The structure of Space (2): formation of a geosynchronous ring

 

A year ago, I published a post on 'The structure of Space'. In that contribution, I discussed structure in orbital element space, identifying spacecraft orbital 'families'. But how about 'structure' in a more traditional spatial sense?

A few days ago, I had some light Twitter-banter with the fantastic Alice Gorman ( aka 'Dr Spacejunk'). She asked: 

"why is it that space junk has not turned into rings around Earth, just like Saturn or Neptune? Kessler and Cour-Palais (1978) argued it was because the smaller particles were removed by atmospheric drag before enough mass could accumulate"

I pointed out that our Earth by all means does have an artificial ring of space debris and functional payloads: the geosynchronous ring. Which, as we will see, is more of a geosynchronous torus, actually. It is not so dense (yet) with objects as the rings of Saturn or Neptune (but give it time!), but it will be long lasting, outliving us humans.

This sparked a few creative days (I had to get my mind off a few things). I wrote a small .NET application that calculates ECEF coordinates of satellites and fed it with all objects from the CSpOC and our classified catalogues: 20058 tracked objects ranging from operational payloads to small debris particles. Next, I used QGIS to make plots of these ECEF coordinates (I know: I often tend to use software for things other than what they originally were developed for).

The results are in the images below: each image pair shows a polar view at left looking down at the north pole, and a side view at right, looking in the equatorial plane. The plots are for 15 September 2020 at 0h UT.

Here is a zoomed in view, showing the objects in lower orbits (left a polar view, right an equatorial view: thickmarks are in units of 2000 km):

Click image to enlarge

As an aside: notice the small circular area with lower object density at the pole, rimmed by a higher density ring (it is also visible in the wider plot below). This is due to the fact that objects in polar orbits tend to have orbital inclinations  a few degrees higher than 90 degrees: notably so to achieve a sun-synchronous orbit (typical orbital inclinations for such orbits are 97-98 degrees).

In the wider, zoomed out plots below that show the higher objects, you can clearly see the geosynchronous ring at ~35785 km in the polar view at left (thickmarks are in units of 10 000 km). It is made up of geostationary and geosynchronous satellites and debris.These are the satellites that bring you satellite television, satellite telephony, and that bring SIGINT and early warning data to the militaries of various governments. The objects inside the outer ring are objects in MEO (e.g. GPS satellites) and GTO (old rocket stages form launches to GEO and other debris):

Click image to enlarge

If you look at the equatorial view at right, you'll note that the geosynchronous 'ring' is actually more a geosynchronous torus. You see a thin line of actual geostationary objects (mostly operational or untill recently operational payloads) in the Earth's equatorial plane with orbital inclination ~0: and a wider band of geosynchronous objects, that have orbital inclinations between roughly 0 and 15 degrees (both operational payloads, defunct payloads including some in a graveyard orbit, and debris).

The latter torus is situated slightly slanted with respect to the Earth's equatorial plane. The orientation of this slant shows a daily cycle, causing a funny 'wave' like behaviour of these satellites over a full day, when we look at their geographic positions in the equatorial plane, as can be seen in this mesmerizing animation that I created:

click animated map to enlarge

In this animation, the colours represent the object density plotted as a kernel density heatmap: red areas are most dense with objects. The small white dots are the actual geosynchronous satellites (plotted for 15 September 2020). There is a thin line of objects at latitude ~0 that are truely geostationary due to stationkeeping: these hardly move. But the geosynchronous objects with inclinations > 0 show a wave-like pattern of movement over the day!

This movement is a tidal effect, created by solilunar perturbations: gravitational perturbations by the sun and (notably) the moon. These tug on these objects a little, so unless you do frequent stationkeeping manoeuvers that keep the orbital inclination near zero, these objects will see their orbital inclinations start to oscillate, between 0 and 15 degrees over a period of roughly 54 years (53-55 years: it depends on the exact altitude of the satellite). This causes the torus, and the slant. The daily 'wave' (wobble) of this torus is caused by a combination of these tidal effects and the daily rotation of the earth, similar to ocean tides.

I have visualized the discussed ~54-year oscillation by plotting the evolution of the orbital inclination against time of Intelsat 1 (1965-028A), the first commercial geostationary satellite that was launched in 1965. It has just completed a full cycle of this moon-and-sun induced oscillation since it's launch:

click diagram to enlarge

In the absense of active stationkeeping (operational payloads make stationkeeping-manoeuvers roughly each two weeks), there is an oscillation in longitude too, induced by the J₂ resonance: due to the uneven mass distribution of the Earth (it isn't a perfect sphere but rather a slightly deformed, bulgy egg), geosynchronous objects without stationkeeping start to oscillate in longitude around one of two "stable" points. These points are at ~75 E and ~105 W longitude: the white crosses in the plot below.

click map to enlarge

This oscillation in longitude about one of the stable points is well visible in 55 years of Intelsat 1 orbital data. Below I have plotted the position of the satellite in longitude from 1965 to 2020. You clearly see it oscillate around one of the equilibrium points (the 105 W point, marked by the dashed line in the diagram), with a periodicity of about 3.1 years:

Click diagram to enlarge

Over time this effect will also tend to concentrate space debris at geosynchronous altitudes around these two points. This effect can be seen in the kernel density heatmap (the coloured band) above the diagram, and in the histogram below (two peaks in the distribution, near the first equilibrium point at 75 E and the second equilibrium point near 255 E = 105 W) although it is to some extend masked by a preference of operational payloads to be at the longitudes of either Asia or the USA, where the biggest commercial markets for satellite tv and satellite telephony are.

click diagram to enlarge

Objects at geosynchronous altitude will not decay in millions to perhaps billions of years to come: so the geostationary ring that formed since 1965 will be here to stay, well after we humans are gone. It will be one of the clearest, longest lasting archaeological signatures of the Anthropocene.

Of course the character of the ring will change. Breakups will fragment the larger objects, decreasing the particle size distribution and increasing the number of objects in the ring even when human launches have stopped. Solar Radiation Pressure will more strongly act on smaller particles, so orbital eccentricities (and presumably also inclinations) will change, causing the ring to get more diffuse in time. I do not know of really long-term simulations (the longest I have been able to find was over a mere 200 years period), so cannot put exact figures on this.

The geosynchronous ring is a remarkable form of planetary change: untill quite recently our planet did not have a ring, but now it has, and it is completely artificial. It formed in a short time. In the animation below, I have broken down the current distribution of objects in the ring (for 15 September 2020) into launch timeframes of 5 years, starting 1960 (i.e. just before the first geostationary launches started) and ending at present:

This shows the gradual, but in terms of geological time nevertheless extremely rapid formation of our planet's artificial ring over the past 55 years. This ring will be a long-lasting, visible human footprint in space, probably outlasting all others (including footprints on the moon, that will be wiped out over time by meteorite impacts).

If you have a telescope or a good camera, you can see this ring of objects every night. Here is a photograph of a small part of it:

Click image to enlarge