Patent Publication Number: US-7219860-B2

Title: Spacecraft including control vanes having variable absorptive, reflective and emissive characteristics

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional application of U.S. patent application Ser. No. 10/346,888 filed Jan. 17, 2003, now U.S. Pat. No. 6,921,050, titled “Solar Torque Control Using Thin Film Directionally Reflective, Emissive, Absorptive and Transmissive Surfaces.” 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to a method and system for maintaining the pointing direction of a spacecraft and, more particularly, to a method and system for maintaining the pointing direction of a spacecraft using control vanes having a directionally reflecting, emitting, absorbing and transmitting surface. 
     2. Discussion of the Related Art 
     When a spacecraft is in space, a variety of environmental disturbances, including solar pressure, gravity-gradient, magnetic and aerodynamic effects, act on the spacecraft producing forces and torques. These forces and torques vary depending on the spacecraft&#39;s orbital altitude. If the spacecraft is in a low Earth orbit (LEO), the forces and torques other than solar pressure are typically dominant because they vary inversely with orbital radius. If the spacecraft is in a high altitude orbit, such as a geosyncronous Earth orbit (GEO), the dominant disturbance is solar pressure. This discussion deals with solar torque. The article, Harris, Christian M. et al, “Effect of Thermal Radiation Torques on the TDRS Spacecraft,”  American Institute of Aeronautics and Astronautics, Inc.,  1990, pgs. 1602–1614 also provides a discussion of solar torque on a spacecraft. 
     Various spacecraft, such as the next generation space telescope (NGST), the terrestrial planet finder (TPF) and the planet imager (PI), require sun shades that can be extremely large in order to protect cryogenic instruments mounted on the spacecraft. These large sunshades are typically opaque and receive large amounts of incident solar radiation, and thus may increase the solar torque on the spacecraft. Spacecraft systems of this type are typically designed to point off-angle from the sun, usually within a 45° “anti-sun” conical region. If the center of pressure (CP) of the incident solar radiation is co-incident with the spacecraft center of mass (CM), then little or no solar torque is produced. However, typical spacecraft designs preclude co-locating the center of pressure and the center of mass because of mission payload configuration constraints. 
       FIG. 1  is a simple schematic of a spacecraft  10 , such as the TPF or NGST, used to illustrate how solar pressure produces spacecraft disturbance torque. The spacecraft  10  includes a bus  12  positioned on one side of a thermal shield assembly  14 , and sensor optics  16  positioned on the opposite side of the thermal shield assembly  14 . The bus  12  houses the spacecraft avionics subsystems and is typically on the “sun side” of the assembly  14 . The thermal shield assembly  14  includes a multi-layer insulation (MLI)  18  on the bus side of the assembly  14 , and a series of angled specular shields  20  that act to reflect light and heat away from the sensor optics  16 . In one design, the optics  16  are on the order of two meters, and the shields  20  are on the order of 10 meters. 
     Based on the spacecraft schematic shown in  FIG. 1 , a simplified schematic of the center of mass  24  and the center of pressure  26  of the spacecraft  10  relative to a solar shield  28  as shown in  FIG. 2 . The solar shield  28  represents the thermal shield assembly  14 . Typically, the spacecraft center of mass  24  is on the bus side of the thermal shield  28 , and the center of pressure  26  is at the geometric center of the thermal shield  28 . 
       FIG. 3  utilizes the schematic shown in  FIG. 2  to depict the forces generated by solar radiation pressure that impinges normal to the shield  28  and the resultant thermal radiation from the shield  28 . Incident photons  30  can be either absorbed, specularly reflected at  32  in a mirror like manner, or can be reflected in a diffuse manner at  34 , sometimes referred to as a Lambertian distribution. The absorbed energy must be emitted as thermal radiation energy with the bulk of the thermal emission occurring from the sun side due to the insulation effectiveness. This emitted thermal energy also typically has a Lambertian energy distribution  35 . The resultant force vector due to the reradiated thermal energy is shown at  43 . Thus, there are four force vectors caused by the impinging photons  30 , including a force vector  40  from the absorption of the incident photons  30 , a force vector  38  from the specularly reflected photons, and force vector  42  from the diffusely reflected photons and the force vector  43  from thermal radiation. The momentum from the specularly reflected photons is twice as much as the momentum of the absorbed photons. The combination of the force vectors  38 – 43  gives an effective force vector  44 . For this depiction, the sunlight is aligned along an axis running through the CM  24  and the CP  26 , where the effective force vector  44  is along this axis. Therefore, the resultant force vectors are the same at both sides of the shield  28 , resulting in no net torque being imposed on the spacecraft  10 . 
     For typical sunshield designs, most of the incident light energy is reflected or absorbed and re-emitted from the shield  28  at the side facing the sun. The thermal insulating nature of the thermal shield  28  reduces heat leakage to one or two percent of the total incident front side energy. Therefore, backside thermal radiation is negligible due to the effectiveness of the thermal shield  28 . In a situation where the CM  24  and the CP  26  are co-aligned relative to the direction of the incident sunlight, there is no net induced torque on the spacecraft  10 . 
     The force on a surface due to photon absorption, i.e., the force due to solar radiation pressure, is given by:
 
