Solar Energy, Vt~l. 19. pp. 767-773. Pergam~m Press 1977 Printed in Great Brilain

TECHNICAL NOTE

An orbitinl~ mirror for solar illumination at night

WILLIAM F. RUSH

Ritter Astrophysical Research Center. Department of Physics and Astronomy. The University of Toledo. Toledo, OH 43606, U.S.A.

( R e c e i v e d 6 N o t ' e m b e r 1975: in ret:ised (o rm I Apr i l 1977)

INTRODUCTION

It is being proposed here that solar energy be employed directly to provide nighttime illumination for large urban areas. The essence of this concept is to place a series of large, flat. light- weight mirrors of very simple design and construction into geo- stationary orbit to provide directly reflected sunlight for ground illumination at night. This proposal offers several advantages:

1. The reflecting surface can be a thin foil or aluminized sheet so that cost and weight are low.

2. No technological breakthroughs are required. 3. Since the reflector is a simple, almost passive device, there

are few components to age and the expected lifetime is ver> hmg.

4. The fluxes involved are low and there is absolutely no danger of accidental pointing error.

5. The high efficiency with which solar energy is used enables one to have a relatively small collecting area.

It should be recognized that the concept of using orbiting mirrors in conjunction with solar energy systems is not new. The concept of such mirrors extends back nearly half a century to Oberth111, who recognized that such satellites are not affected by weather and are exposed to the Sun much more than are points on the Earth. A more recent suggestion by Glaser[2] proposes collecting solar energy in an orbiting satellite, converting it to electrical energy and transmitting the energy to the surface of the Earth as microwaves. Other possibilities for using,orbiting mir- rors to supplement the solar energy flux at a generating sight such thal the facility could be operated at night have been considered by Boeing Aerospace Company[3], but such systems may have large, undesirable ecological impacts.

Notice that any scheme which uses solar energy for night illumination involves collection of solar energy, conversion to electrical energy, distribution through power lines and reconversion to visible light. There are of course losses of energy involved in each step, an inefficiency which seems par- ticularly unsatisfying if the net result is only to transform visible light in one location to visible light in another. If the solar energy system is not used in conjunction with an orbiting mirror, energy for night illumination must necessarily be stored, an additional complication and inefficiency. Rather than undergoing these several steps of energy conversion (and possibly storagel, it is proposed here that the energy for night illumination be provided directly by flat orbiting mirrors. (Since fossil fuels also represent stored solar energy which was collected inefficiently and since such fuels are in demand for other purposes, reconverting an- cient solar energy to visible light for night illumination is also undesirable). In Project Able [4], a large paraboloidal mirror was considered for night illumination in Viet Nam, but the pos- sibilities of using a simple fiat mirror for illumination of large ttrban areas dries not seem to have been considered.

MOTIONS OF THE SATELLITE

The satellite mirror being proposed here will be a flat mirror ultimately having a circular orbit selected so that the mirror remains always above a fixed point on the Earth's equator. Such geostationary satellite orbits have been produced often and pose no problem, merely requiring that the orbital period equal the

24hr period of the Earth's rotation, a condition satisfied by a circular orbit about 36,000 km (22,50(I miles) above the surface. Although the gravitational forces from the Sun and Moon, the elliptical shape of the earth, and solar radiation pressure will all influence the mirror, experience indicates that a geostationary satellite can be maintained at any desired longitude above the equator.

In addition to the revolution of the satellite about the earth every 24 hr, a second motion of rotation of the satellite about its own axis every 48 hr is required in order that the sunlight be directed toward a fixed point on Earth. To see this, consider Fig. 1 in which the target to be illuminated is indicated by a dot. At midnight, the target is on the side of the Earth opposite the Sun and the mirror must reflect the sunlight exactly opposite to the direction from which it came. (This picture immediately suggests the possible problem of eclipsing or having the mirror in the shadow of the Earth. This problem is not serious and is discussed below.I At sunrise, the Earth has rotated about 90 ° and the satellite has revolved the same angle, remaining above the target. Calling the angle between the midnight position and the satellite 0. the direction of rotation of the Earth as seen from the north pole is taken as positive. Let q5 be the angle between the normal to the flat mirror and the target, taking , b - 0 ° when 0 - 0 ° and positive when go is in the same sense as 0. Since the angles of incidence and reflection are equal for a fiat mirror, the angular deviation suffered by the light is twice the angle of incidence. Note that in Fig. 1. go must equal 45 ° when O is 90 ° in order that the target be illuminated. Formally

and

O(t) = ,o,.t ll)

