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Recent advances in analytical satellite theory

Recent work on analytical satellite perturbation theory has involved the completion of a revision to 4th order for zonal harmonics, the addition of a treatment for ocean tides, an extension of the treatment for the noninertial reference system, and the completion of a theory for direct solar-radiation pressure and earth-albedo pressure. Combined with a theory for tesseral-harmonics, lunisolar, and body-tide perturbations, these formulations provide a comprehensive orbit-computation program. Detailed comparisons with numerical integration and observations are presented to assess the accuracy of each theoretical development.

Gaposchkin, E. M.↗

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Liu, J. J. F.↗

Flight Mechanics/Estimation Theory Symposium

Methods of determining satellite orbit and attitude parameters are considered. The Goddard Trajectory Determination System, the Global Positioning System, and the Tracking and Data Relay Satellites are among the satellite navigation systems discussed. Satellite perturbation theory, orbit/attitude determination using landmark data, and star measurements are also covered.

Fuchs, A. J.↗

An economical semi-analytical orbit theory for micro-computer applications

An economical algorithm is presented for predicting the position of a satellite perturbed by drag and zonal harmonics J2 through J4. Simplicity being of the essence, drag is modeled as a secular decay rate in the semimajor axis (retarded motion) with the zonal perturbations modeled from a modified version of Brouwers formulas. The algorithm is developed as an alternative on-board orbit predictor; a back up propagator requiring low energy consumption; or a ground based propagator for microcomputer applications (e.g., at the foot of an antenna). An O(J2) secular retarded state partial matrix (matrizant) is also given to employ with state estimation. The theory has been implemented in BASIC on an inexpensive microcomputer, the program occupying under 8K bytes of memory. Simulated trajectory data and real tracking data are employed to illustrate the theory's ability to accurately accommodate oblateness and drag effects.

Gordon, R. A.↗

An economical semi-analytical orbit theory for micro-computer applications

An economical algorithm is presented for predicting the position of a satellite perturbed by drag and zonal harmonics J sub 2 through J sub 4. Simplicity being of the essence, drag is modeled as a secular decay rate in the semi-axis (retarded motion); with the zonal perturbations modeled from a modified version of the Brouwers formulas. The algorithm is developed as: an alternative on-board orbit predictor; a back up propagator requiring low energy consumption; or a ground based propagator for microcomputer applications (e.g., at the foot of an antenna). An O(J sub 2) secular retarded state partial matrix (matrizant) is also given to employ with state estimation. The theory was implemented in BASIC on an inexpensive microcomputer, the program occupying under 8K bytes of memory. Simulated trajectory data and real tracking data are employed to illustrate the theory's ability to accurately accommodate oblateness and drag effects.

Gordon, R. A.↗

Heating of galactic disks by mergers

The paper considers dynamical aspects of mergers between disks and small satellite companions, with special attention given to: the self-consistent response of disks to satellite mergers, which generalizes an earlier investigation by Quinn & Goodman (1986); the evolution of satellite orbits and debris; and the long-term structure and kinematics of thickened disks as compared with observed properties of disk galaxies. For satellites with masses in the range 0.04-0.2 M sub disk on initially circular inclined prograde orbits merging with disks similar to the thin disk of the Galaxy, it is found that the dynamical coupling between disks and satellites leads to orbital decay. Disks respond to mergers by spreading both radially and vertically. The radial heating is driven largely by the spiral response of the dynamically cool disks to satellite perturbations.

Quinn, P. J.↗

Meteoroid Bulk Density and Ceplecha Types

Determination of asteroid bulk density is an important aspect of NEO characterization, yet difficult to measure. As a fraction of meteoroids originate from asteroids (including some NEOs), a study of meteoroid bulk densities can potentially provide useful insights into the densities of NEOs and PHOs in lieu of mutual perturbations, satellite, or expensive spacecraft missions. NASA's Meteoroid Environment Office characterizes the meteoroid environment for the purpose of spacecraft risk and operations. To accurately determine the risk, a distribution of meteoroid bulk densities are needed. This is not trivial to determine. If the particle survives to the ground the bulk density can be directly measured, however only the most dense particles land on the Earth. The next best approach is to model the meteor's ablation, which is not straightforward. Clear deceleration is necessary to do this and there are discrepancies in results between models. One approach to a distribution of bulk density is to use a measured proxy for the densities, then calibrate the proxy with known densities from meteorite falls, ablation modelling, and other sources. An obvious proxy choice is the Ceplecha type, K(sub B), thought to indicate the strength of a meteoroid. KB is frequented cited as a good proxy for meteoroid densities, but we find it is poorly correlated with density. However, a distinct split by dynamical type was seen with Jovian Tisserand parameter, T(sub J), with meteoroids from Halley Type comets (T(sub J less than 2 ) exhibiting much lower densities than those originating from Jupiter and asteroids (T(sub J greater than 2).

