# Identification of meteorite source regions in the Solar System

Mikael Granvik  Peter Brown  Department of Physics, P.O. Box 64, 00014
University of Helsinki, Finland  Department of Computer Science, Electrical
and Space Engineering, Luleå University of Technology, Box 848, S-98128
Kiruna, Sweden  Department of Physics and Astronomy, University of Western
Ontario, N6A 3K7, London, Canada  Centre for Planetary Science and
Exploration, University of Western Ontario, N6A 5B7, London, Canada

###### Abstract

Over the past decade there has been a large increase in the number of
automated camera networks that monitor the sky for fireballs. One of the goals
of these networks is to provide the necessary information for linking
meteorites to their pre-impact, heliocentric orbits and ultimately to their
source regions in the solar system. We re-compute heliocentric orbits for the
25 meteorite falls published to date from original data sources. Using these
orbits, we constrain their most likely escape routes from the main asteroid
belt and the cometary region by utilizing a state-of-the-art orbit model of
the near-Earth-object population, which includes a size-dependence in delivery
efficiency. While we find that our general results for escape routes are
comparable to previous work, the role of trajectory measurement uncertainty in
escape-route identification is explored for the first time. Moreover, our
improved size-dependent delivery model substantially changes likely escape
routes for several meteorite falls, most notably Tagish Lake which seems
unlikely to have originated in the outer main belt as previously suggested. We
find that reducing the uncertainty of fireball velocity measurements below
$\sim 0.1$ km/s does not lead to reduced uncertainties in the identification
of their escape routes from the asteroid belt and, further, their ultimate
source regions. This analysis suggests that camera networks should be
optimized for the largest possible number of meteorite recoveries with
measured speed precisions of order 0.1 km/s.

###### keywords:

Meteorites , Meteors , Asteroids , Comets , Orbit determination

††journal: Icarus

##  1 Introduction

Understanding meteorite source regions in the solar system is one of the
central problems in contemporary planetary science. Association of certain
meteorite classes with families of asteroids or specific asteroids based on
commonalities in their reflectance spectra is one approach to bridging the
asteroid-meteorite divide (Binzel et al., 2015). As meteorites are delivered
to the Earth through a long process of stochastic gravitational and radiative
perturbations (Morbidelli and Gladman, 1998), the orbit immediately prior to
impact loses memory of its original, specific parent body. However, delivery
from the main asteroid belt is sufficiently rapid and well-understood, that
statistical inferences as to the source region for meteorite classes may be
possible if pre-atmospheric orbits for enough meteorites are measured, a
process which has been understood for some time (Wetherill, 1985; Wisdom,
2017). To date roughly two dozen meteorite falls have had orbits measured
(Borovička et al., 2015a).

The importance of measuring large numbers of meteorite orbits has motivated
development of a new generation of all-sky fireball networks whose primary
goal is the instrumental recording of meteorite producing fireballs (Howie et
al., 2017; Spurný et al., 2007; Colas, 2016). An outstanding question for such
fireball networks is the precision needed in measurement to meaningfully
associate a given meteorite orbit with potential source regions. Clearly the
smaller the measurement uncertainty the better, but at what point do reduced
uncertainties no longer improve the accuracy of statistical associations with
meteorite source regions? Also, what are the limitations on this inversion
process imposed by the assumptions of the delivery model?

In this work we have two goals. First, we aim to examine the currently known
two dozen meteorite orbits and apply a new near-Earth object (NEO) model which
has a size dependence (Granvik et al., 2016) to estimate the probable
escape/entrance routes/regions (ER) from, primarily, the main asteroid belt
for different meteorite classes. This is the necessary first step in trying to
ultimately associate meteorites to original parent bodies, generally presumed
to be associated with asteroid collisional families. Secondly, we use the
database of two dozen meteorite orbits to examine the role measurement errors,
particularly in speed, play in the orbital uncertainty and propagate this
through the ER model of Granvik et al. (2016). We hope to gain quantitative
insight into the corresponding source region uncertainties. This in turn will
provide operational guidance to those building new fireball networks as to the
required velocity measurement precision for meteorite dropping fireballs
needed to make meaningful source region identifications.