 F   absorbed   =SA/c,    (1)
 
where F absorbed  is the absorption force, S is solar flux (power per unit area), A is the projected area, and c is the speed of light. For a specular surface, the angle of incidence of the impinging photons equals the angle of reflection of the reflected photons, resulting in a force opposite to the surface normal vector direction. Thus, when the incident surface is totally specularly reflective, and the surface is normal to the sun vector, the specular reflection force (F reflection specular ) is given by F reflection specular =2SA/C. A diffusely reflective surface, i.e., Lambertian distribution, produces a force given by:
 
 F   reflection diffues =2 SA/ 3 c.    (2)
 
     Emitted photons also result in forces opposite to the direction of travel of the emitted photon. 
     For most spacecraft functions, the pointing direction of the optics, and thus the pointing direction of the entire spacecraft, will be in such a direction that the incident solar radiation is angled relative to the axis through the CM  24  and the CP  26 .  FIG. 4  is a representation of the schematic shown in  FIG. 3  where the shield  28  is angled relative to the incident solar radiation, and the CM  24  is thus tilted to the left. Each of the force vectors generated by the incident, reflected and radiated photons identified in  FIG. 3  are shown in  FIG. 4 . However, the direction of the reflected and emitted radiation is different, and therefore the effective force vector  44  is not aligned with the CM  24  and CP  26  axis. Because the effective force vector  44  is not aligned along the axis between the CM  24  and CP  26 , a torque is created about the CM  24  identified by a moment  46  in the clockwise direction. 
     The net torque T produced by a single surface about the spacecraft  10  body axes is then:
 
 T=L   CP-CM ×( F   absorbed radiation   +F   reflected radiation   +F   emitted radiation )   (3)
 
where L CP-CM  is the position vector from the center of mass  24  to the surface center of pressure  26 . For the spacecraft, the total magnitude of the generated torque T can be determined by an area integration of the cross-product of the local force vector and the respective CP/CM moment arm of the localized surface area elements, dA, given as:
 
 T=∫   A   {right arrow over (L)} (θ,  r , φ) xd{right arrow over (F)}=∫   A   {right arrow over (L)} (θ,  r , φ) x{right arrow over (ƒ)} (θ,  r, φ, Φ   s ) dA    (4)
 
where θ, r, φ are the spherical coordinates in body-axes and Φ s  is the angle of incident sun.
 
