Orbital properties of the West Ford dipole belt

Early in May, 1963 a package containing 4.8×108copper dipoles, each 0.00178 cm in diameter and 1.78 cm in length, was placed into a nearly circular, nearly polar orbit at a mean altitude of 3650 km. A detailed theoretical model including all known perturbing forces was constructed to predict the motion of the individual dipoles from dispensing to final re-entry through the atmosphere. Photoelectric observations, analyzed on the basis of this model, indicate that only about half of the dipoles are orbiting individually. Radar determinations of the spreading of these dipoles along the orbit agree well with the theoretical calculations. Radar observations also confirmed the prediction that the dipole ensemble would exhibit a symmetric, double-jawed structure in the early stages of its development. The ensemble formed a complete belt in about 40 days, as expected. Theory indicated that the in-plane diameter of the physical cross section of the belt would increase most rapidly near perigee and apogee and least rapidly near the semi-latus rectum points, whereas the out-of-plane diameter would increase fastest over the equator and slowest near the poles. In general, the greater the dipole reflectivity and the more isotropic the distribution of dipole tumbling axes, the more rapidly will the cross section grow. Despite the imprecisely known values of these and other initial conditions, predictions were in general accord with measurements: The "half-power width" of the in-plane diameter grew from about 10 km initially to about 140 km near perigee and to about 25 km near the semilatus rectum point 220 days after dispensing; the corresponding out-of-plane growth was from about the same initial value to about 25 km in middle north latitudes, where all measurements were made. The very small in-plane growth at the semilatus rectum point seems to indicate that the effects of dipole-micrometeoroid collisions were substantially less than expected; however, quantitative conclusions cannot yet be reached. The observed double-peak in the dipole density as a function of geocentric range appears to be a consequence of the particular method used for dipole dispensing. Radar determinations of the changes in the orbit that passes through the regions of highest dipole density are in excellent agreement with predictions based on a simple "equivalent-sphere" model, the rms residuals being less than 10 km. The most recent orbit determination, performed 250 days after dispensing, showed that the total decrease in perigee height was more than 800 km, which fortuitously happened to differ from the predicted change by only 1 km. The effects of charge drag were too small to be determined accurately, but could not have caused a decrease in mean altitude at a rate even as low as 10 km/yr, implying that the average magnitude of the electrostatic potential on a typical dipole could not have exceeded 0.15 volt. These results lend credence to the previous prediction that most individual dipoles will have an orbital lifetime of less than three years, and that none will have a lifetime exceeding five years. The dipoles are expected to survive re-entry into the lower atmosphere and to float back to earth unharmed. However, the probability of finding one is minuscule.