Engineering topics
Publications and source records attributed to Liu, A. S..
Radio metric data from the Pioneer 10/11, Galileo, and Ulysses Spacecraft indicate an apparent anomalous, constant, acceleration acting on the spacecraft with a magnitude ~8.5 x 10(sup -8) cm/s(sup 2), directed towards the Sun.
The mathematical theory of the nutation of Mars is derived by classical rigid-body dynamics. The effect of nutation is to produce a 26-m maximum horizontal amplitude oscillation (at the surface of Mars) with a period of half a Martian year. This effect should be detectable in the Viking-Lander data.
When the radio link between two satellites (GEOS-3/ATS-6) is intercepted by the earth's ionosphere and neutral atmosphere, a change in the Doppler frequency results. Travel through the atmosphere causes the Doppler phase to be advanced in the ionosphere's portion and retarded in the neutral portion of the atmosphere. Analysis of the shortening and lengthening of the phase of the Satellite-to-Satellite Tracking (SST) data that passed within 40-700 km above the earth's surface during its ATS-6 to GEOS-3 to ATS-6 path, caused by the atmosphere, results in refractivity versus height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbation from the Moon, Sun and a 15th order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occultation period and a model ionosphere was estimated by a least-square adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the 2 methods were caused by orbital errors, which propagated into the solution. The SST data yielded refractive index profiles in a novel economical manner because no additional or special on-board equipment were required.
An analysis of the shortening and lengthening of the phase of satellite-to-satellite (SST) data that passed within 40-700 km above the earth surface during its ATS-6 to GEOS-3 to ATS-6 path resulted in refractivity vs height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbations from the moon, sun, and a 15th-order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occulation period and a model ionosphere was estimated by a least-squares adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the two methods were caused by orbital errors, which propagated into the solution.
Global lunar gravity field from weighted least squares analysis of Lunar Orbiters elements, deriving zonal and sectorial harmonics from libration data
Lunar gravity field global model from moon orbiters secular and long period trends, noting large anomaly on far side
Variational equations from Herrick variation of parameters method for Icarus encounter with earth
Estimate of Ranger 9 lunar probe flight path and method used for analyzing tracking data
Tracking accuracy prediction program designed for statistical analysis of preflight orbital determination problems
Flight path and tracking study of Ranger VII LUNAR probe