     Various techniques are known in the art to compensate for solar torques. One of these includes employing torque compensating reaction wheels (one wheel is provided for each spacecraft body axis) that provide spacecraft attitude control. As the solar torque acts on the spacecraft, one or more of the wheels is accelerated to compensate for the solar pressure disturbance torque resulting in wheel momentum accumulation. Periodically, it is necessary to unload momentum from the reaction wheels to prevent saturation. 
     Suitable momentum unloading compensation can be performed by magnetic torquers if the spacecraft is in a low Earth orbit, where the Earth&#39;s magnetic field strength is sufficiently large to produce appreciable magnetic torques. In this situation, a magnetic dipole is generated using onboard magnetic torque rods that interact with the Earth&#39;s magnetic field to produce a torque. However, as the spacecraft orbital altitude gets farther from the Earth, the Earth&#39;s magnetic field strength reduces rapidly, thus reducing the ability to provide this type of momentum unloading. For high orbit altitudes where momentum unloading cannot be provided by Earth&#39;s magnetic field, typically the spacecraft thrusters are used to provide momentum unloading of the wheels. However, spacecraft weight is an important design consideration, and therefore, thrusters firing should be minimized in order to reduce on board propellant requirements. 
     Some spacecraft designs employ appendages (e.g., solar sails) to align the spacecraft center of pressure with the spacecraft center of mass to reduce solar torques. Other possible approaches for mitigating solar torque include active devices such as moveable fins or electrochromic surfaces. However, these types of devices are typically expensive and heavy, and are generally unproven and have a limited reliability. A simple, low cost approach to mitigating the effects of solar torque on spacecraft which have large surface areas, is thus needed. 
     When a spacecraft failure occurs, the onboard computers typically direct the spacecraft to a sun-pointing safe-hold attitude. Sun-pointing provides power with proper solar array orientation, and by design provides a benign or low torque, stable thermal environment. The spacecraft can typically remain in this orientation indefinitely while ground based diagnostics examine telemetry and implement failure work arounds. Typically, reaction wheels are shut down, and the spacecraft thrusters are used to orient the spacecraft to maintain the sun-pointing direction. 
     Various systems are known in the art for accumulating and unloading angular momentum, as well as for directing the spacecraft to the sun-pointing direction. However, these systems are typically complicated and expensive. What is also needed is a passive method of reducing solar induced torque and achieving and maintaining sun-pointing. 
     SUMMARY OF THE INVENTION 
     In accordance with the teachings of the present invention, a spacecraft is disclosed that includes thermal control vanes that have variable absorptive, reflective, emissive and/or transmissive properties to provide a torque on the spacecraft to maintain it in a sun-pointed orientation in the event of system failure. The control vanes may include x-axis and y-axis control vanes to provide control torques about both the x and y-axes. The control vanes can be attached to the solar arrays of the spacecraft. 
     In one embodiment, the control vanes include an embossed film formed on an insulation layer. The embossed film has ridges containing a long, near flat side formed with a white or reflective material and a short, near vertical side formed with a black or absorptive material where the long side is reflective and the short side is absorptive. The embossed film is formed on opposite sides of the control vane, where the film is oriented in opposite directions to provide the pointing control. 
     Additional advantages and features of the present invention will become apparent to those skilled in the art from the following discussion and the accompanying drawings and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is simple schematic diagram of a spacecraft; 
         FIG. 2  is a schematic diagram of the spacecraft shown in  FIG. 1  depicting the spacecraft center of mass and the shield&#39;s area centroid (i.e., same as center of solar pressure for a flat shield surface) on the spacecraft; 
         FIG. 3  is the schematic diagram shown in  FIG. 2  depicting the forces on a thermal shield of the spacecraft where the solar radiation is normal to the shield; 
         FIG. 4  is the schematic diagram of the spacecraft shown in  FIG. 2  depicting the forces and resultant torque on the thermal shield of the spacecraft where the solar radiation impinges on the thermal shield at an angle; 
