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Moon MOON-SHADOW-5000-3.tif [1116/1120]
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Moon MOON-SHADOW-5000-3.tif [1117/1120]
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Moon MOON-SHADOW-5000-3.tif [1118/1120]
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Moon MOON-SHADOW-5000-3.tif [1119/1120]
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Moon MOON-SHADOW-5000-3.tif [1120/1120]
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Moon MOON-SHADOW-5000-3.tif [1143/1143]
M``T[```-.P``#3L```T[```-.P``#3L```T[```-.P``#3L```T[```-.P``
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#1127
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Moon MOON-SHADOW-5000-3.tif [0001/1120]
The line-of-sight distance (LOSD) formula is well known. The distance
to the horizon for any height, h, above a spherical body is d = sqrt(2*R*h + h^2) where d is distance to horizon and R is mean radius of the spherical body. Where h, d and R are all expressed in units of meters, the Earth horizon for a 1.7 meter tall observer at sea level, the horizon is at 4.65km. (R=6371km) For Luna, using R=1737.1, the horizon is 2.43km away for the same observer. Of course the length of a shadow is infinite at any point along the terminator but if the sun angle is known then h can be calculated for any object casting a finite shadow of length d on that body. If A is the sun angle with respect to a plane normal to the base of h, the length of the shadow would be proportional to R cos(A). Since the sun for all intents is infinitely far away from the moon compared to an observer on a crater rim, the line of sight from the rim to a point on the surface at the shadow edge can be considered to be on the line from the sun to the shadow. (Equivalent to the horizon for that observer looking away from the sun.) So if we can measure the length of the shadow at maximum extent, (minimum sun angle), before the shadow goes infinite or reaches the opposite rim, we can get a pretty good idea how high above the crater floor the rim would be. For a 1000 meter tall object, the LOSD is 58.92km. You can try it out here. http://newton.ex.ac.uk/research/qsys...ysics/horizon/ |
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