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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

The equations of motion of an artificial satellite in nonsingular variables

The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power of r/r prime; r prime being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the moon or sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.

Giacaglia, G. E. O.↗
NASA NTRS1975

Solutions of the motion of synchronous satellites with arbitrary eccentricity and inclination

A first order, semianalytical theory for the long term motion of resonant satellites is presented. The theory is valid for all eccentricities and inclinations and for all commensurability ratios. The method allows the inclusion of all the zonal and tesseral harmonics as well as luni solar perturbations and radiation pressure. The method is applied to a synchronous satellite including only the J sub 2 and J sub 22 harmonics. Global, long term solutions for this problem, eccentricity, argument of perigee, and inclination are obtained.

Nacozy, P. E.↗
NASA NTRS1976

Optimal perturbation models for averaged orbit generation

Averaging techniques applied to the variation of parameters (VOP) formulation of the equations of motion are being investigated as methods for long-term prediction of artificial satellite orbits. Analytically averaged equations were compared with numerically averaged equations with respect to accuracy and efficiency for computation of zonal and nonresonant third-body perturbations. Numerically averaged equations were also evaluated for computation of long-period effects from resonant third-body, tesseral harmonic, and atmospheric drag perturbations. Guidelines will be presented for application of averaged VOP equations to a broad class of orbits.

Long, A. C.↗
NASA NTRS1977

The equations of motion of an artificial satellite in nonsingular variables

The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power of r/r', r' being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the moon or sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.

Giacaglia, G. E. O.↗
NASA NTRS1980

A semianalytical satellite theory for weak time-dependent perturbations

The modifications of the semianalytical satellite theory required to include these 'weak' time dependent perturbations are described. The new formulation results in additional terms in the short periodic variations but does not change the averaged equations of motion. Thus the m monthly terms are still included in the averaged equations of motion. This contrasts with the usual approach for the strongly time dependent perturbations in which the m monthly (or m daily, if tesseral harmonics are being considered) terms would be eliminated from the averaged equations of motion and included in the short periodics computation. Numerical test results for the GPS case obtained with a numerical averaging implementation of the new theory demonstrate the accuracy improvement.

Cefola, P.↗
NASA NTRS1981

Orbit improvement of the satellites of the outer planets

Data reduced from 127 plates showing Jupiter's and Saturn's satellites in the interval 1972 to 1974 are available on computer cards in the form of (O-C) residuals. Initial orbit calculations and several later orbit improvements for Jupiter XIII (Leda) culminated in an extended ephemeris for Leda to the year 2000. The possible existence of several small satellites just outside Saturns rings was predicted. De Sitter's incomplete theory for the motion of the Galilean satellites was reviewed and an outline for a revised, complete theory was developed. Observations of nearly 100 relative positions of the Galilean satellite with a mean accuracy of about 100 km (0.03 arc sec) were used to improve Sampson's theory for these satellites. Results were published on (1) a long term upper limit to Jupiter's orbital eccentricity; (2) deviation of an accurate modern value of the ellipticity of Uranus from balloon-borne images and consequent evaluation of the planet's rotation rate; and (3) identification of features in Saturn's rings as produced by heretofore undetected tesseral harmonics of Saturn's gravitational field.

Aksnes, K.↗
NASA NTRS1982

Long-term motion of resonant satellites with arbitrary eccentricity and inclination

A first-order, semi-analytical method for the long-term motion of resonant satellites is introduced. The method provides long-term solutions, valid for nearly all eccentricities and inclinations, and for all commensurability ratios. The method allows the inclusion of all zonal and tesseral harmonics of a nonspherical planet. We present here an application of the method to a synchronous satellite including J2 and J22 harmonics. Global, long-term solutions for this problem are given for arbitrary values of eccentricity, argument of perigee and inclination.

Nacozy, P. E.↗
NASA NTRS2019

Stability and Spin-Orbit Resonance Analysis of Low Altitude Martian Orbits

Orbit stability has been thoughtfully studied in various celestial bodies. In particular the focus has been placed on the Moon, due to the unstable natural perturbations of its gravity field. The increasing interest in Mars orbiters brings the question of the likelihood of natural decay in low altitude regimes. This paper studies the change in shape of low altitude Mars orbits by carrying out large sets of numerical high fidelity simulations. Results showed that various configurations of the orbital elements gave perturbations that result-ed in unstable orbits. The paper also studies the potential causes of the observed unstable regions. First by taking a close look at zonal and tesseral harmonics to find the implications of Mars mass concentrations of the used gravity fields, and second by computing theoretical spin-orbit resonances to study their implications in the stability at low altitudes.

gravity perturbations↗
NASA NTRS1966

Satellite orbit studies

Earth-satellite orbits in resonance with tesseral perturbation, and motion near earth-moon libration point

TESSERAL HARMONICS↗
NASA NTRS1975

Long period nodal motion of sun synchronous orbits

An approximative model is formulated for assessing these perturbations that significantly affect long term modal motion of sun synchronous orbits. Computer simulations with several independent computer programs consider zonal and tesseral gravitational harmonics, third body gravitational disturbances induced by the sun and the moon, and atmospheric drag. A pendulum model consisting of evenzonal harmonics through order 4 and solar gravity dominated nodal motion approximation. This pendulum motion results from solar gravity inducing an inclination oscillation which couples into the nodal precession induced by the earth's oblateness. The pendulum model correlated well with simulations observed flight data.

Duck, K. I.↗
NASA NTRS1983

Inference of variations in the gravity field from satellite-to-satellite range rate

An analytic scheme for inferring variations of the gravity field from satellite-to-satellite range rate (low-low) is developed. As a test, it is applied to a pair of satellites in polar orbit, at altitude 160 km and spacing 100 km, with 72 data points per revolution. An assumed gravity field of tesseral spherical harmonics up to the eighth degree is completely recovered in three iterations over 64 revolutions. It is apparent that data points at regular intervals enable the use of data analysis techniques that avoid massive matrix inversions.

Kaula, W. M.↗
NASA NTRS1976

Expansion of the gravitational potential with computerized Poisson series

The paper describes a recursive formulation for the expansion of the gravitational potential valid for both the tesseral and zonal harmonics. The expansion is primarily in rectangular coordinates, but the classical orbit elements or equinoctial orbit elements can be easily substituted. The equations of motion for the zonal harmonics in both classical and equinoctial orbital elements are described in a form which will result in closed-form expressions for the first-order perturbations. In order to achieve this result, the true longitude or true anomaly have to be used as independent variables.

Broucke, R.↗