         FIGS. 5(   a )– 5 ( b ) are sun side views of a thermal shield of a spacecraft positioned in a normal direction and an angled direction relative to the direction of the solar radiation, respectively, including directionally reflective segments on the shield, according to an embodiment of the present invention; 
         FIG. 6  is a broken away cross-sectional view of the thermal shield shown in  FIG. 5  showing an embossed film with a directionally reflective grid of grooved surfaces, according to an embodiment of the present invention; 
         FIG. 7  is a graph showing the directional emittance characteristics for uniform opaque material; 
         FIG. 8  is a graph showing the directional emittance characteristics for grooved surfaces; 
         FIG. 9  is the schematic diagram shown in  FIG. 4  for a thermal shield employing the reflectance and emittance properties of the present invention; 
         FIG. 10  is a simplified spacecraft schematic diagram including x-axis and y-axis solar torque control vanes to provide pointing control, according to another embodiment of the present invention; 
         FIG. 11  is a broken-away cross-sectional view of one of the y-axis control vanes shown in  FIG. 10 ; and 
         FIG. 12  is a stability diagram showing y-axis control torque polarities generated by the y-axis control vanes of the spacecraft shown in  FIG. 10 . 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     The following discussion of the embodiments of the invention directed to providing a directionally reflectance surface on a spacecraft for controlling solar torque or spacecraft pointing is merely exemplary in nature, and is in no way intended to limit the invention or its applications or uses. 
       FIGS. 5(   a )– 5 ( b ) show a sun side view of a thermal shield  50  for a spacecraft. The shield  50  is shaped like a disc in this embodiment, but as will be appreciated by those skilled in the art, can have other suitable shapes.  FIG. 5(   a ) shows the shield  50  in an orientation normal to the incident sunlight, where the CM  24  and the CP  26  are aligned with the direction of the incident sunlight, and  FIG. 5(   b ) shows the shield  50  angled relative to the direction of the incident sunlight. In  FIG. 5(   b ), the shield  50  has been rotated about the CM 24  such that the top half of the shield  50  is angled forward (i.e., out of page) and the bottom half of the shield  50  is angled backwards (i.e., into page) so that the shield area centroid (as viewed from the sun line) is tilted upward. Thus, in order for there to be no solar torque on the shield  50  in the angled configuration, the “effective” center of solar pressure  26 A must move downward to be aligned with the spacecraft center of mass  24 . This shift in “effective” CP location is caused by the imbalanced optical properties of an embossed grid as viewed from the sun line direction. 
     In accordance with the teachings of the present invention, the shield  50  is provided with a directionally absorptive and reflective layer  52  on its sun side. In one embodiment, the layer  52  is made of Polytetrafluoroethylene (PTFE), or other suitable material consistent with the discussion herein, and has a thickness on the order of 5 mils. As will be discussed below, the layer  52  changes color in shades of black and white as the shield  50  changes its orientation relative to the direction of the sunlight, so that the reflection, absorption and emission of photons of the shield  50  is changed in a desirable manner. In other words, as the angle of the shield  50  changes relative to the direction of the sunlight, one side of the shield  50  appears darker and the opposite side of the shield appears lighter, so that the absorptive, reflective and emissive characteristics of the shield  50  change to move the “effective” center of pressure  26 A in a desirable way (i.e., in alignment with S/C center of mass). 
