and launched by the Canadian Space Agency, with 100.7 min orbital period, total cost $1.145 billion. Radarsat 1 (mass 2750 kg) was launched in 1995 and has completed 15 years of data collection in a sun-synchronous orbit near 807 km altitude. As suggested in Figure 5.8 (Radarsat-2, 2200kg, launched in 2007), these satellites access a 1000 km width ofland along their path with a synthetic aperture radar (SAR), which uses a phased array of transmitting elements. The high-resolution mode addresses at minimum a swath 45 km in width, larger than the 7.5 km rectenna envisioned for the geosynchronous earth orbit (GEO) satellite of Figure 5.7. The “SAR” antenna elements are stationary and the directionality is accomplished by timing or phasing of the signals from those elements. The satellite always faces the sun at approximately the same angle, and the advantage, if this were turned into a solar power satellite, is that tracking of the sun to optimize power would be facilitated.

The satellite does 14 7/24 orbits in its fixed plane as the earth rotates once underneath it, in 24 h. A small effect associated with the particular angle 98.594° tilts the orbital plane a tiny amount each day so that during the course of the year the

same side of the satellite continues to face the sun. This is a “sun-synchronous” orbit, a special type of polar orbit.

All of the orbits go through points close to the north and south poles, and the orbits are most widely spaced, about 2860km ~ 1780 mi, at the equator. At 40 °N latitude, this spacing is 1363 mi.

One can imagine a power satellite version of the Radarsat-2 satellite whose orbit passes over New York City. Distinct rectenna locations within a swath of 1000 km =

621.5 mi width could then be provided power, while the satellite is overhead. The antenna would have to be larger (our previous estimate was 500 m diameter) to reduce the minimum swath from 45 km, to focus only on our chosen rectenna area, 139 m in diameter. The maximum Radarsat-2 power is 5 kW, and the antenna mass is 750kg. The Radarsat antenna is 15 m x 1.447 m = 21.705 m2, and contains 10 240 radiating elements [61], which are organized in 2 wings, each with 2 antenna panels. If we assume that each radiating element is 1/2 wavelength, spaced longitudinally by l/2, and columns of elements are spaced laterally by 1 wavelength l, then the area of the antenna would be 10 240 x l2 = 10 240 x (0.052)2 = 27.7 m2, which is similar to the stated area, 21.705 m2. The whole satellite is rotated along its direction of motion, in a roll maneuver taking 10 min, to switch from a right view to a left view. So the rapidly accessible addresses on the ground are in a single 500 km swath on one side or the other of the orbital ground track.

But the time above a given location turns out to be insufficient for useful power delivery, on this model. If we take the longitudinal addressable length as the satellite altitude, A = 807 km (which would allow angles up to 45 ° from the vertical), then the

useful time it can send power to a single location on the ground is

AT = TA/lpRe = 100.7 min x (807/2pRe) = 2.034 min, (5.4)

with T the orbital period, Ro = Re + A = 7164 km, altitude A = 807 km [61], taking Re = 6357 km for the polar radius of the earth. AT = 2.034 min is clearly too short a time for useful power transfer, so the orbit should be adjusted to a higher altitude. This will require a larger antenna to keep the same resolution on the ground. To get a useful time, let us choose 2.034 h, 60 times longer. We can find the new orbit radius Ro = R >e + A’to make the period AT ‘ = 60 x 2.034min = 2.034 h by using Kepler’s law

(T )2/(Ro)3 = constant. (5.5)

To find the new parameters T’, A’, R’o such that AT ‘/AT = 60, setting Ro/Ro = x, and Re/Ro = a = 0.887 we take the ratio based on Equation 5.4, and using Equation 5.5:

AT’/AT = 60 = (T’/T)(A’/A) = x3/2[(x-a)/(1-a)] = x3/2(x-0.887)/0.113, or

(5.6)

6.78 = x3/2(x—0.887). (5.6a)

The solution to this numerical equation is x « 2.55, corresponding to orbit radius Ro = 2.875 Re, A’=1.875 Re = 11 918 km, and period T’ = 6.83 h. These numbers return AT’ = 2.03 h using Equation 5.4. (A slight change to make the period 6.0 h will be assumed below, to give exactly four orbits per day.)

We are pursuing a design of a solar power satellite based on scaling the properties of the Radarsat, and have found that to make the time the satellite is in view of a particular location long enough to transfer a significant amount of energy, we have had to make altitude A = 11 918 km versus the 807 km, an increase by 14.8. (This altitude is about 1/3 of the geosynchronous orbit at 36 300km mentioned in Figure 5.7.) The new orbit is not assured of being sun-synchronous, but we will assume that it is [62], or can be adjusted to become sun-synchronous, (For example, if the period T’ is adjusted to 6h from 6.83 h, then the satellite will make exactly four earth orbits per day.) The sun will always be approximately at right angles to the track of the satellite, so that the vertical solar cell panels in Figure 5.8 will be reasonably oriented to absorb light from the sun year-round. In the larger orbit we have assumed, there will be no period of eclipse, realizing that the orbit radius is now 2.9 earth radii. The width of the ground that can be accessed is about A [Re/(A + Re)] = 0.655 Re = 0.655 x 6357 km = 2600 mi. If the satellite is above New York, its power could be tapped in locations 1300 miles to the west, which would include Chicago and a bit more. Even so, we are insisting on resolution to restrict the incoming energy to a receiving region 1309 m in diameter. This requirement will make the transmitting antenna large in dimension, but still could contain only the 10 240 elements in the Radarsat, the elements would be more widely spaced.

