Today’s guest post was provided by Marco Langbroek, Leiden, NL, a keen back-yard astronomer and past contributor to ESA’s ATV blog. He updates us on his efforts to track GOCE’s (now famous) re-entry, which occurred on 11 November 2013. The intro below was provided by ESA’s Holger Krag, from the Space Debris Office at ESOC.

It’s a pleasure for the professionals at ESA’s Space Debris Office to note the strong support for re-entry analysis and, indeed, accurate and valid scientific participation, by ‘citizen scientists’ like Marco Langbroeck. Thank you Marco, for sharing your methods, results and enthusiasm.
H. Krag, ESA Space Debris Office

In the evening of 10 November, near 19:54 CET, I was standing beside a car along a rural road in the mid-Netherlands, watching the western sky. We were on our way home from a full day of searching in a suspected meteorite drop zone. But we knew that something else would drop out of the sky that very night: ESA’s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE). Hence why we stopped alongside the road, turning an eye to the sky for a few minutes.

GOCE would pass just west of the Netherlands around 19:54 CET. Late the previous evening, my last re-entry forecast had shown that this pass would be in the ‘re-entry uncertainty window’, even if the nominal forecast was for a later re-entry time. Wouldn’t it be cool to see it break up?!

GOCE over Leiden, NL, 29 September 2013. Credit: M. Langbroek

GOCE over Leiden, NL, 29 September 2013. Credit: M. Langbroek

Alas, we did not see GOCE: it passed in darkness in the Earth’s shadow and was evidently not burning up yet; we already knew our chances of seeing it were small of course. As I came home two hours later, fresh orbital elements from JSpOC [USAF Joint Space Operations Centre – Ed.] and timely blog messages from ESA showed me that GOCE was still in orbit, if barely, clinging on to life for a few more hours. A new forecast suggested re-entry closer to midnight. This meant I would not get to see this re-entry: but who would? And when? These were interesting questions.

Predicting satellite re-entries

I have seen many meteoric fireballs, but witnessing a satellite re-entry so far has proven to be very elusive. Knowing when to expect such a re-entry would of course help. The US Air Force Joint Space Operations Center (JSpOC) provides re-entry forecasts via their Space-Track site, but I have turned to making my own re-entry forecasts as well. I most recently did this for GOCE, the topic of this blog post.

My forecasts use timely professional tracking data and two software programs called SatAna and SatEvo. The latter was programmed by Alan Pickup, formerly of the Royal Observatory in Edinburgh, Great Britain. Alan’s software is based on orbital decay theories developed by Desmond King-Hele, a British researcher that was in the forefront of research into satellite orbital dynamics from the 1960s to the 1980s.

Of Alan’s two programs, the SatEvo program is used for the actual re-entry forecast. You feed it with a recent orbit for the satellite and information on current solar activity, and it will then evolve the orbit into the future and forecast the moment of re-entry. How accurate this forecast is depends on a lot of factors. Re-entry forecasts based on orbital determinations done well before the actual re-entry date have a large uncertainty window – up to days.

The uncertainty window of a forecast done 24 hours before the actual re-entry is typically still as large as ten hours. Re-entry forecasts done with orbital determinations from the last few orbits just before re-entry are, however, increasingly precise.

It’s a drag

Yet there are always uncertainties caused by factors that are sometimes difficult to quantify. The most important but also most uncertain factor is drag. Atmospheric drag acting on a low-orbiting satellite is variable. Not only does it vary with altitude but it also varies because of varying solar activity.

When solar activity temporarily increases (e.g. due to a solar flare), the density of the Earth’s upper atmosphere increases in response to the influx of solar particles, which means the satellite will experience more drag. Drag can even vary over one orbital revolution of a satellite: the atmosphere is denser at the day-time side of the Earth compared to the night-time side, and, in the perigee [the point in the orbit of a satellite orbiting the earth that is nearest to the centre of the Earth] of an elliptical orbit the satellite moves through a denser part of the atmosphere than in the apogee [… furthest from the centre of the Earth].

