A procedure is given for deriving elevation-error and range-error correction equations in a form suitable for use in the rapid processing of satellite tracking data. The refractivity of the troposphere is assumed to have spherical symmetry, but may have any given profile that does not depart greatly from standard. When the procedure was tested for numerical accuracYby application to an exponential profile, the corrections calculated agreed with those obtained by ray tracing to 0.3% or better over a range of surface refractivity from 200 to 450 and a range of radiowave arrival angles from horizontal to vertical. and the straight-line distance or slant range is R. The range error is then the difference CORRECTION OF SATELLITE TRACKING DATA 225 Bean, B., and G. Thayer (1959), Models of the atmospheric radio refractive index, Proc. IRE, 47, 740-755. Blake, L. (1968), Ray height computation for a continuous nonlinear atmospheric refractive-index profile, Radio Sci., $(1), 85-92. Concus, P., D. Cassatt, G. Jaehnig, and E. Melby (1963), Tables for the evaluation of J'o • x•e-:I(x) dx by Gauss-Laguerre quadrature, Math. Computation, 17(83), 245-256. Freeman, J. (1962), Range-error compensation for a CORRECTION OF SATELLITE TRACKING DATA 23! troposphere with exponentially varying refractivity, J. Res. Nat. Bur. Stand. Sect. D, 66(6), 695-697. Hopfield, H. (1969), Two-quartic tropospheric refractivity profile for correcting satellite data, J. Geophys. Res., 74(18), 4487-4499. Hopfield, H. (1971), Tropospheric effect on electromagnetically measured range: prediction from surface weather data, Radio Sci., 6(3), 357-367. Lance, G. (1960), Ntgnerical Methods/or High Speed Computers, Iliffe and Sons Ltd., London. Marini, J. (1971), Closed form satellite tracking data corrections for an arbitrary tropospheric profile, Goddard Space Flight Center Rep. X-551-71-122. Reichley, P. (1967), The ray equation in the earth's atmos-phere, Jet Propulsion Lab. Space Programs Summary 37-43, IV, 314-321. Rowlandson, L., and R. Moldt (1969), Derivation of closed functions to compensate range and angle errors in an exponential atmosphere, Radio Sci., 4(10), 927-933. Thayer, G. (1961), A formula for radio ray refraction in an exponential atmosphere, J. Res. Nat. Bur. Stand. Sect. D, 65(2), 181-182. Thayer, G. (1967), A rapid and accurate ray tracing algorithm for a horizontally stratified atmosphere, Radio Sci.,

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Gi ven. the voltage distribution alonlS t he slot, expression s for t he radiation pattern , Inpu t adm Ittance, a nd t h e external effi clCncy of an insulated slo tted-s phere antenna surrounded by a homogeneous, isotropic, strongly ion ized sheath are obtained. At low frequen cies t he input impedan ce is propor t ion al to the sum of t h e in t rin sic impeda nce of t he sheath a nd an equiva lent indu ctance due to t he in sulating coating, t h e rad IatIon p at ter n redu ces to t hat of a s m all lo~p ,. while ~h e extern a l effi ciency is the produ ct of t hree factors lI:l"lSlll g because .o f .the power dISS Ipated JI1 t he sheath by higher order m odes t hat c~n tnbu te lIttle t? t h e rad iatIOn fi eld , atte nu ation t hrough t he s heath of t he modes that do radiate, a nd refl ectIOn loss of t h ese m odes at the ou ter s urface of t he sheath. . Sin ce t he r eflection loss. d ecreases wit h in cr eas in g fr equ en cy whi le t he attenu ation lll creases, t her e eXIsts a n op t Imum freq uency of operation. At t h is frequ ency, t he ioni zed sheath ha a t hickn ess equa l to two-a nd-one-ha lf s kin depths.

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