Illustration of shadow hiding

Illustration of shadow hiding
Illustration of shadow hiding At the bottom is the ground on Ceres with greatly exaggerated crystals of salt pointing in random directions. (Shadow hiding occurs even with very small grains.) The white dashed lines show light from the sun, and each ray traces the light to the tip of a crystal and then to the point beyond. The solid black lines along the ground and the crystals are in shadow. That is, the incoming light cannot reach those places. Therefore, when Dawn is in the position on the right, looking along the same direction as the incoming light, it cannot see those shadows, because there is no line of sight to those hidden locations. In that special position, where Ceres is at opposition, every point on the ground Dawn sees is lit. When Dawn is in the position on the left, it does have a direct line of sight to some (although not all) shadows, as shown by the black dotted lines. Some of the ground it sees is lit and some is not. The difference between these two perspectives is the shadow-hiding component of the opposition surge. (Remember that these crystals are too tiny for Dawn to discern. One pixel in the explorer’s camera would take in this entire scene, so what matters is the total lit surface here, not the fine details.) Now at location 1, there are crystals that happen to point directly at Dawn when it is on the left, and at location 2, there are crystals that point directly at Dawn when it is on the right. You can see that at opposition, the shadows are hidden for both crystal orientations. But when Dawn is on the left, crystals pointing directly at it don’t provide a fully lit scene. Shadows are still visible. So, shadow hiding does not depend on any special alignment of crystals on the ground. It is the special observing location that matters. In summary, the ground appears brighter to Dawn when it is at opposition than when it is elsewhere. Although all crystals here are the same size, different crystal sizes may yield different shadowing and hence different opposition surge signatures. So, with a good measurement of the opposition surge, the crystal sizes may be determined. The self-portrait at right (biceps not to scale) is provided to illustrate your correspondent’s artistic skills. It should help you calibrate the fine details of the rest of the image. There are many simplifications here. In other words, take this diagram with a grain of sodium carbonate. NASA / JPL-Caltech

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