How much drag a satellite experiences is in addition influenced by the shape of the satellite, and whether it is tumbling or not. The size and spatial orientation of the satellite matter, especially at lower altitudes as we will see later in this post.

The structural integrity of the satellite also plays a role, as it determines at what altitude the satellite will start to break up. In general however, once a satellite has descended to 80 km altitude, it is doomed – at that altitude the orbital speed has become too low to complete an orbit around the earth and the descent trajectory becomes ballistic instead of the satellite continuing to move in an orbit.

One other problem to deal with is that satellite orbit determinations, even professional ones, contain analytical error. This is especially the case during the last few orbital revolutions just before re-entry, when the orbit (and drag)  changes very quickly and dynamically between successive detections of the satellite by tracking stations. One orbital element particularly affected by such analytical error is the satellites’ drag parameter, in itself already variable. And that one is particularly important to satellite re-entry predictions.

GOCE’s increasingly rapid plunge

GOCE’s increasingly rapid plunge Data source: Space-Track. Image credit: M. Langbroek

GOCE’s drop rate Data source: Space-Track Image: M. Langbroek

GOCE’s drop rate Data source: Space-Track Image: M. Langbroek

In a set of orbital elements for a satellite, the atmospheric drag factor is expressed by the so-called (pronounced ‘n-dot’) drag parameter. This ṅ parameter is actually an important factor in determining the future orbital evolution of a satellite.

Take a number of orbit determinations on a satellite, and the ṅ values of these will scatter around a trend due to the aforementioned analytical error. The re-entry predictions produced by SatEvo will scatter in sync with this scatter in ṅ. In addition, there is scatter in ṅ due to real but short-term fluctuations in solar activity and atmospheric conditions.

This is where SatAna comes in. The ‘Ana’ in SatAna stands for ‘Analyser’. You feed the software a number of recent orbits (an orbital arc) as well as the solar activity for the time in question, and it projects a new synthetic orbit near the end of the arc, with a drag value fit to the set of orbits you used based on a decay theory. This synthetic orbit, one which has a much more realistic drag value than the original individual orbits, you then feed to SatEvo for a re-entry prediction.

In reality, it is not this simple, of course. The process also involves making informed decisions on what length of arc to use, which orbits to include (I try to exclude orbits that appear erroneous) and what analytical step size to use.

predictions_diagramThe result of pre-processing with SatAna before running SatEvo is a re-entry forecast that scatters less widely (and wildly) than it would if you fed original single orbit determinations to the software. For example, forecasts based on single orbit determinations without preprocessing by SatAna showed a considerable multi-day scatter during the two weeks prior to GOCE’s re-entry. By contrast, orbits processed with SatAna provided a much more consistent re-entry date, consistently hovering within less than a day of midnight UT of 10-11 November (see diagram above).


Unlike other satellites or rocket boosters, GOCE was designed to minimize drag. Its design however minimized drag only when the satellite maintained a specific attitude (orientation) with regard to its direction of movement.

Were it to lose that orientation, then drag would suddenly and dramatically increase. From the moment the ion engine cut off [due to fuel depletion – Ed] on 21 October, GOCE relied on magnetic torques (coils that orient the spacecraft with respect to Earth’s magnetic field) and its aerodynamic body design to maintain its orientation. It was not guaranteed that this would keep functioning up to re-entry. It actually did in the end, as we now know. Had it not, the whole picture would have become radically different: if attitude would have been lost and drag would have suddenly gone up as a result, GOCE would have suddenly dropped like the proverbial brick.

Why I initially had it wrong (… but redeemed myself later)

GOCE’s special design also had other implications for the re-entry forecast that I initially (up to the evening of 10 November)  had not taken into account. As a result, my re-entry forecast made after I returned from my meteorite hunt on the evening of 10 November came out slightly too early.

When I came home on the 10th and ran a forecast near 10 pm, it suggested a re-entry near 23:10 CET. This led me to post a tweet for Australian observers to monitor the 15 minutes after that moment, when GOCE would pass over Australia.