     To accomplish the desired results, as the shield area centroid  26  shifts away from the center of mass  24 , the side of the shield  50  on which the spacecraft center of mass  24  lies should become more reflective and the opposite side should become more absorptive, thus effectively shifting the shield&#39;s center of pressure towards the S/C center of mass. As discussed above, a specularly reflected photon imparts twice as much momentum on the spacecraft  10  as an absorbed photon. Thus, by making the side of the shield  50  angled away from the sun lighter or more reflective, and making the side of the shield  50  angled towards the sun darker or more absorptive, more pressure is provided at the light side than the dark side, and the effective center of pressure  26 A shifts towards the center of mass  24  accordingly. By designing the absorptive, reflective and emissive characteristics of the shield  50  in a desirable manner, the effective center of pressure  26 A will remain approximately co-aligned with the center of mass  24 , so that minimal solar torque is imparted on the spacecraft. The directionally reflective layer  52  need not totally cancel the solar torque, but can reduce the solar torque to levels where residuals can be readily handled by standard momentum storage devices such as reaction wheels with periodic momentum unloading required. 
     Many materials and structural configurations can be used that change the absorptive, reflective and emissive properties of the shield  50  relative to the sun incidence angle. While most spacecraft typically use opaque surfaces, some applications also exist where variable direction transmissive effects can also be used to generate solar torques. Of note, are the class of transparent inflatable RF reflectors. High transmissivity is desirable to minimize both torque and solar array shadowing. Directional modification of transmissive properties can also serve to generate counter balancing torques. 
     The present invention contemplates providing any such materials or configurations that are suitable for a thermal shield or deployable panel/membrane on a spacecraft. These various materials include holographic materials and diffraction gratings providing the various absorptive, emissive, reflective and transmissive characteristics. 
     In the design depicted here, the shield  50  is partitioned into a plurality of “pie-shaped” sections  54 , where each section  54  includes an embossed surface  58  formed on an MLI layer  60 .  FIG. 6  is a broken away, cross-sectional view of the shield  50  showing the embossed surface  58 . The embossed surface  58  includes elongated, triangular-shaped ridges  62  where a near flat long side  64  of the ridges  62  face towards a center line of the shield  50 , and a near vertical short side  66  of the ridges  62  faces away from the center line. The long side  64  of each ridge  62  is formed with a white or reflective material and the short side  66  of each ridge  62  is formed with a black or absorptive material. In one embodiment, the layer  52  is a plastic layer that is embossed to form the ridges  58 , and the sides  64  are metallized with an aluminum layer by vacuum deposition. In one embodiment, the reflectance and absorption characteristics of the layer  52  are cosine dependent. 
     In  FIG. 5(   b ), the shield  50  has been rotated about its diameter line such that the top half of the shield  50  is angled forward (i.e., out-of-page) and the bottom half of the shield  50  is angled away (i.e., into page) so that the short sides  66  on the top half become more exposed to sunlight, and the long sides  64  on the bottom half become more exposed to sunlight. This imbalance causes the effective center of pressure  26 A to move towards the spacecraft center of mass  24 , which nulls the solar torque. The use of the separate sections  54  allows the shield  50  to have any orientation toward the solar vector, i.e., the spacecraft  10  can rotate about the sun line, and still be able to balance the solar torque. 
     The embossed thin film approach discussed above was selected as a primary candidate for varying the reflective and emissive characteristics of the shield  50  for several reasons. These reasons include easy, low cost fabrication techniques, variable angled grooves in the same embossed film can allow for directional tailoring of optical properties versus offset angle, variable areas with similar characteristics can be pieced together at different angles, i.e., into a mosaic, to also allow the tailoring of optical properties versus offset angle to meet mission specific requirements, and the film can be fabricated using space stable, flight proven materials. However, it is stressed that other types of surfaces can be used on the thermal shield  50  to provide controlled reflectance and emissive properties, consistent with the discussion herein, as long as the film of the shield  50  can be designed so that the effective force vector  44  is maintained through the center of mass  24  by varying the absorptive/reflective/transmissive/emissive shield characteristics as a function of solar offset angle. 
     A simplified estimate of the magnitude of the differential torque T can be generated by assuming an insulated disk normal to the solar vector, with one half black and the other white (100% specularly reflective). The differential torque T is then given by:
 
