Jonathan's Space Pages

Catalog of Space Debris Clouds - Plot Descriptions

KEY - Blue: initial elements; Green: current elements if still up; Black: last elements if reentered.

For each debris cloud four sets of plots are provided, described below. We define the following concepts:

• Initial orbit - the earliest available orbital elements for an object. Note that debris objects are often cataloged years after the event, and so because of atmospheric drag this `initial orbit' may be significantly different from the true initial orbit of the object immediately after the debris event. But, it's the best we can do!
• Final orbit - the last orbital data for an object prior to its reentry or prior to when it became lost.
• Current orbit - the most recent orbital data at the time the catalog was updated, for objects still in orbit.
• Height - the orbital height of a debris object in km, meaning the mean of its perigee and apogee, i.e. (A+P)/2 or, equivalently, equal to the semi-major-axis minus the Earth equatorial radius, (a-Re).
• Inc - the orbital inclination in degrees relative to the Earth equator of date.
• Spread - the value S = (A-P)/2 = ae, half the difference between apogee and perigee heights. I use S in km rather than the dimensionless eccentricity e because I have more of a sense of what a given value means.
• Node - the right ascension of the ascending node of the orbit in degrees. The orbital node precesses with time, so comparing node values for objects measured at different times isn't useful. Initial orbit node values are propagated back to the event time using a simple first order J2 correction and current/final values are propagated to the present (i.e. epoch of catalog update).
• Apse - I use this term to refer to either the perigee or apogee height. For example, an object in a 200 x 500 km orbit has two apse values, 200 and 500. In a debris cloud whose parent was in a circular orbit at height h, the initial orbits of the debris objects usually have either their apogee or their perigee equal to h. I make a histogram of these apogee and perigee values (lumped together) and find the mode of that histogram (in km). This ApseMode value is often a good estimate of the height at whch the debris event occurred.

• Set 1: orbit data plots

  
  In set 1, a variety of plots explore the cloud orbital parameters:

  • Top left: Height-Inc Scatter. A scatter plot of orbit height vs inclination for each debris object in the cloud. The initial orbit values are given in blue; final orbit values of decayed objects are in black; and current orbit values of objects still in orbit are in green. Comparing the positions of the blue points with those of the green and black points lets you assess the effects of atmospheric drag on the cloud since its formation.

    
    The red box gives the region enclosed by the height range containing 95% of the objects and the inclination range containing 95% of the objects, using the initial orbit values. The green box represents the same but using the final orbit values. These boxes can be used to assess whether a new debris object is likely to be a part of this cloud.

  • Top right: Height-Spread Scatter. Again, blue points are the initial orbital data, black points are final orbits of decayed objects, and green points are current orbits of objects still in orbit. This plot contains similar information to the traditional Gabbard diagram, but I find it easier to read as it only has one point per object orbit rather than two. For an energetic debris event in a circular orbit, the blue points tend to form a V-shape whose apex is at zero spread and at the height of the parent object. The left hand (low altitude) arm of the pattern for the green and black points slumps towards lower spread values because of the effects of atmospheric drag, while to the right (high altitudes) drag has less effect.
  • Middle row, first plot: Height Histogram. Histogram of object heights. Blue line: initial orbits. Green line: current orbits of objects still in orbit. Magenta lines indicate the range within which 95 percent of the green histogram lies and correspond to the height boundaries of the green box in the top left plot.
  • Middle row, second plot: Inc Histogram. Histogram of inclinations for initial orbits. Magenta lines indicate the range within which 95 percent of the histogram lies and correspond to the inclination boundaries of the red box in the top left plot.
  • Middle row, third plot: Node histogram. Histogram of orbit ascending node values. Blue histogram - initial orbits. Green histogram - current orbits. The initial orbits should reflect the orbital plane of the parent object at the time of the intiial debris event.
  • Middle row, fourth plot: Height-Node scatter. Shows orbit ascending node vs orbit height. As before, blue points are initial orbit values, black points are final orbit values for decayed objects, and green points are current values for objects still in orbit. This plot usually isn't terribly helpful.
  • Third row, first plot: Apse histogram. Apse values for initial orbits are shown. See the discussion of the apse values at the top of this page. The mode of the histogram is indicated, as an estimator of the height at which the event occurred.
  • Third row, second plot: Spread histogram. Blue line - initial values. Green line - current values for objects still in orbit. For cases where the parent object was in a circular orbit, the spread distribution is a measure of how energetic the event was. The effects of atmospheric drag over time tend to circularise the orbits of the objects, and so the green histogram tends to be shifted to lower values of spread compared to the blue one.
  • Third row, right hand plot: Height-Spread zoom. This plot shows a region of the height vs spread parameter space centered on the Apse Mode (red line), zoomed in from the upper right plot. Only the initial orbit values are shown. They will usually form a triangular pattern whose apex is at zero spread and at the height of the Apse Mode.

  
  

• Set 2: Height vs Time plot.
  • Height-Time. This is a single plot with one blue line for each debris object in the cloud, showing its orbital height versus time. For lower altitude objects in older clouds, the periodic effect of the solar cycle is visible in some cases.

  
  

• Set 3: Gabbard diagram.
  • Gabbard diagram This is a single plot showing height versus orbital period. The latest orbital data are used. There is one red point and one blue pooint for each debris object. Red points are (perigee, period) and blue points are (apogee, period).

  
  

• Set 4: Angular Momentum These plots show the specific angular momentum vectors (i.e. angular momentum per unit mass) of the objects in the debris cloud.
  • Top plot: RA vs Dec - shows the RA and Dec of the orbit normal. Blue points: initial orbits; green points: current orbits. The declination is usually characteristic of the cloud, while the RA spreads out due to precession effects.
  • Second row, left plot: Magnitude histogram. The angular momentum vector has units of length squared per unit time. Here we give the histogram of the magnitude of this vector scaled by the Earth equatorial radius Re to give units of km/s. The blue line shows the initial values, the green line shows the current values for objects still in orbit.
  • Second row: center plot: RA histogram. Shows the histogram of angular momentum right ascension values.
  • Second row, right plot: Dec histogram. Shows the histogram of angular momentum declination values.