1 1 go(t) - ~ w,,t = ~ O(t) (21

where ~o. is 15°/hr and t = 0 at midnight. One point which should be noted is that both sides of the

mirror must be reflective in order for the mirror to be useful every day. This can be seen from eqns (1) and (2) by noting that after 24 hr, a5 is 180 °, indicating that the normal faces away from the Sun. This same conclusion can be reached from study of Fig. I by increasing g in 90 ° steps while increasing go by 45 ~teps. At the second "midnight" the back of the mirror will be seen to face the Earth. The details of the double reflective surface are discussed in the next section.

The revolution and rotation motions discussed above serve to provide approximate delivery of the reflected sohtr light on a ground area at the equator. However, latitudes not on the equator and different longitudes can be reached by motions which leave the revolution and rotation rates unaltered. This is discussed in the next section.

The geometry of the Earth-Sun-satellite system dictates that the satellite will be eclipsed Imove into the shadow of the Earthj according to the approximate schedule shown in Fig. 2. The longest duration eclipse is about 71 rain about 21 March and 21 September, the middle of the eclipse coming about midnight at the sub-satellite point. Although nothing can be done to prevent

767

768

SUNLIGHT

Technical Note

X M I R R O R AT

SUNRISE o : 9 0 °

/ / / ~ e : 4 5 °

sunrise j~

AT NOON J MIRROR ,,mr.,... noon midnight AT MIDNIGHT

I

I O : e = O ° J

Fig. I. The period of rotation about the satellite axis must be 48 hr while the period of revolution about the Earth is 24 hr because of the "optical doubling" of the mirror. At sunrise the mirror must be inclined at 45 ° to the Sun in

order to direct the light at the target.

1 0 0 min .

5 0 m i n .

ECLIPSE DURATION

,/ d M ;, A 3 A s

/ o N 6 ;

MONTH Fig. 2. The approximate duration of the eclipse of the satellite is shown as a function of the day of the year.

such eclipses, the target can still be illuminated by the use of a series of mirrors distributed along the equator. Strategies for dealing with the eclipse problem are discussed in the section on "Operations."

It should be remarked in passing that orbits other than circular geostatiouary orbits are possible and perhaps useful for special purposes. An example of one such possible application is a frost preventing reflector discussed in the applications section.

The reader interested in investigating non-circular orbits for special applications can use Kepler's laws to determine parameters. All non-circular orbits of interest will be ellipses. If Rm~,, and R ..... are respectively the minimum and maximum distances between the center of the Earth and the satellites, the distances and period of revolution are related by

Rmi n + R,,~ x - 83,t)00(P) '/~ k m = 52.000(P) 2/3 miles,

where P is measured in days. More detailed discussions can be

found in most texts on classical dynamics (for example, see Marion[5]). An important point to consider in selecting such non-circular orbits is that the long axis of the ellipse remains pointed in a fixed direction in space. In short, if an elliptical orbit is chosen so that the point of closest approach of the satellite to the earth occurs at dawn in the spring, the satellite will approach the Earth most closely at sunset in the fall.

An example of a special purpose orbit is given in the dis- cussion of frost prevention.

SATELLITE STRUCTURE

Perhaps the most important aspect of the device being pro- posed here is the intended simplicity of design and construction, the intent being to avoid costly, high technology design. The satellite consists of 2 mirrors placed back to back and separated by at least 4 spacer arms of adjustable length. In practice, many spacer arms will probably be required.

The structure of each individual reflector is shown in the view

Technical Note 769

Fig, 3. The front and side views of the mirror illustrate the ~,tructure and pointing mechanism of the mirror. By changing the length of the variable lengths spacer arms, the mirrors can be skewed relative to each other, allowing

pointing.

of Fig. 3. The outer frame is a lightweight structure, resembling the frame of a trampoline. Located inside the frame where the canvas would be on a trampoline) is a tightly stretched sheet of highly reflective foil or plastic sheet, kept taut by stretching springs of material. Rolled shades are provided at each end so that the mirrors can be covered if no ground illumination is desired. Alternatively, illumination can be reduced by moving the mirrors off target. The foil might be backed by a honeycomb structure to provide ridigity and limit the extent of any tears in the reflective surface.

