The linear diameter of the image disk at Earth is (p + a + t)R. A plot of the irradiance and its equivalent stellar magnitude for optimum conditions (k = 1) is shown in Figure 2 as a function of spacecraft range from Earth. The curve is parametric in rsacos(a/2) which represents the projected area of an equivalent perfect reflector and a/(p + a + t), which is the beam divergence factor. 3.1.2 Structure Characteristics The calculation of reflected solar intensity from the various satellite system elements requires description of the elements and description of the geometry of potential reflectance paths. To reduce the calculation to a tractable problem only the nominally flat element surfaces were considered since the curved surfaces spread the light making their contribution negligibly small at the large orbital distances. In addition, the curved surfaces were found to be a small fraction of the total reflection areas. Each surface is further defined by its approximate reflectivity and an estimate of its "flatness". In addition to determining that a surface is likely to reflect a significant intensity, it is also necessary to determine the conditions under which it will illuminate a portion of the earth. The orientation of each reflecting surface is therefore also necessary. To simplify the presentation of the element orientation,a number of convenient coordinate systems are used. The convention used was to define a coordinate system for each vehicle and to reference each element to that vehicle reference system. Each orientation can then be transformed to any other system such as a solar or an earth reference system, as may simplify a particular calculation. These data describing the reflecting elements are provided below in section 3.1.2.1. The reflected intensity is also dependent on the material properties and surface qualities of the reflecting surface. In section 3.1.2.2, the wavelength dependence of the reflectivity is presented for the several materials. The bidirectional reflectivity of the paint used on many surfaces is also provided.
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