Blaauw, R. C.↗

Meteoroid Bulk Density and Ceplecha Types

The determination of asteroid bulk density is an important aspect of Near Earth Object (NEO) characterization. A fraction of meteoroids originate from asteroids (including some NEOs), thus in lieu of mutual perturbations, satellites, or expensive spacecraft missions, a study of meteoroid bulk densities can potentially provide useful insights into the densities of NEOs and PHOs (Potentially Hazardous Objects). Meteoroid bulk density is still inherently difficult to measure, and is most often determined by modeling the ablation of the meteoroid. One approach towards determining a meteoroid density distribution entails using a more easily measured proxy for the densities, then calibrating the proxy with known densities from meteorite falls, ablation modelling, and other sources. An obvious proxy choice is the Ceplecha type, KB (Ceplecha, 1958), which is thought to indicate the strength of a meteoroid and often correlated to different bulk densities in literature. KB is calculated using the air density at the beginning height of the meteor, the initial velocity, and the zenith angle of the radiant; quantities more readily determined than meteoroid bulk density itself. Numerical values of K(sub B) are sorted into groups (A, B, C, etc.), which have been matched to meteorite falls or meteor showers with known composition such as the porous Draconids. An extensive survey was conducted to establish the strength of the relationship between bulk density and K(sub B), specifically looking at those that additionally determined K(sub B) for the meteors. In examining the modeling of high-resolution meteor data from Kikwaya et al. (2011), the correlation between K(sub B) and bulk density was not as strong as hoped. However, a distinct split by dynamical type was seen with Jovian Tisserand parameter (T(sub J)), with meteoroids from Halley Type comets (T(sub J) < 2) exhibiting much lower bulk densities than those originating from Jupiter Family comets and asteroids (T(sub J) > 2). Therefore, this work indicates that the dynamical classification of a meteoroid is a better indicator of the density than the strength proxy, a somewhat surprising result.

Blaauw, R. C.↗

Investigation of environmental perturbations on passive asymmetric satellite

The effects of environmental perturbations on the attitude of a slow tumbling earth-oriented satellite are investigated. The environmental perturbations considered were aerodynamic drag, gravity-gradient, solar radiation pressure, and magnetic torques. The Euler attitude equations were solved numerically for the Skylab spacecraft. Results are presented for both torque-free motion and for cases in which aerodynamic and gravity-gradient torques are acting in a slow tumble mode. Simulations show gravity-gradient effects on satellite momentum to be cyclic and to increase the precession rate of the angular momentum vector about the radius vector. This also tends to align the minor axis along the radius vector. Aerodynamic drag initially decreases angular momentum, slowly precesses the momentum vector about the radius vector, and finally drives the satellite into an unstable mode. Combined gravity-gradient and aerodynamic torques reduce angular momentum and energy, and induce a steady precession rate of the momentum vector about the radius vector.

Tate, V.↗

A semi-analytical method of computation of oceanic tidal perturbations in the motion of artificial satellites

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.

Musen, P.↗

The variations in eccentricity and apse precession rate of a narrow ring perturbed by a close satellite

The first-order perturbations of orbital eccentricity and apse precession rate for the case of a narrow ring, due to a close satellite whose orbit is also eccentric, are described by means of a Hamiltonian. The present treatment covers cases in which the satellite crosses the ring, and the level curves of the Hamiltonian are displayed for several parameter values. The results obtained are applied to the interaction of Saturn's F ring with its inner shepherd satellite.

Borderies, N.↗

Tidal perturbations on the satellite 1967-92A

The orbit of the 1967-92A satellite has been studied to ascertain the extent to which tidal forces contribute to orbital perturbations. This study has permitted an estimation of the magnitudes of ocean tide effects on the satellite's inclination, in particular for the M sub 2 and S sub 2 constituents. The ocean tide estimates are based upon the use of a value of 0.3 for the solid earth tide Love number and a lag angle of zero deg in the orbit determination procedure. The amplitudes and phases of these tidal effects are in good agreement with those calculated from numerical models of the tidal parameters derived from surface data.

Felsentreger, T. L.↗

Tidal perturbations on the satellite 1967-92A

The orbit of the 1967-92A satellite was studied to ascertain the extent to which tidal forces contribute to orbital perturbations. Parameters describing the ocean tide potential-in particular for the M2 and S2 constituents-were estimated. Since the ocean tide potential is less well known than the solid Earth tide, the ocean tide parameter estimation is based upon the use of a value of 0.3 for the solid Earth tide Love number in the orbit determination procedure. These tidal parameter values are in good agreement with those appearing in numerical models of the M2 and S2 tides derived from surface data.

Felsentreger, T. L.↗

Analytic short period lunar and solar perturbations of artificial satellites

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.

Fisher, D.↗

Analytic short period lunar and solar perturbations of artificial satellites.

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.

Fisher, D.↗

Secular perturbations of the Uranian satellites - Theory and practice

A simple revised secular perturbation theory which incorporates the averaged secular effect of first-order near-resonances is derived. By including the effects of these near-resonances, the largest error in the secular frequencies is reduced from 16 percent to less than 3 percent. It is concluded that the revised secular perturbation theory is adequate for the quantitative modeling of the long-term perturbations in the Uranian satellite system. If incorporated within the general theory of Laskar (1986), this theory would lead to completely analytic theory.

Malhotra, R.↗