The side view in Fig. ~; shows the essential features of the pointing system--spacer arm~, of variable length, each of which can be operated independently so that the mirrors may be skewed with respect to each other. This allows pointing the mirror in different directions with expenditure of fuels which would have to be re-supplied. Since the system is isolated, small symmetric motions of the mirrors leave the revolution and ro- tation of the satellite unaltered. North-south motion of the illuminated area is executed by simultaneously contracting tor expanding) the top spacers while expanding (or contracting) the bottom spacers. East-west motions are executed by changing the left and right spacer arms in opposite senses.

Occasional adjustments to the orbit can he provided by the addition of ion thrusters. Energy for the ion thrusters is provided by a bank of conventional solar cells included in the station keeping unit. These cells also provide electrical power for the operation of the spacer arms, shades and radio receiver for instructions from the ground. A small telescope could be provided to enable pointing control to be achieved using a small laser on the ground.

Several possible problems immediately' suggest themselves, but the resolution of most appears within presently existing tech- nology. For example, if care is not exercised in the choice of materials, thermal expansion and contraction of the frame and reflective sheet us the mirror moves into and out of the Earth's shadow may cause stresses or sagging. However, it should be possible to select frame, sheet, and "stretching spring" materials to that their differential contraction effects will not cause com- plications.

A more serious difficulty is the problem of frame rigidity'. Motion of the spacer arms will tend to give rise to oscillations in both the reflecting sheet and the stretching frame. Reducing this problem requires that the reflecting material be stretched as tightly as possible and that it be as light as possible: that the spacer arms be attached to the frame near nodes of the normal modes of oscillation so as to reduce exciting these modes: and

that the spacers he extended and contracted in such a way that their length changes with time so as to reduce normal mode excitation.

The structural analysis of the large flat orbiting mirror requires more investigation than any other aspect of this proposal. However, an analysis of the type conducted[6] employ- ing well developed computer programs for analysis of large space structures could be carried out without great difficuhy. Such further investigation would settle the question of rigidity definitively. Qualitatively it is clear that lightweight material stretched tightly will have several advantages: the lightweight will have low inertia opposing the small motions required for adjusting of the mirror and low weight combined with tight stretching will give rise to high frequencies of os- cillation which can be expected to be damped more quickly. Tailoring of the time dependence of the spacer arm motion to reduce normal mode excitation can be seen to be a simple technique to further reduce structural oscillation problems. In essence, this '~tailoring'" would simply consist of stopping the spacer arm motion when the natural oscillations tend to want to increase the arm length and expanding the arm length when the natural oscillations tend to contract the arm. Care must also be taken in designing the mirror to see that its normal modes are not resonant with its rotational frequency, since the normal modes would then be excited by the tidal forces resulting from the gradient of the gravitational field of Earth.

Construction of the mirror being proposed here could be undertaken ahmg one of several lines. It is anticipated that the ~,pace shuttle ~,y~,lem will be operative by the end of this decade and with its ad,,ent we will have a transport system which carries more volume at lower cost than systems presently available. One option for constructing mirrors of this type would be to subas- semble the nnits on Earth so as to permit them to be stowed in the space shuttle, launch them to low Earth orbit, complete assembly, and thus use a space tug chemical rocket to carry the mirror to geostationary orbit.

The complexity of the structural problems cannot be assessed until the dimensions of the mirror are specified, since clearly these problems diminish greatly with decreasing mirror size. Because of a feature inherent in this system, the optimum size of the mirror can be selected most easily after the flatness of the reflecting material and the target size and illumination have been specified. Mirror flatness and general optical considerations are discussed in the next section. There will also be a tradeoff between the advantages in constructing a small mirror and the requirement of providing each mirror with a station keeping unit.

