Orbit perturbation analysis of West Ford needles clusters

Abstract

Abstract. The West Ford package placed in orbit in 1963 contained almost 500 million copper dipoles. Due to a delay in releasing the needles in orbit a number of clusters of needles formed. Analysis of 34 years of mean orbital elements of 20 different clusters has revealed perturbations of 10 km or more in the semimajor axis due to direct solar radiation pressure, atmospheric drag, and Earth albedo pressure. The orbits have perigee heights ranging from 1500 km to 3600 km. A simplified Earth albedo model has been adopted to account for the long periodic perturbations observed in the semi-major axis. The periodic terms are a function of the sun and cluster nodal longitude angles. The atmospheric drag perturbation was modeled by extending the CIRA72 model atmosphere to heights above 2000 km. Cluster area-to-mass ratios were determined from fitting direct solar radiation pressure coefficients over 25 to 30 year data spans. Twenty to thirty year semi-major axis fits produced mean atmospheric density factors for hydrogen and helium for each cluster. These factors show a very high correlation with average perigee height. The results show that average hydrogen concentrations are from 3 to 5 times greater than given by the CIRA72 model. Helium concentrations also are from 1.5 to 4 times greater than predicted for these heights.

A New Empirical Thermospheric Density Model JB2006 Using New Solar Indices

“…The analysis method was described previously 22 from the long-term orbit perturbation analysis of West Ford needles' orbits. A semi-analytical integrator was developed using the perturbations in the semi-major axis from atmospheric drag, solar radiation pressure, and earth albedo.…”

“…This method avoids non-linear variations in a, and allows good convergence in the solution coefficients. The long-term solution parameters included density correction factors for hydrogen and helium, a direct solar radiation pressure coefficient, the initial semi-major axis value, and several long-term albedo coefficients 22 . The drag coefficient C D was modeled to account for the dominance of different atomic and molecular species.…”

“…The CIRA72 model atmosphere was selected for the analysis because it integrates the diffusion equations to any altitude as opposed to using predefined lookup tables that stop at 2500-km altitude. The previous paper 22 lists the fit results for 20 West Ford needles clusters. The long-term (20 to 35-year) best-fit solution for each satellite contains the solar radiation pressure and albedo coefficients for the satellite.…”

Modeling of the radial and transverse components of the albedo function

“…Sehnal (1979), considered the Earth's albedo as a potential function such as that of the Earth. The Earth's albedo was considered constant in the analysis of the reflected radiation pressure, such as Green (2002), Bowman (2000), de Pater and Lissauer (2001), Sehnal (1979), Anselmo et al (1983), and Martin and Rubincam (1993). Also, Levin (1962), Wyatt (1963), Sehnal (1965), Smith (1969), and Baker (1965), have taken into account a constant albedo.…”

A New Navigation Force Model for the Earth’s Albedo and Its Effects on the Orbital Motion of an Artificial Satellite

“…The Earth's albedo was considered as constant in the m analysis for the reflected radiation pressure in many literatures for example see [6][7][8][9]. Moreover [10][11][12][13][14] have taken into account a constant albedo.…”