3.1.3 Ground Illumination Reflected sunlight from Satellite Power System spacecraft is directed toward earth for prescribed vehicle orientations and orbit locations. Mathematical relationships that determine where these reflections will strike earth and how large an area is illuminated are presented in the first subsection. Calculations of ground irradiance for a variety of conditions where the illumination is bright are cited in the second subsection. 3.1.3.1 Geometrical Considerations In determining possible ground illumination, two cases are considered: 1) the reflecting surface rotates in orbit such that its orientation to the earth is constant (e.g., the satellite antenna) and 2) the orientation of the reflection surface to the sun is constant (e.g., the satellite solar arrays). Since in both cases the angle 0 is dependent only on the orbital altitude, it only remains to determine the relative values of angles a and 0 for the two cases. In the first case, it is seen that a is a constant, ac- As the reflecting surface orbits, therefore, only the value of 0 changes. From Figure 21 it is seen that the values of 0 for which reflected light will fall on the earth must be between ($ - «c) and ($ + ac): When the center of the earth is not in the plane defined by the incident and emergent light beams the above relationships remain valid as long as the value of $ is reduced accordingly. Once the orientation of a surface is found using the techniques of Section 3.1.1.1 it is a relatively simple matter to determine whether or not that surface will reflect the sun's light to the earth. Expressions for these angles may be determined from the following relationships.
RkJQdWJsaXNoZXIy MTU5NjU0Mg==