770 Technical Note

A more efficient technique for building the structure would be to launch equipment for extruding structural members while in orbit. This has the advantage of reducing considerably the num- ber of launches required, since sub-assembled units will probably have an inefficient packing fraction. Such extrusion techniques would capitalize on the advantages of zero gravity and structural members could be built to have any length desired, and there are clearly many other advantages to constructing the mirrors in space. The possibility of using a lightweight, stiff plastic should be considered. Boron nitride fiber material is both lighter than aluminum and some six times stiffer.

Construction of the reflecting surface presents several in- teresting possibilities. The material might be extruded in space and aluminized, thereby using the high vacuum readily available. It is probably desirable to bond the reflecting surface to a reinforcing mesh or honeycomb structure in order to prevent the spread of tears and provide structural rigidity. It might be pos- sible with a suitable choice of materials to bond the material to the mesh while the material is in a semi-liquid state, thereby allowing the surface tension in the material film to cause it to be quite flat.

OPTICAL CONSIDERATIONS AND MIRROR PARAMETERS

The optical considerations involved in this project are simple, for only geometric optics of a flat surface need be considered. In order to qualitatively visualize the functioning of the mirror, recall from geometric opticst that a perfect plane mirror simply reflects the light incident on it in such a fashion that the light (as seen by an observer in front of the mirror) seems to come from behind the mirror. To visualize how a perfect mirror would operate in orbit, one can imagine a "window" in the night sky through which an imaginary sun shines, In this picture, the night sky is an opaque sphere of radius 42,000 km (26,000 miles). The mirror can be thought of as a window through which light passes from an imaginary sun located behind the opaque sphere.

Such a model immediately produces several interesting results. For example, what is the largest mirror which could be usefully built'? Since it is useless to build the "window" larger than the size of the image Sun and since the angular diameter of the Sun is approximately 0.5 °, the maximum diagonal for a square mirror would be such that it subtended 0.5 °, at a distance of 36,000 km (22,000 miles), the height of a geostationary orbit above the surface of the Earth. This corresponds to a diagonal of 307 km (192 miles) or an edge of 217 km ( 135 miles). While such a mirror is clearly too large for practical construction, the visualization technique of considering an "image Sun" shining through a window frame enables us to predict the effect of the changing of the position of the mirror with respect to the Sun. Returning to Fig. 1, notice that when the satellite mirror is in the midnight position, an observer experiencing midnight sees the image Sun coming through the square window frame. However, at dawn, the angle between the observers line of sight and the normal to the mirror is 45 o . Hence the projection effects cause the window frame to appear to have its full height (i.e. dimen- sions perpendicular to the plane of the page in Fig. 11 but its width is reduced to

W ' - (cos &)W, (3)

where W is the apparent width at midnight and W' is the width when the angle between the normal to the mirror and the direc- tion of incident sunlight is &. Using eqns (1) and (2) it is readily seen that the effective area of the reflecting surface is

A,,, - W'- (cos 4~). (4)

If the mirror were perfectly flat and the Sun were a point

tCareful consideration of coherence lengths and diffraction limitations shows that geometric optics can be used with confidence in discussing this problem, a fact pointed out to me by Dr. Robert Stubbs of NASA Lewis Research Center.

source of light, the mirror would illuminate an area on the ground given by eqn (4) with one solar flux. Since the mirror will not be flat and the Sun is not a point source, the area illuminated will be larger than that given by eqn (4) and the light flux will be correspondingly reduced.

It is essential to recognize that any mirror, independent of shape, will spread its light over a circular region of ap- proximately 300km (190 miles) in dia. This is because the Sun has an apparent angular diameter of 0.5 °, rather than being a point source. Since the sunlight has an intrinsic angular spread in its rays of 0.5 °, no mirror geometry can be designed to focus the light into an angular spread less than this value. From the calculation above, it can be seen that at geostationary orbit distance, a beam with this angular spread will cover a circle on Earth of approximately the dimension claimed on reaching Earth. It is important to recognize that it is not possible to focus in any fashion. Smaller areas of illumination on Earth can only be obtained from lower orbits.

