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Analytic formulations for satellite perturbations due to solar radiation pressure and lunar and solar gravitational forces
Formulas for long term perturbations of satellite components due to high order zonal harmonics
Position determination from simultaneous observation of Pageos and Geos 2 satellites, assuming known covariance matrix and applied corrections
Center of mass small displacement effects on satellite orbits by solving variational equations for scalar potential function employing matrix formalism
Atmospheric densities from satellite drag data
Calculation of Lagrange planetary equations derived in form suitable for satellites of arbitrary eccentricity
Seasonal variations in geopotential and effect on long period variations in orbital elements of satellites
Martian atmospheric temperature and pressure and temperature gradient determination by least squares differential correction of satellite photometric solar eclipse data
A short period luni-solar theory was generalized for application to arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements were derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.
Laser ranges to the Beacon Explorer C spacecraft from a single Goddard Space Flight Center tracking system were used to determine the change in latitude of the station arising from polar motion. A precision of 0.03 arcsecs rms was obtained for the latitude during a five-month period in 1970.
By reformulating Brouwer's first-order satellite theory in terms of the Hill variables, it is demonstrated that these variables possess several advantages over the Delaunay variables. The final algorithm is simpler and more compact, there is no singularity at zero eccentricity, and the process of deriving the perturbations is considerably simplified. An algorithm for the computation of position and velocity is presented which is significantly simpler and faster in use than Brouwer's algorithm. Moreover, whereas the latter algorithm breaks down for circular and equatorial orbits, the present one holds for all eccentricities less than one and for all inclinations, with the exception of the critical inclination.
The matrizant of the two-body problem is developed in terms of elements that are free from singularities for zero eccentricities and zero- and ninety-degree inclinations. Retrograde equinoctial elements eliminate the singularity for inclinations near 180 degrees, with only minor changes in the expressions for the matrizant. The 'single-averaged' variation-of-parameters equations for these elements are developed for third-body, oblateness, and drag effects. Higher order terms are included in the expansions for the third-body and oblateness potential. A computer program that uses these equations to predict orbital evolution is described. Numerical results are given for a near-circular orbit.
The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorial elements of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal 'waves' over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the 'global' Love numbers for the Earth.
The method of expansion of the satellite's perturbations, as caused by the oceanic tides, into Fourier series is discussed. The coefficients of the expansion are purely numerical and peculiar to each particular satellite. Such a method is termed as semi-analytical in celestial mechanics. Gaussian form of the differential equations for variation of elements, with the right hand sides averaged over the orbit of the satellite, is convenient to use with the semi-analytical expansion.
Measurements of the range to the Beacon Explorer C spacecraft from a single laser tracking system at Goddard Space Flight Center have been used to determine the change in latitude of the station arising from polar motion. A precision of 0.03 arc second was obtained for the latitude during a 5-month period in 1970.
Very-long-baseline interferometric observations of radio signals from the TACSAT synchronous satellite, even though extending over only 7 hours, have enabled an excellent orbit to be deduced. Precision in differential delay and delay-rate measurements reached 0.15 nanosecond and 0.05 picosecond per second, respectively. The results from this initial three-station experiment demonstrate the feasibility of using the method for accurate satellite tracking and for geodesy.
The short period luni-solar theory of Kozai is generalized for arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements are derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.
Survey of averaging and multirevolution methods for long-term orbit prediction. A technical approach with the following features is recommended: (1) averaged variation-of-parameter equations, (2) analytical expressions for oblateness and third-body effects, (3) definite integrals for atmospheric drag and lunar effects (for long-period orbits), (4) nonsingular equinoctial element formulation, (5) multistep numerical integration processes, and (6) precise osculating-to-mean element transformation. Several orbital predictions illustrate the contribution of this technical approach to overall accuracy and efficiency. Future development of the analytical averaging method in nonsingular coordinates by automated manipulation of literal series is discussed.