Given the second radial derivative Vrr(P)|σ S of the Earth's gravitational potential V(P) on the surface σS cor-responding to the satellite altitude,by using the fictitious compress recovery method,a fictitious regular harmonic field rrVrr(P)* and a fictitious second radial gradient field V*rr(P) in the domain outside an inner sphere Ki can be deter-mined,which coincides with the real field Vrr(P) in the domain outside the Earth.V*rr(P) could be further expressed as a uniformly convergent expansion series in the domain outside the inner sphere,because rrVrr(P)* could be expressed as a uniformly convergent spherical harmonic expansion series due to its regularity and harmony in that domain.In another aspect,the fictitious field V*(P) defined in the domain outside the inner sphere,which coincides with the real field V(P) in the domain outside the Earth,could be also expressed as a spherical harmonic expansion series.Then,the harmonic coefficients contained in the series expressing V*(P) can be determined,and consequently the real field V(P) is recovered.Prelimi-nary simulation calculations show that the second radial gradient field Vrr(P) could be recovered based only on the second radial derivative Vrr(P)|σ S given on the satellite boundary.Concerning the final recovery of the potential field V(P) based only on the boundary value Vrr(P)|σ S,the simulation tests are still in process.
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