These are generous assumptions and we use them to judge the feasibility of a power satellite to deliver 1 GW to earth. The solar array will have to be enlarged to provide 1.5 GW on the satellite, and if we assume the cells are 40% efficient (at present possible only with advanced cells using mirrors for light concentration), the cells will need to intercept 1.5 GW/0.4 = 3.75 GW. At 1.366 kW/m2 the area of the solar collector is 2.745 x 106m2, or a square area whose side L is 1656 m (about 1 mile). This large solar array could be assembled in orbit along the lines of the International Space Station, as suggested by Figure 5.7. If the cells are in thin-film form, they might conceivably be unrolled once in orbit, making use of weightlessness. The weightlessness in orbit means that the supporting structure for the arrays ofsolar cells and antenna elements need not be strong, and thus they need not add a lot of mass. But the overall mass of the cells, antenna elements, and the transmitter and cabling will still be large and make it expensive to put the system into orbit. Let us make minimal estimates of the masses that would be required.

The working part of a thin-film solar cell needs only to be a few micrometers in thickness. A common commercial thin film is 1/2 mil mylar, aluminized to form a “space blanket” that reflects heat back to keep the person warm. If our solar cells are 10 pm thick of semiconductor and conducting metal, plus 1/2 mil of mylar, then the overall thickness is 10~5m + 0.5 (2.54cm/1000) x 0.01m = 2.27 x 10~5m. If we assume this thin-film solar cell to have an average density ofaluminum, 2700 kg/ m3, then the solar panel as modeled, to deliver 1.5 GW, will have mass

M = 2700 x 2.27 x 10~5 m 2.745 x 106 m2 = 168 000 kg.

At 907 kg per U. S. ton, this is 185 tons of solar collector. The International Space Station mass is 417 289 kg, is only about 2.5 times bigger. This mass is unavoidable and cannot be reduced, to intercept 3.75 GW of sunlight.

The antenna mass of Radarsat is given as 750 kg, and is 1.5 m wide. The power satellite antenna width will be much larger, although it may not need a larger number of elements, for two reasons. The altitude ratio is 14.8 as noted above, and the desired resolution on the ground is to be reduced to 139 m from 45 km, this is a ratio 323, so the total width enlargement factor is 323 x 14.8 = 4791, and the new width of the transmitting antenna is 7186 km. This is extraordinarily large, but could be thought of as an array of widely spaced dipole elements: the overall size, not the density or weight, is the determining factor. As the second estimate, we extrapolate from 500 m antenna for GEO (Figure 5.7) at 36 000 km altitude by 1/3 for altitude 12 000 km, and multiply by 7.5 km/139 m (since we require the rectenna to occupy only two football fields, versus 7.5 km), we get an estimate for antenna dimension = (500/3) (7500/

139) = 8992 m, fairly close to the earlier estimate of 7186 km. These two estimates are quite close, and impractically large.

To finish our projection ofthe Radarsat to make a 1 GW power satellite, let us take the new dimension as 8000 m, compared to the 1.5 m antenna width on Radarsat.

If we were to linearly scale the mass of the antenna (750 kg on Radarsat), we get an antenna mass estimate 4 x 106kg, or 10 times the mass of the International Space Station. It seems likely that the transmitter mass is more likely the right quantity to

scale, since the antenna can be obtained at nearly constant mass just by spacing more widely a fixed number of elements. Although the transmitter element mass is not known to us, it may well amount to the 4 x 106 kg mass we just obtained. This rough estimate can be presented as 1 GW/(4 x 106 + 168 000) kg = 240W/kg.

For comparison, an estimate of the mass of a 4 GW space station as 80 000 tons = 80 x 106kg has been presented (http://en. wikipedia. org/wiki/Space-base- d_solar_power.) corresponding to 50W/kg. This mass is larger in part because it assumed conventional solar panels, not thin-film solar cells.

Our estimates suggest that the mass of one power satellite to deliver 1 GW to areas on earth, the size of two football fields, is at least 10 times the mass of the International Space Station. If we take the cost as proportional to mass, then the cost of the proposed 1 GW power satellite is at least 10 times the cost of the ISS, 10 x $135 billion, with cost at least $1350/W. This is a thousand times more expensive than solar power on earth, wind power on earth, or a conventional coal – or gas-powered electrical plant. In fact, a constellation of at least four such satellites would be needed to extend the 2 h above a given location to the peak power of the working day. If four were in orbit, then any part of the country could obtain power but the total power available would still only be 4 GW.

From an entrepreneurial viewpoint, there may be organizations willing to pay much higher prices for reliable electrical power literally at the ends of the earth. Power could be in this way reliably be provided at the poles ofthe earth, anywhere at sea, or in remote mountainous locations to support perhaps drilling or mining operations. The polar regions ofthe earth are much easier to colonize than the moon, and interested groups might find solar power beamed from the sky a reason to build a colony at the South Pole. The military might use this as they have used the global positioning system (GPS): it is difficult to protect oil tanker trucks from harassment by even a minimally equipped group of determined attackers, while invisible power from the sky would be hard to obstruct.

In the larger picture of world energy supply, all of these analyses mean that space power satellites are not in any way economically competitive.

A similar conclusion was reached by Dr. Simon Peter Worden (http://www. thespaceshow. com/detail. asp? q=1127, http://www. nasa. gov/centers/ames/about/ centerdirector. html.) (Brigadier General, USAF, retd.), Director of the NASA Ames Research Center (ARC), who stated on March 23, 2009, “Space based solar power is about 5 orders of magnitude more expensive than solar power in the Arizona desert.” This is an estimate of $105/W. Dr. Worden cited the high cost of putting materials into orbit.