[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.