| 摘 要： | Given the second radial derivative Vr r ( P ) |S of the Earth’s gravitational potential V ( P ) on the surface S corresponding to the satellite altitude, by using the fictitious compress recovery method, a fictitious regular harmonic field rrVr r( P )* and a fictitious second radial gradient field Vr *r ( P) in the domain outside an inner sphere K i can be determined, which coincides with the real field Vr r( P ) in the domain outside the Earth. Vr *r ( P)could be further expressed as a uniformly convergent expansion series in the domain outside the inner sphere, because rrVr r( 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. Preliminary simulation calculations show that the second radial gradient field Vr r( P ) could be recovered based only on the second radial derivative Vr r ( P )| S given on the satellite boundary. Concerning the final recovery of the potential field V ( P ) based only on the boundary value Vr r ( P )|S, the simulation tests are still in process.
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