Returning to the window method of visualizing the optics of the system, we have a small window through which the light is admitted. However. the large size of the Sun enables one to see a small parl of its surface from any location within the 300 km dia. illuminated area. Because it is the size and shape of the Sun which determine from which points on Earth the reflected solar surface is visible, the shape of the mirror (or imaginary window) affects the illuminated area very little. This implies thai as the area of the mirror (A,,, in eqn 4), is changed, the size of the illuminated area is unaltered but the flux illuminating that area is changed. In particular, if F. is the direct solar flux, F,. is the reflected flux reaching the ground, and A~ is the illuminated area,

F, ,4~ "' (5)

where reflective losses are neglected. In addition to the spreading of the solar flux due to the finite

angular extent of the Sun, there are two additional effects which should be considered. The first factor is the deviation of the reflecting surface from the ideal plane geometry. Imagine the surface to be divided up into many small square elements. In a perfect mirror, the normal to each of these little surface elements would all be parallel. In practice, the normals would be dis- tributed in various directions deviating by angles a0 from the desired direction. In the absence of data, we may assume that the a0 values are distributed according to some probability dis- tribution. For example, let

p,ao,_ 1 F-2(A0)- ' ] V'(2-rr)~ exp [ ~ / ' (6l

where o- is the r.m.s, deviation of the normals from the desired direction. Provided that o- is small compared to 0.5 ° / the spread in the beam due to the finite angular size of the Sun), the additional beam spread due to a non-flat reflector will be slight. Equation (6) allows us to set limits on how flat the material must be. Note that a o" value of 0.05 ° would be perfectly satisfactory for this application, although this is far from being optically flat in the usual sense of the term. In terms of physical dimensions, this permits deviations of a mirror element from its ideal location of approximately l mm over a distance of a meter of mirror surface. This is not a terribly demanding flattness. The price which must be paid for having a surface of this flatness is that the radius of the illuminated area is increased by about 10 per cent.

There is a second effect which acts to effectively concentrate the sun rays lightly. This is due to the fact that the center of the solar disk is brighter than its edges. The edge is also known to astronomers as the "limb." This so-called limb darkening causes the intensity of light at larger angles of spread to be lower than the intensity of the more nearly central rays. The effect is not large, but is about comparable with the angles of divergence caused by a non-teal flat surface just discussed. There is more limb darkening in visible wavelengths than IR. Curves of solar disk intensity as a function of distance from the disk center can

Technical Note 771

be found in most standard astronomy texts (for example, see Aller[7]).

In practice, the detailed prediction of the intensity profile of the reflected light is the convolution of (6) with the appropriate expression for limb darkening and the precise angular diameter of the Sun. Such detailed considerations require specification of the flatness of the mirror material.

APPLICATIONS

The device proposed here is primarily designed for outdoor night lighting, although frost control and fog removal are pos- sibilities which are also considered. As a particular example, assume a mirror or series of mirrors having a total area of 38 km 2 (15 miles 2) directed slightly north and east of the point where the borders of the states of Pennsylvania, Maryland and Delaware intersect. Included within a 160 km (100 mile) radius of this point are New York, Trenton, Wilmington, Newark, Washington, D.C., Baltimore, Philadelphia, Atlantic City and Harrisburg. Sur- rounding both New York City and Boston are similar areas of high population density. For definiteness, assume 15 identical mirrors making up the required area, distributed along the equator.

Application of i5) shows that the illuminating flux will be 4.8 x 10 4 times the solar flux, under ideal conditions with no reflection loss, cloud cover, or projection effects of the type discussed in developing eqn (4). Assuming the mirror to have the reflectivity of aluminum (0.90) and an average angle. ~, of 22 °, the flux is reduced to 0.83 of the maximum value, or 4 x 10 ~ of the noon lime solar flux. Using the light meter of a SLR camera, measurements were made of exposure conditions on a clear day, a cloudy day. and at night directly under a very bright streetlight. These measurements indicate that the illumination directly beneath a bright streetlight corresponds to approximately 2.5 x 10 4 of the noon flux on a clear day, suggesting that a 38 km ~ mirror can light a city very effectively to twice the brightness presently found under bright streetlights. Such illumination would also be much more even than that presently employed. This light level is probably unacceptably bright for night il- lumination, but shades over part of the mirror surface could be employed to reduce this problem on clear nights. Camera light meter measurements indicate that moderate cloud cover would reduce the light level by a factor of 2-4, leaving the light level for a 38 km~" mirror at an acceptable level. However, heavy cloud cover reduces light levels by a factor of 8-10, requiring the use of supplementary illumination of the type presently in use. It is possible that the more even illumination provided by this system will reduce contrast at night compared to present systems, al- lowing vision at overall lower average levels than now needed. Notice that because measurements are made relative to noontime flux at the surface, atmosphere losses are already taken into consideration.