 T=L   CPwhite-CM ×( F   absorbed-white   +F   reflected-white   +F   emitted white )− L   CPblack-CM ×( F   absorbed-black   +F   reflected-black   +F   emitted black )=× L   CPwhite-cm (0+2 SA   white   /c+ 0)η−× L   CPblack-CM , ( SA   black   /c+ 0+2 SA   black /3 cη )   (5)
 
and if the CM  24  is in the plane of the disk and A black =A white =A disc/2, then:
 
| T|= ( SA   disc /6 c ) L   CPblack/white-CM 
 
where L CPblack/white-CM =distance from CM 24  to area centroid of each half-disk (i.e., A black , A white )=4R disc /3η where R disk  is the radius of the disc.
 
Equation (5) assumes that the reflected and emitted energies are directed back towards the direction of incident solar radiation and neglects thermal radiation due to energy from other sources.
 
       FIG. 7  is a graph with directional emissivity ε relative to angle of emission θ that shows the directional emittance characteristics for uniform opaque materials. This type of diagram is typically referred to as a Lambertian distribution diagram, as these emission characteristics follow a near cosine distribution. 
       FIG. 8  is also a graph with directional emissivity ε relative to angle of emission θ showing directional emittance characteristics for grooved surfaces. These diagrams show that it is in fact possible to change the reflective, absorptive, and emissive characteristics of a material, and with appropriate design, to operate in the manner discussed herein. 
       FIG. 9  is a force diagram of the type shown in  FIG. 4  that depicts the emissive, reflective and absorptive characteristics of the layer  52 . The geometric center of the thermal shield ( 27 ) is now offset from the center of pressure. The change in the absorptive, reflective and emissive characteristics of the shield  28  as the angle of the sunlight changes relative to the shield  28 , changes the combinal force vector ( 44 ) in a desirable manner aligning it through the center of mass  24 . Particularly, the specularly reflected photons on one side of the shield  28  produce larger forces than those on the other side. Also, the Lambertian emission on one side of the shield  28  is greater than the Lambertian emission on the opposite side of the shield  28  as a result of the change in the absorptive and emissive characteristics. This has the desirable effect of changing the resultant force vectors so that the effective force vector  44  is maintained through the spacecraft center of mass  24 . 
     Force vector  80  represents a decreased reflective force vector due to high solar absorption, force vectors  82  represent an increased radiative force vector due to high solar absorption and thermal reradiation, with non-Lambertian directional distribution. Force vector  84  represents the direct incident force vector on the sun side of the shield  28 . On the other side of the shield  28 , the force vector  88  represents an increased reflective force vector due to low solar absorption, and the force vectors  90  represent a decreased radiative force vector due to low solar absorption and thermal re-radiation, with non-Lambertian distribution. Force vector  92  represents the direct incident force vector on the sun side of the shield  28 . This gives rise to the net effective force vector  44  on the thermal shield  28 . 
     A spacecraft can lose attitude control from system failures for a number of reasons. When this happens, it is generally desirable to orient the spacecraft to a safe-hold attitude where the solar arrays are pointed towards the sun. In this “safe mode”, the reaction wheels are typically turned off to conserve power. Usually, sun sensors are used to get attitude measurements with respect to the sun line, and thrusters are used as control actuators to maintain this orientation. It would be desirable to provide a passive means for S/C attitude control to provide and maintain a sun-pointing orientation. The discussion above with respect to eliminating solar torque by passively controlling the shield&#39;s effective center of solar pressure  26 A location with respect to the spacecraft center of mass  24  can be extended to passive attitude control for solar pointing purposes. 
       FIG. 10  is a simplified schematic of a spacecraft  100  including a spacecraft bus  102  and solar arrays  104  and  106 . The spacecraft body-axes are designated by the coordinate system x b , y b , z b . The inertial orientation of the spacecraft  100  is shown relative to an x i , y i , and z i -axis inertial coordinate system. 
