[UPDATED] The 21 September fireball: a small Aten asteroid?

-- edited/corrected 25/9 15:25 UT. I initially made a small error in the used trajectory azimuth (not properly taking into account effects of a spherical earth). That is corrected, but the conclusions do not alter. --

In my previous post I presented clear evidence that the splendid fireball seen over NW Europe on September 21st, 2012, was a meteoric fireball. I also presented a first, very preliminary idea of its trajectory.

Based on that trajectory, I can now present some very first, very cautious conclusions about the heliocentric orbit of this meteoroid.The solutions strongly favour an identification as an Aten asteroid.

The entry azimuth of the fireball from the reconstructed preliminary trajectory is around 80 95 degrees. Based on observations by Ramon van der Hilst who observed the fireball from Bussloo, the estimated entry angle for the fireball is about 5 degrees only: a very shallow, earthgrazing angle which explains the long trajectory. (I asked Ramon to estimate the angle of the fireball with respect to the horizontal at the moment Ramon was looking roughly perpendicular to the preliminary trajectory. That angle, about 5 degrees as Ramon reports, should be close to the entry angle)

I used these values and an 18-20 km speed estimate to compute a nominal heliocentric orbit: and then played around by widely varying the values for speed, entry angle, entry azimuth around these nominal values.

The interesting point is, that for all of these, I get an Aten orbit as a result. Aten asteroids are asteroids whose perihelion lies within the orbit of the earth and who's aphelion lies only just outside the orbit of the earth. They have a semi-major axis < 1.0 AU and aphelion (just) over 1 AU.

The aphelion values I get for the approximate fireball orbit, are in the range 1.0 - 1.15 1.05 AU, the semi-major axis values are in the range 0.9 to 0.6 AU. Solutions based on higher speeds (I varied between 12 km/s and 30 km/s in my calculations) favour the slightly larger aphelion values and shorter semi-major axis.

A wide variation in entry azimuth (I tried between 60 and 110 120 degrees) and entry angle (I tried for values between 5 and 45 degrees, the latter clearly a too large value by the way) does not alter this picture much: they all result in Aten orbits.

I need to alter the trajectory direction to values significantly larger than entry from a direction of  120 degrees (well past due east) to get aphelion values that start to get well beyond 1.15 AU and semi-major axis values > 1.0 AU.

For the current very preliminary nominal trajectory solution (entry azimuth ~82 ~95 degrees, entry angle ~5 degrees) I get these values when varying the assumed entry speed of the fireball:

[editted table 15:25 UT to reflect new calculations/correction of error]

Vini    q    Q     a     e     i

12.0   0.82  1.00  0.91  0.10  6.5
15.0   0.46  1.02  0.74  0.39  15.0
18.0   0.31  1.04  0.67  0.55  20.7
20.0   0.24  1.05  0.65  0.62  24.8
25.0   0.16  1.09  0.62  0.76  37.4
27.0   0.13  1.11  0.62  0.79  43.7
30.0   0.11  1.14  0.62  0.83  54.5

Vini is the initial speed (in km/s), q the perihelion distance (in AU), Q the aphelion distance (in AU), a the semi-major axis (in AU), e the eccentricity, i the inclination.

These values should be taken with caution and only as rough indications. There are (still) large uncertainties in the trajectory and entry angle, as well as the speed of the fireball. They do show however (as well as variations on the trajectory not listed here) that an Aten-orbit is the implied solution.

The Earth encountered the meteoroid close to the meteoroid's aphelion, when it was moving almost in parallel with the Earth.

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NOTE / UPDATE 26/09/2012, 19:25 UT: There is some confusion on the web regarding my analysis and the "retrograde"/ "prograde" character of this object.
The "retrograde"character is only true for an earth-centered orbit (i.e., an object orbiting the earth, such as an artificial satellite). An east-west movement in that case means it is "retrograde" (against the motion of the earth's rotation).
This is not necessarily the case for a sun-centered orbit however. An east-west moving object then can be (and is, in this case!) in a normal, "prograde" orbit (=moving in the same direction around the sun as the planets). The difference is the frame of reference: earth-centric versus sun-centric.
So beware: the "retrograde" orbit refers to what the orbit would be for an earth-orbiting satellite (which this object was not). The Aten heliocentric orbit presented here, is however prograde.

More on the 21 September 2012 fireball: why it definitely was a meteor

I should have done this analysis earlier but did not have the time available until now. What follows now is a quick and back-of-the-envelope kind of calculation, but in my (not so) humble opinion it is adequate to the question at hand.