Telephone conversations with various city officials in Cle- veland and Toledo, Ohio indicate that large cities use about 3.4 × Ill ~ kWh/km-'/yr 18.8 × l0 ~ kWh/mile-'/yr). For Cleveland, this corresponds to approximately $2 million/yr to illuminate its 195kin ~ i76milesZ)+ This excludes the cost of illumination provided by businesses and individuals for outside night il- lurnination. Estimating that private illumination costs equal minicipal costs, a typical city is using approximately 140 million/kWh/yr at a cost of $4 millionlyr, exclusive of equip- ment. maintenance and equipment amortization. Real costs are prohably close to $6 millionlyr based on data from Cleveland. These data suggest that a flat orbiting mirror located as discussed above would save approximately $65 million/yr at present energy costs based on the assumption that cities use energy for il- lumination at the same rate as Cleveland and estimates of urban area in the designated target area. Considering that the launching of the structural frame of the mirror under consideration is likely to be the most expensive part and that it should last almost indefinitely, obtaining a 6(I yr lifetime would seem to be quite reasonable, leading to an estimated saving of approximately $4 billion over 6(I yr. The anticipated dollar return will increase if energy costs increase over the $0.03]kWh assumed in this cost estimate.

In addition to the economic advantages, there are energy conservation benefits of providing illumination in this rather direct fashion. This process used approximately 80 per cent of the solar energy incident on the mirror on a clear night, a figure which compares favorably with systems which involve one or more energy conversions and transmission losses. Additional benefits are more even illumination than presently available and illumination of areas now dark at night. A recent Gallup poll]S] indicates that in cities of 500,000 and more people, over 50 per cent of the population is afraid to go out after dark. Benefits derived from greater personal safety and possibly redticed crime losses are difficult to estimate.

The capability of illuminating large ground areas may have unusual applications in addition to lighting cities. For example. search, rescue and disaster operations which are hampered by darkness could be made easiec provided only that cities were willing to revert to convention illumination techniques while mirrors were redirected. On clear nights even this would be unnecessary since the 38kin ~ mirror can provide considerably more light than is necessary for city illumination. This device might also have military uses.

Another possible application of the flat mirror is the prevention or reduction of frost damage to crops. It is proposed that after assembly of the mirror in low Earth orbit, but before transfer to geostationary orbit, the mirror should be placed in an elliptical orbit with apogee and perigee distances approximately 6500 km (4100 milesl and 200kin (125 miles) above the surface of the Earth. The orbit should be so chosen that the major axis of the ellipse points toward the Sun in early spring and the mirror~ should be positioned in their orbits such that they are nearly overhead in Florida shortly before sunrise, at which time the~ are approaching apogee, These conditions are chosen so that the satellite is in the best possible position for illuminating areas used for growing citrus fruits, the intention being to warm these area~ slightly in the critical pre-dawn hours. Cloud co~er will not be a problem, since it is primarily on clear nights that frost damage occurs due to radiation losses to the clear sky, The orbital parameters sugested above correspond approximately to an orbit of period 0.111 day. Equations (1) and (2) can be modified for angular velocities which are integer multiples of the angular velocity of the Earth. The integer condition arises front the requirement that the mirror must make an even or odd number of rotations on its axis for each revolution in its orbit if it i~ to always illuminate the ground target,

Non-synchronous orbits involve several difficulties beyond the scope of this discussion. In particular, the satellite moves more slowly at apogee than perigee: hence for frost prevention of the satellite should be at apogee when overhead so that more of its time can be spent illuminating the target. Also. elliptical orbits are such that the angular velocity of the satellite changes, requir- ing adjustments of the skew angles of the 2 mirrors in order to remain on a target. Finally, for non-synchronous orbits, the difference in angular velocity between the satellite and the Earth must be taken into account. None of these complications is serious. The relevant point is that a set of approximate orbital parameters such as given above can lead to possible frost prevention.

