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Saturn’s largest satellite, Titan, transited the Crab Nebula on 5 January 2003. We observed this astronomical event with the {\it Chandra} X-ray Observatory. An ``occultation shadow’’ has clearly been detected and is found to be larger than the diameter of Titan’s solid surface. The difference gives a thickness for Titan’s atmosphere of 880 60 km. This is the first measurement of Titan’s atmospheric extent at X-ray wavelengths. The value measured is consistent with or slightly larger than those estimated from earlier Voyager observations at other wavelengths. We discuss the possibility of temporal variations in the thickness of Titan’s atmosphere.

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