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For the hydrogen coma of comet P/Halley, both a Lyman-alpha image and extensive Lyman-alpha scan data obtained by the Pioneer Venus Orbiter Ultraviolet spectrometer as well as H-alpha ground-based spectral observations obtained by the University of Wisconsin Space Physics Group were successfully interpreted and analyzed with our Monte Carlo particle trajectory model. The excellent fit of the model and the Halley data and the water production rate determined near perihelion (9 Feb. 1986) from 13 Dec. 1985 to 13 Jan. 1986 and from 1 Feb. to 7 Mar. 1986 are discussed. Studies for the circumplanetary distribution of atomic hydrogen in the Saturn and Neptune systems were undertaken for escape of H atoms from Titan and Triton, respectively. The discovery of a new mechanism which can dramatically change the normal cylindrically symmetric distribution of hydrogen about the planet is discussed. The implications for the Titan-Saturn and Triton-Neptune are summarized.