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Collision frequency of artificial satellites - The creation of a debris belt

As the number of artificial satellites in earth orbit increases, the probability of collisions between satellites also increases. Satellite collisions would produce orbiting fragments, each of which would increase the probability of further collisions, leading to the growth of a belt of debris around the earth. This process parallels certain theories concerning the growth of the asteroid belt. The debris flux in such an earth-orbiting belt could exceed the natural meteoroid flux, affecting future spacecraft designs. A mathematical model was used to predict the rate at which such a belt might form. Under certain conditions the belt could begin to form within this century and could be a significant problem during the next century. The possibility that numerous unobserved fragments already exist from spacecraft explosions would decrease this time interval. However, early implementation of specialized launch constraints and operational procedures could significantly delay the formation of the belt.

Donald J Kessler

On the Tesseral-Harmonics Resonance Problem in Artificial-Satellite Theory, Part 2

Equations were derived for the perturbations on an artificial satellite when the motion of the satellite is commensurable with that of the earth. This was done by first selecting the tesseral harmonics that contribute the most to the perturbations and then by applying Hori's method by use of Lie series. Here, are introduced some modifications to the perturbations, which now result in better agreement with numerical integration.

Romanowicz, B. A.

The Effect of Solar Radiation Pressure on the Motion of an Artificial Satellite

The effects of solar radiation pressure on the motion of an artificial satellite are obtained, including the effects of the intermittent acceleration which results from the eclipsing of the satellite by the earth. Vectorial methods have been utilized to obtain the nonlinear equations describing the motion, and the method of Kryloff-Bogoliuboff has been applied in their solution.

Bryant, Robert W.

Lunar perturbations of artificial satellites of the earth

The disturbing function for the lunar perturbations of an artificial satellite are derived, using ecliptic elements for the moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the earth. The results can then be applied to numerical integration by using coordinates of the moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the moon's motion represented by a precessing and rotating elliptical orbit.

Giacaglia, G. E. O.

Third-order solution of an artificial-satellite theory

A third-order solution was developed for the motions of artificial satellites moving in the gravitational field of the earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations were derived by the Hori perturbation method. All quantities were expanded into power series of the eccentricity, but the solution was obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth, small-eccentricity satellite with an accuracy of better than one cm over a period of one month.

Kinoshita, H.

Third-order solution of an artificial-satellite theory

A third-order solution is developed for the motions of artificial satellites moving in the gravitational field of the earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations are derived by Hori's perturbations method. All quantities are expanded into power series of the eccentricity, but the solution is obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth satellite with a small eccentricity with an accuracy of better than 1 cm over 1 month.

Kinoshita, H.

Development of the Lunar and Solar Perturbations in the Motion of an Artificial Satellite

Problems relating to the influence of lunar and solar perturbations on the motion of artificial satellites are analyzed by an extension of Cayley's development of the perturbative function in the lunar theory. In addition, the results are modified for incorporation into the Hansen-type theory used by the NASA Space Computing Center. The theory is applied to the orbits of the Vanguard I and Explorer VI satellites, and the results of detailed computations for these satellites are given together with a physical description of the perturbations in terms of resonance effects.

Musen, P.

The Theory of Artificial Satellites in Terms of the Orbital True Longitude

The author's previous theory of the artificial satellite is derived in terms of the. disturbed eccentric anomaly. The present development, in terms of the orbital true longitude, is a substantial improvement over the earlier work in that it leads to the faster convergence for large eccentricities and to a smaller number of terms in the series representing the perturbations. Moreover, each approximation of the radius vector and of the parameters determining the position of the orbit plane is obtained not in the form of a truncated infinite series but in the form of trigonometric polynomials in two arguments. These arguments are the mean true anomaly and the mean argument of the latitude. The present theory, like the previous one, permits the computation of perturbations of any desired order. Thus, any future information about earth's gravitational field can easily be included.

Musen, Peter

The Influence of the Solar Radiation Pressure on the Motion of an Artificial Satellite

This article reports an investigation of the effect of solar radiation pressure on the motion of an artificial satellite. The theory has been applied to the orbit of the Vanguard I satellite, and is found to produce significant perturbations in the perigee height of that satellite. In the case of a satellite with a large ratio of area to mass the major terms introduced by solar radiation pressure can reduce the perigee distance at the rate of 1 to 2 km per day, so that the lifetime of the satellite will become considerably shorter than it would be without this effect.

Musen, Peter

Investigations of the ionospheric using radio signals from artificial satellites

The occurrence and characteristics of ionospheric irregularities in medium latitudes and in polar regions were measured using radio signals from artificial satellites. Ionospheric changes during quiet and disturbed conditions were also measured. Electron density, elevation angle, and amplitude and frequency of these high frequency signals were determined as well as the direction of their arrival.

Titheridge, J. E.