Using these rough numbers, at apogee the illuminated area will be a circle of radius

R~ h .tan(0.25°).

where h is the height of the satellite above the ground and the 0.25 ° is half of the spread in the Sun's rays. For this case. the illuminated area is approximately 2500kin ~ I1000 miles2). Ten mirrors of area 2.5 km 2 (1 mile 2) together would provide 0.01 solar fluxes, neglecting projection effects and reflection Insect. Since 15 mirrors are being proposed here, the losses will be neglected and it will be assumed that 0.01 solar flux is attainable. The orbit suggested can provide this light intensity for ap- proximately 90 rain in the critical period before dawn.

Although 0.01 solar flux does not readily convince the intuition that it is sufficient to prevent frost, there is some evidence that it may be sufficient. Data presented in a report on the Study of

772 Technical Note

Critical Environmental Problems[9] suggest that large cities generate waste heat at a rate equivalent to between 0.01 and 0.05 solar fluxes, the larger number being regarded as the better value for use in this calculation. Cities have also been shown to exhibit the "heat island" phenomenon, which is=simply due to the fact that they are warmer than the surrounding countryside. The respor of the Study of Man's Impact on Climate[10] reports that cities are typically 2-6°C (3.6-I1°F) warmer than their sur- roundings. Even under the most unfavorable assumptions (that cities generate 0.05 solar flux as waste heat, and the cor- responding temperature rise is 2°C), the heat provided by the mirrors could raise the air temperature measurably. Air tem- perature increases of 3°C appear feasible. Exact implications for frost damage prevention are difficult to predict since absorption of light by the leaves may alter their temperature by an amount different from the air temperature change. Transpiration rates might also be affected and the present technique of using smudge pots makes it difficult to compare urban data with rural con- ditions. The question of frost prevention should be investigated more carefully.

Experiments to determine the feasibility of solar mirrors to remove fog could be conducted while the mirrors are in the intermediate orbits and not being used for other purposes.

ENVIRONMENTAL CONSIDERATIONS

The proposed orbiting mirror involves relatively low flux levels of visible, infrared, and UV light and presumably will involve no uncertainties as to the effect of this radiation on the environment. Fears that such light levels will harm plant growth and hopes that the illumination will aid plant growth can probably be dismissed with the observations that plants growing under bright street lights do not demonstrate any unusual growth patterns for near solar spectral distributions. However, the habits of some noc- turnal animals might be altered by this light level and this question will require further research if the orbiting reflector appears economically desirable. Studies of the ecosystems of geographic areas experiencing the "midnight San" phenomenon may provide clues on this question. Similarly, the psychological impact of these mirrors would be expected to be similar to the impact of the midnight Sun on humans.

Since the sunlight cannot be concentrated by any mechanisms whatever, there is no fear of an accidental straying of a beam. The flux is too small to do any harm.

A more serious consideration is the aesthetic impact of il- luminating the night sky. The observer in the illuminated area would see as many small, bright points of light as there are mirrors. The sky in the illuminated area would probably acquire a diffuse glow similar to that presently seen in large cities. However, the presently dark skies of the countryside might also become brighter, destroying the beauty of the dark sky. Under no circumstances should such a mirror system be used to il- luminate areas near major astronomical observatories unless provisions are made to relocate those observatories.

In short, the low flux levels of familiarity with the harm- lessness of sunlight suggest that environmental impact of this proposed system should be minimal.

OPERATIONS

After construction and assembly in low Earth orbit, the mir- rors would be placed in an elliptical orbit for a period of time during which frost prevention experiments could be conducted. When not in use, the reflectors would be covered by their dark shades or directed off target. While in this intermediate orbit, experiments in fog removal and night illumination of selected areas can also be conducted.

Due to the wide beam being reflected, extreme pointing ac- curacy is not required. Errors of 0.05 degree could be tolerated. Spacecraft technology presently available can easily point satel- lite telescopes to accuracies an order of magnitude better than that required here. A low power laser beam directed at the mirror could be used for alignment purposes.