It concerns, of course, the splendid slow fireball seen widely over NW Europe near 21:55 UT on 21 September 2012. I posted on it before, focussing on saying "no" to the suggestion that this could have concerned a satellite reentry. In the post that now follows, I further strengthen the conclusion that it was not a satellite reentry, but a genuine meteoric fireball.

The map above gives a quick (and not particularly accurate) back-of-the-envelope reconstruction of the fireball trajectory. It is based on trajectory descriptions from Bussloo in the Netherlands and Dublin in Ireland: by taking reported altitudes (with respect to stars) and general directions of reported start and endpoints, and an assumed altitude of 50 km, the trajectory above is what approximately results. (update 19:10 UT, 24 Sep: an updated version of the map is at the bottom of this post).

The resulting trajectory is some 1000-1200 km long. In what now follows, I have taken 1100 km as the distance travelled by this fireball.

Observers near the western and eastern ends of the trajectory would probably not see the complete trajectory. Observers approximately mid-way, in mid-Britain, would potentially see most if not all of the trajectory (from experience I know you can see bright fireballs from distances of 500 km).

Observers report durations between 20-60 seconds: most video's on the web suggest a 40+ seconds duration.

It would take a reentering satellite travelling at 8 km/s (the orbital speed at decay altitudes) about 138 seconds or roughly 2.25 minutes to travel this distance. While the reported fireball durations are long, none of the reports nor videos comes even remotely close to that value.

A meteoric fireball travelling at the lowest speed possible for such an object, 11.8 km/s, would take 93 seconds to travel that distance. This is still longer than almost all of the reports suggest, but clearly getting closer.

If we take an estimated duration of 60 seconds, the 1100 km trajectory length results in a speed of  approximately 18 km/s.

18 km/s is a very reasonable speed for a slow, asteroidal origin fireball.

(it is, let me repeat, also way too fast for a satellite reentry).

Meteorite dropping fireballs typically have speeds between 11.8 and 27 km/s. A speed near 18 km/s sits squarely in the middle of that speed interval.

(update: diagram added 14:45 UT, 24 Sep)

(click diagram to enlarge)

The 60 seconds probably represents the upper boundary value for the duration of the fireball. If we take a shorter duration of 40 seconds, the speed already increases to 27.5 km/s.

This quick back-of-the-envelope reconstruction therefore shows that this must have been a meteoric fireball, quite likely of asteroidal origin, and we definitely can exclude a satellite reentry.

The fragmentation described and filmed is not unusual for meteorite dropping fireballs (see the video's of the Peekskill meteorite fall in my previous post). The object probably entered the atmosphere under a very shallow angle, which together with the slow speed explains the unusually long duration of the event.

Meteors of this kind are rare, but they have been seen before. Think of the Peekskill meteorite fall, but also the famous 1972 daylight fireball over the Grand Tetons (that had a duration of over 100 seconds) and the Cyrilid Meteor Procession from 1913 (that lasted minutes).

Note: a previous post gives a number of other lines of evidence which likewise suggest this fireball was not man-made space debris.

UPDATE: a further update is given in a new post: a very cautious orbital solution suggests an Aten orbit.

Note 2: on how I made this quick and (emphasis) rough trajectory reconstruction. I took observations that contain clear sky locations: e.g. a sighting from Dublin stating it went "through the pan of the Big Dipper"; the description from Bussloo observatory in the Netherlands; and later adding a.o. a photo from Halifax, UK, showing it just above the tail of Ursa Major. These descriptions can be turned into directions and elevations. Next, I drew lines from these sighting points towards the indicated directions, marking distances roughly corresponding to 30, 50 and 80 km altitude as indicated by the observed elevation [ distance = altitude / tan(elevation) ]. Near the start of the trajectory I marked 50 and 80 km, for Britain and Ireland I marked 30 and 50 km. These points then provide you with a rough trajectory.
From Dublin the object passed through North towards west. From Bussloo the object started NE (azimuth 60 degrees): these are important points of information too as it shows that the object started at least as far east as the Dutch-German border (and more likely over Sleswig-Holstein in N-Germany) and had its endpoint at least as far west as the northern part of Ireland.

Above: Updated map version, 24 Sep 19:10 GMT , also showing the principle of how it was reconstructed for three sighting locations. With thanks to Ramon van der Hilst for providing more detailed information on sky trajectory as seen from Bussloo (NL) on request.