In reality, GOCE would not re-enter until two hours later. This became quickly apparent when ESA reported that the Troll tracking station on Antarctica had received telemetry from the spacecraft near 23:42 CET, half an hour after my forecast had it reenter!

Entering a transition zone

The reason the re-entry happened later and that my late-10-November forecast was off by two hours had, amongst other things, to do with something that is only of relevance during a short, final period when the satellite has descended to very low altitudes: in the case of GOCE, below 146 km altitude, a threshold it passed near 09:00 CET on 10 November.

During this period, the satellite enters a region where the so-called ‘atmospheric mean free path’, a measure of the distance between individual gas molecules in the atmosphere at the altitude in question, starts to become similar to the satellites’ length. This has an odd effect that does not occur at higher altitudes (where the atmosphere is so thin it is basically absent).

Any atmospheric gas molecules that hit the spacecraft and are deflected from its surface (the process that causes drag on the satellite) will start to interfere with air molecules in front and just aside of the spacecraft, and will in turn deflect some of these before they can hit the spacecraft and exert drag. As a result, these latter-deflected air molecules will not interfere with the spacecraft. This actually reduces drag on the satellite! In this atmospheric transition zone below 146 km altitude, the drag a satellite actually experiences is hence less than you would calculate from the atmospheric density at these altitudes. This prolongs the lifetime of the satellite in orbit.

In the case of GOCE, which was 5 metres in length, it prolonged it by about 1.5 orbital evolutions or close to two hours.

What I did not know until Alan e-mailed me about it late in the evening of the 10th, is that SatAna and SatEvo actually have an experimental option to take this effect into account. Once Alan told me how to incorporate that option, the forecast (or rather an ‘aftercast’ by that time, as it was done after the actual re-entry) became much closer to the actual moment of re-entry for GOCE, which we actually know quite well in this case as the re-entry was observed  by eyewitnesses on the Falkland Islands.

GOCE_reenryr_3D_nompos_NEWFinal results

Taking the last five orbital element sets released for GOCE  (a seven-hour tracking period) as input to SatAna, with an average F10.7 cm solar flux value of 154 and the influence of the spacecraft length of 5 metres incorporated, SatEvo suggests that GOCE’s reentry started near 00:13 UT (01:13 CET), at approximately latitude 69 S, longitude 52 W (red dot on map above). At that moment it was passing over the icy Weddell Sea near the tip of the Antarctic peninsula, northbound for the Falkland Islands.

Remarkably, JSpOC and ESA estimate the re-entry to have commenced only minutes from my estimate, at 00:16 UT (01:16 CET) near 56 S 60 W (blue dot on map above).

Moreover, on the Falkland Islands just to the North of this point, Bill Chater actually observed GOCE breaking up within a few minutes of 00:20 UT (01:20 CET), and he filmed and photographed the vapour cloud the spacecraft’s disintegration left in the sky, providing tangible proof that the re-entry estimates of myself and JSpOC/ESA were close to the real position.

Photo of GOCE reentering the atmosphere taken by Bill Charter in the Falklands at 21:20 local time on 10 November.

Photo of GOCE reentering the atmosphere taken by Bill Charter in the Falklands at 21:20 local time on 10 November.

Note that the actual spacecraft break-up and disintegration during re-entry is not something happening at a fixed position in space and time, and in this sense re-entry forecasts that give a time and position are a bit deceptive. Break-up and disintegration happen along a trajectory, over a time span of minutes.

In all honesty, the very good agreement of my personal final re-entry estimate and that of JSpOC/ESA, confirmed by the actual break-up observations from the Falklands, involves an element of dumb luck.

Alan does not claim a precision of a few minutes for his software; still, this good agreement shows that forecasts of satellite re-entries using Alan’s software can be surprisingly accurate, with results that do not much differ from the results of ESA and JSpOC professionals.

The author wishes to warmly thank Alan Pickup, UK, for making available his fine SatAna and SatEvo software and for discussions. Note that any factual errors in the post above are solely mine.

Ed: Thanks, Marco, for an informative and detailed post!