Routine operations will require that eclipsing and cloud cover strategies be developed. Presently existing illumination systems can, of course, be employed when required. However. placing a

set of mirrors along the equator would guarantee that at least some of the mirrors would be able to contribute light during the periods when other mirrors are eclipsed. During periods when an area is under heavy cloud cover, conventional night illumination could be employed in one area while mirrors normally employed to illuminate that area are directed to another area.

Maintenance should be minimal on the mirror since it could derive all power needed for station keeping from solar cells and the use of ion thrusters for orbit maintenance should reduce the need for providing propellant on a frequent basis. Since the system makes pointing changes all electrically and is symmetric, no propellant is exhausted in making pointing changes. In- structions for changing direction and opening and closing shades can be sent from the ground.

COST ESTIMATES

Since the greatest area of uncertainty regarding this proposal is the question of the structure necessary to maintain the required rigidity, cost estimates are not easy to make. Assuming a baseline design of a 1.6 km (1 mile) mirror, assume a reasonable average mass density of (I.5 kg/m -~ (0.1 Ib/ft 2) and a very high estimate of 4 km/m 2 (I lb/ft2), in addition to a fixed mass of 2000 kg (4400 Ib) for the station keeping unit. Since a mirror is actually two reflectors, back to back, the 2.6 m 2 mirror has a total area of 5.2kin 2 (2 miles-~), leading to a mass of 2.5 × 10"kg (5.6× 1061 for the reflector and station keeping units under the 0.5 kg/m 2 as- sumption.

Although a reliable cost estimate is impossible without further investigation, an order of magnitude guess is possible and helps by suggesting at what point this project is too expensive. Any reasonable estimates for development and material costs indicate that these are negligible in comparison with the cost of launching this much material into space. Taking the space shuttle capacity as 27,000kg (60,0001bl, the launching of 15 mirrors requires about 1400 shuttle flights at a baseline estimate. Taking the order of magnitude of launch costs as $200/kg ($100/Ib), the cost of launch is of the order of $0.6 bil l ion. The estimate discussed above that the target area of New York to Washington, D.C. uses $65 million worth of energy for night illumination leads to an estimated payback time of 10yr assuming no energy cost in- creases and no increase in night illumination levels during this period. If either of these assumptions is altered, the payback time will be reduced. Doubling of energy costs, for example, would reduce the payback time to 5 yr. Since virtually all of the cost will be in the launching of frame material, replacing the reflecting material will be relatively inexpensive. Thus, a long lifetime should be anticipated for this device.

CONCLUSION

The construction of a large, flat orbiting reflector has been proposed primarily for illuminating large areas at night from geostationary orbit. The principle points of this discussion are:

1. The minimum area which can be illuminated is a circle of 160 km (100 miles) radius.

2. A mirror or series of mirrors 39 km 2 (15 miles'-) is adequate to illuminate this area to the intensity of an area directly under a bright street light, despite the projection effects and some cloud cover.

3. The large illuminated area inherent in this system makes extreme structural rigidity and optical surface flatness un- necessary,

4. Such a mirror could be used in experiments for prevention of frost damage, an application which might prove as valuable as the illumination applications.

5. While the reflector being proposed is large by present stan- dards, it is not predicated on any major technological advances or cost reductions.

6. Although this device cannot be used for power generation because of the low fluxes, it can relieve other generating facilities of a load of more than 0.3 billion kWh annually at present rates by eliminating the night illumination requirements.

It should be clear to the reader that there are still several aspects of this proposal which require further investigation be- fore its feasibility can be definitely established. The areas of

Technical Note 773

principle uncertainty are those having to do with materials which are sufficiently light, stiff and easily fabricated to keep costs low and the device used to transfer from low Earth orbit to geo- stationary orbit. However, apart from these questions, the concept appears feasible and realistic with the potential for great energy savings.

This proposal is being made in the hope of arousing sutficient interest in this concept that further investigation of its economics and practicality will be undertaken.

Aeknoa,led~,ements--I would like to express my deep ap- preciation to Robert Stubbs and Donald Alger of NASA Lewis Research Center. both of whom provided advice, encourage- ment. and insight during the development of the ideas presented here. Without their assistance, this paper would never have been completed.

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