##  2 Methods

###  2.1 Computation of meteorite orbits

Our computation of the pre-atmospheric heliocentric orbit and associated
uncertainties for meteorite falls follows well-established algorithms used to
convert apparent meteor trajectories to orbits (Ceplecha, 1987). The method
has been validated through comparison with independent numerical approaches
(Clark and Wiegert, 2011). The essence of the algorithm is to use an in-
atmosphere local trajectory for a fireball and then translate this to an
equivalent heliocentric orbit. Here we take the trajectories reported in
various literature sources and transform the measured Right Ascension (RA) and
Declination (Dec) of an apparent radiant and the measured speed $v_{\infty}$
to the initial state vector. We assume that the average speed
$\overline{v}=v_{\infty}-1.0\,\mathrm{km}\,\mathrm{s}^{-1}$. The nominal
uncertainties on all measured quantities are also taken from published sources
when available. The Meteor Toolkit (Dmitriev et al., 2015), the only open-
source implementation of meteor orbit computation software as far as we know,
would have been an alternative to our in-house orbit computation software. As
it produces very similar results to the technique based on Ceplecha (1987),
which was also used in the majority of the fireball producing meteorite fall
studies published to date, we chose to remain with that original software.

A major systematic uncertainty in all meteorite computed orbits is the
correction applied for pre-luminous flight deceleration. For most published
meteorite orbits, insufficient information is provided in the original
references to compute this correction or even determine if it has been applied
to the final orbital elements. We do not explore this correction further, but
merely emphasize that for those studies which do not model the meteoroid
entry, the apparent initial speed may be underestimated by of order a few tens
of meters per second in some extreme cases.

###  2.2 Prediction of meteorite escape routes

A key ingredient for predicting a meteoroid’s likely source region in the
solar system is a model describing NEO orbit and size distributions (Granvik
et al., 2016). The model also provides probabilistic information about NEO ERs
as a function of semimajor axis $a$, eccentricity $e$, inclination $i$ and the
absolute magnitude $H$ for NEOs with $17<H<25$. The $H$ range corresponds to a
diameter $35\,\mathrm{m}\lesssim D\lesssim 1400\,\mathrm{m}$ when assuming an
average geometric albedo $p_{V}=0.14$ (Pravec et al., 2012). The model
accounts for 7 different ERs in the solar system: Hungaria asteroids, Phocaea
asteroids and Jupiter-family comets as well as asteroids escaping through the
$\nu_{6}$ secular resonance or the 3:1J, 5:2J and 2:1J mean-motion resonances
(MMR) with Jupiter. We note that less important yet non-negligible escape
routes have been incorporated into the adjacent main resonances.

When neglecting correlations between orbital elements derived from a meteoroid
trajectory, the probability for a meteoroid with orbital elements and
corresponding uncertainties ($a\pm\delta a$,$e\pm\delta e$,$i\pm\delta i$) to
originate in ER $s$ is

$\begin{split}p_{s}(a,e,i,\delta a,\delta e,\delta i)=\\\
\frac{\displaystyle{\int_{a-\delta a}^{a+\delta a}\int_{e-\delta e}^{e+\delta
e}\int_{i-\delta i}^{i+\delta
i}\int_{H=17}^{25}N_{s}(a,e,i,H)\,\mathrm{d}a\,\mathrm{d}e\,\mathrm{d}i\,\mathrm{d}H}}{\displaystyle{\sum_{s}\int_{a-\delta
a}^{a+\delta a}\int_{e-\delta e}^{e+\delta e}\int_{i-\delta i}^{i+\delta
i}\int_{H=17}^{25}N_{s}(a,e,i,H)\,\mathrm{d}a\,\mathrm{d}e\,\mathrm{d}i\,\mathrm{d}H}}\,,\end{split}$
(1)

where $N_{s}(a,e,i,H)$ is the debiased differential number distribution of
NEOs originating in ER $s$. So in essence the probability is the ratio of the
number of asteroids on the specified orbit originating in ER $s$ and the total
number of asteroids on the specified orbit. In practice, $N_{s}(a,e,i,H)$ is
discretized with bin sizes ($\Delta a$, $\Delta e$, $\Delta i$, $\Delta H$)
and used as a four-dimensional look-up table. In what follows Eq. 1 is
therefore approximated as

$\begin{split}p_{s}(a,e,i,\delta a,\delta e,\delta i,\Delta a,\Delta e,\Delta
i)=\\\
\frac{\displaystyle{\sum_{j=j_{\mathrm{min}}}^{j_{\mathrm{max}}}\sum_{k=k_{\mathrm{min}}}^{k_{\mathrm{max}}}\sum_{l=l_{\mathrm{min}}}^{l_{\mathrm{max}}}\sum_{m=1}^{M}N_{s}(a_{j},e_{k},i_{l},H_{m})}}{\displaystyle{\sum_{s=1}^{7}\sum_{j=j_{\mathrm{min}}}^{j_{\mathrm{max}}}\sum_{k=k_{\mathrm{min}}}^{k_{\mathrm{max}}}\sum_{l=l_{\mathrm{min}}}^{l_{\mathrm{max}}}\sum_{m=1}^{M}N_{s}(a_{j},e_{k},i_{l},H_{m})}}\,,\end{split}$
(2)

where the summation over $s$ is over all 7 ERs and the summation over $m$ is
over all $M$ $H$ bins available. The limits for the summation over $j$ are
defined as

$j_{\mathrm{min}}=\begin{cases}\lceil\frac{a-\delta a-a_{\mathrm{min}}}{\Delta
a}\rceil&\text{when }a_{\mathrm{min}}<a-\delta a,\\\ 1&\text{when
}a_{\mathrm{min}}\geq a-\delta a.\end{cases}$
$j_{\mathrm{max}}=\begin{cases}0&\text{when }a_{\mathrm{min}}>a+\delta a,\\\
\lceil\frac{a+\delta a-a_{\mathrm{min}}}{\Delta a}\rceil&\text{when
}a_{\mathrm{min}}<a+\delta a<a_{\mathrm{max}},\\\ J&\text{when
}a_{\mathrm{max}}\leq a+\delta a.\end{cases}$

where $a_{\mathrm{min}}$ and $a_{\mathrm{max}}$ are the minimum and maximum
semimajor axes covered by the model, respectively, $J$ is the number of
semimajor axis bins in the discretized model, and $\lceil x\rceil$ denotes the
ceiling of $x$. The limits for $k$ and $l$ are obtained by replacing
($j_{\mathrm{min}}$, $j_{\mathrm{max}}$, $a$, $\delta a$, $a_{\mathrm{min}}$,
$a_{\mathrm{max}}$, $\Delta a$, $J$) with ($k_{\mathrm{min}}$,
$k_{\mathrm{max}}$, $e$, $\delta e$, $e_{\mathrm{min}}$, $e_{\mathrm{max}}$,
$\Delta e$, $K$) and ($l_{\mathrm{min}}$, $l_{\mathrm{max}}$, $i$, $\delta i$,
$i_{\mathrm{min}}$, $i_{\mathrm{max}}$, $\Delta i$, $L$), respectively.

The model by Granvik et al. (2016) is bounded by
$a_{\mathrm{min}}=0.3\,\mathrm{au}$, $a_{\mathrm{max}}=4.2\,\mathrm{au}$,
$e_{\mathrm{min}}=0$, $e_{\mathrm{max}}=1$, $i_{\mathrm{min}}=0^{\circ}$, and
$i_{\mathrm{max}}=180^{\circ}$. Note that Granvik et al. (2016) did not force
$a_{\mathrm{min}}=0.3\,\mathrm{au}$, but this is a naturally occuring lower
limit caused by the fact that there does not exist a mechanism to decouple an
asteroid’s orbit from that of Mercury. In terms of the resolution ($\Delta
a,\Delta e,\Delta i$) we here use both low resolution
($0.1\,\mathrm{au},0.04,4^{\circ}$) and high resolution
($0.05\,\mathrm{au},0.02,2^{\circ}$).

As with the NEO model of Bottke et al. (2002), the calculation assumes that
the meteoroid orbit is similar to the orbit of its asteroidal (or cometary)
parent body and the estimate for the source region applies, strictly speaking,
to that parent body. We emphasize that, although large objects affect $p_{s}$,
this value is primarily driven by the smallest objects included in the NEO
model, that is, those with diameters of a few tens of meters or so, due to the
steep NEO size distribution.

##  3 Data

We collected the observed trajectories as well as meteorite classifications,
densities, and cosmic-ray exposure ages (the latter three collectively called
geophysical data hereafter) for known fireball-producing meteorite falls from
the literature (Tables 1 and 2). The list of meteorite falls should be
complete less a few recent and as of yet unpublished events. All meteorite-
producing fireballs with orbits that we have used have trajectories and speeds
computed using some combination of instrumental records, including dedicated
camera networks, calibrated casual video recordings, seismic, infrasound,
satellite or pre-atmospheric telescopic detection. Details of the nature of
each event and quality of the resulting orbits is discussed in Borovička et
al. (2015a). We have extracted from the original published reference for each
event (all primary references are listed in Tables 1) the local trajectory and
corresponding quoted uncertainties, and then independently computed orbits for
consistency.

Table 1: Equivalent trajectory data for meteorite falls having instrumentally
measured orbits. All angular elements are J2000.0. Latitude and longitude for
the reference positions, equivalent equatorial geocentric radiant coordinates,
speeds prior to deceleration from the Earth’s atmosphere ($v_{\infty}$) are
extracted from references, but modified to agree with published primary data
in some cases. In cases where references do not provide formal errors, the
last significant figure is taken as the uncertainty.

