To: sea_urchin who wrote (120 ) 1/25/2005 4:10:21 AM From: GUSTAVE JAEGER Respond to of 418 Re: So don't worry about the shadow -- even though the picture was most likely taken in the Western Sahara! Did you check the MOC Image Gallery? Click on the link and you'll see that they (MOC operators) claim to have shot over 175,000 pictures of Mars!!!! I tell you: those pics from Titan are actually inedited Martian pics that were uploaded to Cassini by NASA --and subsequently sent back as "Titan pics".... As far as I'm concerned, I wasn't suspicious so much about the "shadow/ghost" as about the narrowness of the picture --the way it was trimmed edgewise... My point being that, given a wide enough picture, it's possible to calculate the radius of the planet where the picture was shot....(*) Gus (*) Limits of Precision A spherical object appears as an elliptical, parabolic or hyperbolic outline on a movie frame. In theory it is straightforward to measure five different points on that outline, calculate the coefficients of the conic section, and infer the field of view and the 3D position of the sphere in units of its radius. In practice there are several possible sources of difficulty, imprecision and ambiguity in the measurements or in the inference. Firstly, the image does not contain spatial information finer than a pixel. Therefore it is impossible to pick sample points more precisely than within one pixel inside or outside the ideal horizon curve. Uncertainties will propagate into the inferred conic coefficients and thence to the derived parameters of the sphere. Secondly, the horizon may not be completely measurable. In the best possible scenario, we can pick measurement points that are roughly evenly spaced on all sides of an ellipse. Both the semimajor and semiminor axes are well constrained from both the left and right (top and bottom) sides. However if one side of the globe falls off the edge of the image, or is invisible because of obstruction or shadow, then that side is poorly constrained. The inferred ellipse has a lot of scope for variation in the direction of the unmeasured side, for very tiny deviations on the choices of reference points in the measurable sides. In the worst possible cases, the majority of the horizon is off the edge of the screen and we can only measure a tiny angular arc, which appears almost straight. The axes of the curve become practically unmeasurable, and even the type of conic section may be indeterminate. Attempts to read the local radius of curvature are misleading and provide neither upper nor lower limits, because the field of view is unknown and the aspect ratio of the ellipse/hyperbola is unknowable. As the camera tilts away from a sphere, the area and eccentricity of the onscreen ellipse both increase. An image that is tilted far offscreen is thus magnified and distorted compared to the appearance it would have when centred in the field. When only a small, flat arc is visible and the field of view is unknown then the distortion and magnificiation are inestimable. Circular approximations are only useful when the disk is entirely within the field of view and close to the centre of frame. If the disk is measurably indistinguishable from a circle then we automatically know that the sphere is close to the line of sight and the field of view is narrow.