     The spacecraft  100  further includes a plurality of solar torque control vanes extending from the arrays  104  and  106 , including two x b -axis control vanes  110  and a y b -axis control vane  112  extending from the solar panel  104 , and two x b -axis control vanes  114  and a y b -axis control vane  116  extending from the solar array  106 . In one embodiment, the control vanes  110 – 116  are Kapton blankets covered with a directionally emissive and reflective film of the type discussed above. The use of the control vanes  110 – 116  at the ends of the solar arrays  104  and  106  is by way of a non-limiting example, in that the control vanes as discussed herein can be placed at other suitable locations on the spacecraft  100 . For example, control surfaces can be formed on the spacecraft surfaces themselves. 
       FIG. 11  is a broken-away, cross-sectional view of the y b -axis control vanes  112  and  116 . The x b -axis control vanes  110  and  114  would be similar to the y b -axis control vanes  112  and  116 , except they would be rotated by 90° relative to the z b -axis. The control vanes  110 – 116  can be an embossed film on an multi-layer insulation blanket  118 . In this embodiment, the control vanes  112  and  116  include an embossed film  120  including segments  122  on one side of the layer  118 , and an embossed film  124  including segments  126  on the other side of the layer  118 . As above, the long side of each segment  122  and  126  is formed with a white or reflective material and the short side of each segment  122  and  126  is formed with a black or absorptive material. 
     In this embodiment, the orientation of the films  120  and  124  are opposite to each other, as shown. Particularly, the film  120  is oriented on the control vanes  112  and  116  so that the short sides of the segments  122  oppose each other, and the film  124  is oriented on the control vanes  112  and  116  so that the long sides of the segments  126  oppose each other. As with the control surface on the thermal shield, different reflective materials and configurations can be used on the control vanes  110 – 116  to provide the desired reflectivity and emissivity characteristics. 
     The orientation of the spacecraft  100  relative to the inertial coordinate system can be changed depending on the absorptivity, reflectivity and emissivity of the control vanes  110 – 116 .  FIG. 12  is a torque stability diagram for a spacecraft bus  130  and solar arrays  132  and  134  representing the spacecraft  100  above. If the spacecraft systems failed, it would typically be desirable to orient the spacecraft in the safe-hold attitude, where the solar arrays  132  and  134  would be pointed towards the sun line. The spacecraft bus  130  would be designed so that if the sun line was pointed towards the spacecraft bus  130  from the direction represented by arrow  136 , a torque balanced configuration results which yields zero net solar torque on the spacecraft bus  130  which keeps the spacecraft bus  130  pointing towards the sun. If the sun line is directed along arrow  144 , the control vanes on the −x b  solar array wing would appear more reflective than those on the +x b  solar array wing resulting in a stability control torque on the spacecraft bus  130  about its y b -axis in the counter-clockwise direction. This in effect rotates the spacecraft z b -axis back towards the sun line direction and causes the spacecraft bus  130  to rotate towards the equilibrium attitude (i.e., aligned with sun line). If the spacecraft bus  130  is pointed in a direction so that the sun line is aligned with arrow  146 , the opposite effect occurs. In other words, the generated solar torque from small offset angles would tend to reorient the z b -axis to the sun. 
     If the sun line is aligned with any direction of the arrows  138 ,  140 ,  142 ,  148  and  150 , the spacecraft attitude is unstable, and the control vanes  110 – 116  will produce control torques which rotate the spacecraft bus  130  back to the stable equilibrium attitude in which the z b -axis is aligned with the sun line (i.e., as identified by the arrow  136 ). Because the embossed film on the −z b  side of the control vanes  110 – 116  is oriented opposite to the embossed film on the +z b  side of the control vanes  110 – 116 , the opposite effect occurs when the sun line is coming from the directions  148  or  150  as for directions  144  or  146 , causing the z b -axis of the spacecraft bus  130  about to rotate back to the only stable direction (i.e., aligned with sun line). The x b -axis control vanes  110  and  114  provide control torques about the S/C x b -axis which causes rotation of the spacecraft bus  130  about the x b -axis to align the z b -axis with the sun line. 
     The foregoing discussion describes merely exemplary embodiments of the present invention. One skilled in the art would readily recognize that various changes, modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims.