The LDEF was gravity-gradient stabilized, so that the long axis was always directed at the sub-satellite point on the Earth's surface. Rotation about the long axis was inhibited by a magnetic damping system. Thus, one of the long faces was always the "leading", or "ram" edge, facing the velocity direction. The opposite edge was then the "trailing" or "wake" edge. One end of the cylinder was always facing space, the other end always towards the Earth. The faces perpendicular to both the long axis and the velocity vector were nominally "north" and "south", continuously facing +61.5 ° and -61.5 ° declination respectively. Post-flight analysis of LDEF surfaces indicated that the spacecraft was rotated (in "yaw") about 8.2 ° from the intended orientation about the long axis. Analysis of the IDE solar sensor data confirms this result independently for the first 11½ months of the mission. The normal to the leading edge was thus rotated about 8.2 ° away from the velocity vector, with the normal to the "north" edge rotated 8.2 ° towards the velocity vector. The scheduled return of LDEF to Earth was delayed, first by scheduling problems, and then by the loss of the Challenger. Exceptionally intense solar maximum activity accelerated the decay of its orbit and it became clear that if LDEF was not recovered, it would re-enter the atmosphere in early 1990, with the loss of all of its data. It was retrieved at an altitude of 330 km by the crew of the Columbia on 12 January 1990, and returned to Earth on 20 January, the same day that NORAD had predicted as its most probable atmospheric re-entry date.
Figure 1. Cross-section of typical MOS impact detector. The IDE sensors used 0.4 and 1.0 micrometer thick dielectric.
An on-board tape recorder was included to record the time of each impact, identified by panel and by wafer thickness, but not by specific detector. The time resolution of the IDE clock was about 13.1 seconds. About every 2.4 hours, there was also a dump to the tape of the status (illuminated or dark) of six sun sensors, the status (active or shorted) of each detector, and other "housekeeping" information. Sunrise and sunset information from the sun sensors allowed calibration of the IDE clock. IDE activation occurred at 1984 April 07d 17h 23m 43.8s ± 0.3s UTC.
Tape was only supplied for the nominal 9-month mission, and it ran out on day 348. Post-flight verification shows that there was only one recording anomaly during this time and no significant data were lost. About 15,000 impacts were recorded on the 459 detectors during the active phase of the mission. For the remaining 4.7 years of flight, the detectors continued to receive impacts which left physical craters, but no time-resolved information was recorded. Since the LDEF IDE detectors were recovered, integrated fluxes for this time period have been determined by visual examination of the detector surfaces.
In contrast with these earlier studies, the controlled orientation and high time-resolution of the IDE data provide, for the first time, a detailed, extensive data set well adapted to analysis of the spatio-temporal characteristics of orbital debris in near-Earth orbit. An examination of the IDE data (Figure 2) shows immediately that the detected particle fluxes were neither uniform in time nor in space. All impacts on the 0.4 micrometers IDE detectors are displayed in this "seismograph" plot. The entire 346-day active data recording phase of the mission is represented along the horizontal axis. The impact rate on each of the six orthogonal surfaces is indicated by the vertical amplitude of each trace. Note that the impact rates represented in this figure are raw rates, uncorrected for effective area. This does not significantly change the appearance of the plot.
Figure 2. All impacts recorded on the 0.4 micrometer dielectric thickness (high sensitivity) IDE detectors during the 346-day time-resolved phase of the mission.
Examination of Figure 2 suggests a number of interesting points:
Figure 3. Observed activity on the leading (ram) edge of LDEF as recorded by the high sensitivity (0.4 micrometer dielectric) detectors of IDE. Note that every impact is displayed. The lack of impacts between the obvious events is real.
Figure 4. Impacts on the high activity surfaces as a function of LDEF orbital position and time for the 346 day time-resolved data set. Note that the orbital longitude axis partially repeats at the top.
The regular spacing of the impacts matches the LDEF orbital period of approximately 94 minutes. The final trace of this figure displays a single 94-minute segment of the 4 June data. All the impacts during this segment occurred during a period of less than five minutes. As may be seen in these figures, the IDE data set contains many impacts which occurred in "bursts", during which numerous impacts were recorded in a short time. Such a burst we have designated an event. At the finest resolution, events may show structure. For example, the 4 June event illustrated here appears to be double. A number of these multi-event sequences appear in the IDE data set. As illustrated in Figure 3, events may be seen to reoccur each time the LDEF returned to the same point in its orbit. These we call multi-orbit event sequences (MOES).
A significant conclusion resulting from the high-time resolution of LDEF IDE data displayed in Figure 3 is that the instantaneous fluxes observed are much greater than the mean fluxes. As shown in the text imbedded in the figure, the mean flux calculated from the 346-day data set is 0.0017 impacts/second/sq. meter. The peak flux, observed with the IDE time resolution of 13 seconds, was 12 impacts/second/sq. meter, almost 4 orders of magnitude greater! While long-term fluxes may be useful for engineering structures and similar purposes, there are circumstances where peak fluxes may be more useful. The IDE results indicate that an optical surface such as a window (which could be degraded by small particle impacts) could need replacement far sooner than would be predicted by mean fluxes.
While the structure of an individual MOES is illustrated in Figure 3, the distribution of the observed MOES with orbital location and time is best illustrated in a plot such as Figure 4. In this figure, all impacts on the high sensitivity detectors mounted on the North, Ram, and South LDEF surfaces are plotted as a function of LDEF orbital longitude and time. A number of MOES are indicated. Also indicated are “spikes”, defined as sudden bursts of impacts which occurred on only a single orbit. These spikes were the most intense individual events observed by IDE. In addition to their lack of multiple-orbit repetition, spikes differ from the events of an MOES by frequently appearing as pairs of events, separated in orbital longitude by 10 to 30 degrees. This "bifurcated" structure of spikes is visible in Figure 4.
As developed by us, the process is an iterative one. The orbital inclination of the debris orbit is estimated. We assume that the location on the LDEF orbit of the MOES impacts represents the point of closest approach between the two orbits. The differential precession between the resulting candidate orbit and that of LDEF is calculated. The result is compared with the observed change in the orbital intersection point and a new estimate of the candidate orbit inclination is obtained. In general, convergence is rapid.
One of the most prominent multiple orbit event sequences observed by IDE began on May 13, 1984, and so has become known as the "May swarm." This MOES can be characterized as being of low intensity (~3 impacts per orbit) and long duration, lasting for over 20 days (300 LDEF orbits), with several hundred impacts recorded on the IDE trays facing in the LDEF ram direction and towards the south pole of the orbit, the majority occurring on the south-facing tray. The long duration of this MOES made it an especially suitable choice for analysis by the differential precession.
The results of applying the Method of Differential Precession are illustrated in Figure 5 where apogee and perigee are plotted as a function of eccentricity for a set of candidate orbits. Deduced values of the inclination, Longitude of the Ascending Node, and Longitude of Perigee are indicated on the figure. Note that the semi-major axis varies little with the eccentricity; in this case, the variation in a is so small that we could confidently set a = 6746.5 km, regardless of the eccentricity. The dual requirement that the candidate orbits have perigees of greater than 200 km in altitude (i.e. that they lie above the atmosphere), and that they intersect the LDEF orbit, placed strict limits on the allowed values of the eccentricity which must be greater than 0.0165 and less than 0.025.
Figure 5. Perigee and Apogee of family of May swarm candidate orbits.
One of the candidate orbits (e = 0.017) was then chosen for a series of checks on the results of the method. The first check involved the computation of the particle velocity of impact over the duration of the May swarm. These velocities were then resolved into components along the LDEF body axes in order to determine the impact speeds on the IDE trays. For this particular orbit, only the south tray and the ram-facing tray were struck, with the south impact speed being larger than that for the other tray for most of the encounter (see Figure 6). This is in good agreement with the IDE observations of the May swarm, in which these same two trays recorded large numbers of impacts, with the south tray receiving the most hits.
Figure 6. Particle impact speeds in the direction IDE tray normals for the e=0.017 candidate orbit.
The second check consisted of a comparison of the sky track of the points of closest approach between the two orbits to the sky positions of the individual impacts comprising the May swarm. As can be seen from Figure 7, the agreement is excellent, with the sky track of close approach passing neatly through diffuse band of impact positions. The particles are moving in a northerly direction, whereas LDEF is moving along its orbit from left to right. At the onset of the May swarm, the impacts are located at the position labeled "Onset", with the impact positions gradually moving towards the lower right as time progresses.
Figure 7. Sky track of close approach between the May swarm candidate orbit and that of LDEF. Arrows on the orbital paths at time of onset indicate direction of motion. Both orbit tracks shift to the right with time due to precession.
It is important to note that the orbits determined are the instantaneous orbits of the microparticles at the time of impact. Because micrometer sized particles are subject to rapid decay due to non-gravitational forces, the particle orbits do not necessarily represent the original orbits of these particles. To find the progenitor orbits, it is necessary to "back-project" the impact orbits, taking into account all appropriate forces. Work is currently in progress to carry this process out on a sample of MOES.
Figure 8. Location of LDEF ground track (sub LDEF terrestrial latitude and longitude) during spikes.
A plot of all spikes observed on the North LDEF surface as a function of the sub-LDEF terrestrial latitude and longitude is shown in Figure 8. These events were almost all concentrated above the northern hemisphere, and between longitudes 80 and 200 degrees east. An examination of launch activities has shown no correlation between Soviet or other launches and the occurrence of spikes. In the process of studying the event times of spikes, it was realized that many, especially those that exhibited bifurcation, appeared to have a 15.5 day periodicity (see Figure 9). This could be explained if the source of the spikes was a highly concentrated clump of material in an orbit whose beat frequency with LDEF was 15.5 days. Unfortunately, the short lifetimes of micrometer sized orbital debris particles does not allow such a clump to have a lifetime measurable in days, much less months. It appears more likely that the spikes result from material leaving some long-lifetime orbiting object. Again, this hypothetical source object must have an orbit which has a 15.5 day beat frequency with LDEF. One possibility that we have examined is the Solar Maximum Mission satellite (SMM). SMM was in virtually the same orbit as LDEF, differing only in semi-major axis. After deploying LDEF in April, 1984, the shuttle Challenge then increased its altitude by about 20 km. and undertook the repair of the SMM. The beat frequency between the LDEF orbit and that of an object 19.3 km. above (or below) is 15.5 days. The spikes do not, however, coincide with the times of closest approach between LDEF and SMM, as calculated from the appropriate orbital elements. It seems likely, however, that material from SMM is involved in the IDE spikes. The terrestrial latitude and longitude concentration shown in Figure 8 would then presumably be a coincidence.
Figure 9. Spikes on LDEF North surface as a function on time. Note that many spikes occurred very near to multiples of 15.5 days (as indicated by the vertical plot divisions).
This document produced by
Dr. Bill Cooke; bjc@ufl.edu