Meteorite name | Fall date and time | Lat | Lon | RA | Dec | $v_{\infty}$ | Ref.
---|---|---|---|---|---|---|---
| UTC | [deg] | [deg] | [deg] | [deg] | [km/s] |
Příbram | 1959-04-07 | 19.5033 | 49.510 | 14.830 | $192.34\pm 0.01$ | $17.47\pm 0.01$ | $20.93\pm 0.01$ | 27,34,35
Lost City | 1970-01-04 | 2.2333 | 36.005 | -95.090 | $315.0\pm 0.1$ | $39.0\pm 0.1$ | $14.235\pm 0.002$ | 18,19,20
Innisfree | 1977-02-06 | 2.2939 | 53.415 | -111.338 | $7.43\pm 0.3$ | $66.52\pm 0.01$ | $14.5\pm 0.1$ | 13,14
Benešov | 1991-05-07 | 23.0647 | 49.662 | 14.635 | $227.62\pm 0.01$ | $39.909\pm 0.002$ | $21.272\pm 0.005$ | 4,5
Peekskill | 1992-10-09 | 23.8000 | 39.663 | -78.206 | $208.9\pm 0.2$ | $-29.2\pm 0.3$ | $14.72\pm 0.050$ | 27,32,33
Tagish Lake | 2000-01-18 | 16.7283 | 60.000 | -134.200 | $90.4\pm 1.9$ | $29.9\pm 2.8$ | $15.8\pm 0.6$ | 38,39,40
Morávka | 2000-05-06 | 11.8639 | 50.230 | 18.450 | $250.1\pm 0.7$ | $54.95\pm 0.25$ | $22.5\pm 0.3$ | 26,27
Neuschwanstein | 2002-04-06 | 20.3383 | 47.304 | 11.552 | $192.33\pm 0.03$ | $19.55\pm 0.04$ | $20.960\pm 0.040$ | 28,29
Park Forest | 2003-03-27 | 5.8406 | 41.130 | -87.900 | $171.8\pm 1.3$ | $11.2\pm 0.5$ | $19.5\pm 0.3$ | 31
Villalbeto de la Peña | 2004-01-04 | 16.7792 | 42.771 | -4.789 | $311.4\pm 1.4$ | $-18.0\pm 0.7$ | $16.90\pm 0.40$ | 41,42
Bunburra Rockhole | 2007-07-20 | 19.2311 | -31.450 | 129.827 | $80.70\pm 0.05$ | $-14.22\pm 0.04$ | $13.395\pm 0.007$ | 6
Almahata Sitta | 2008-10-07 | 2.7611 | 20.858 | 31.804 | $348.1\pm 0.1$ | $7.6\pm 0.1$ | $12.760\pm 0.001$ | 1,2
Buzzard Coulee | 2008-11-21 | 0.4453 | 53.183 | -109.875 | $290.0\pm 0.7$ | $77.0\pm 0.3$ | $18.05\pm 0.40$ | 7,8
Maribo | 2009-01-17 | 19.1411 | 54.585 | 13.657 | $124.7\pm 1.0$ | $19.7\pm 0.5$ | $28.30\pm 0.20$ | 21,22,23,24
Jesenice | 2009-04-09 | 0.9944 | 46.662 | 13.692 | $159.9\pm 1.2$ | $58.7\pm 0.5$ | $13.80\pm 0.25$ | 15
Grimsby | 2009-09-26 | 1.0496 | 43.534 | -80.194 | $242.60\pm 0.26$ | $54.98\pm 0.12$ | $20.95\pm 0.19$ | 12
Košice | 2010-02-28 | 22.4128 | 20.705 | 48.667 | $114.3\pm 1.7$ | $29.0\pm 3.0$ | $14.90\pm 0.35$ | 16
Mason Gully | 2010-04-13 | 10.6036 | -30.275 | 128.215 | $148.36\pm 0.05$ | $9.00\pm 0.05$ | $14.68\pm 0.011$ | 25
Križevci | 2011-02-04 | 23.3444 | 45.733 | 16.430 | $131.22\pm 0.05$ | $19.53\pm 0.04$ | $18.21\pm 0.07$ | 17
Sutter’s Mill | 2012-04-22 | 14.6036 | 38.804 | -120.908 | $24.0\pm 1.3$ | $12.7\pm 1.7$ | $28.6\pm 0.6$ | 36,37
Novato | 2012-10-18 | 2.7417 | 36.295 | -123.463 | $268.1\pm 0.5$ | $-48.9\pm 0.6$ | $13.75\pm 0.12$ | 30
Chelyabinsk | 2013-02-15 | 3.3389 | 54.454 | 64.477 | $332.81\pm 0.14$ | $0.29\pm 0.14$ | $19.03\pm 0.13$ | 9,10
Annama | 2014-04-18 | 22.2358 | 68.775 | 30.787 | $213.0\pm 0.2$ | $8.8\pm 0.4$ | $24.20\pm 0.50$ | 3
Žd’ár nad Sázavou | 2014-12-09 | 16.2806 | 49.941 | 18.002 | $69.31\pm 0.02$ | $26.98\pm 0.02$ | $21.97\pm 0.030$ | 43
Ejby | 2016-02-06 | 21.0750 | 55.449 | 11.912 | $77.74\pm 0.09$ | $26.89\pm 0.38$ | $14.50\pm 0.100$ | 11

  * 1.

1Jenniskens et al. (2009) 2Welten et al. (2010) 3Trigo-Rodríguez et al. (2015)
4Spurný (1994) 5Borovička et al. (1998) 6Spurný et al. (2012a) 7Milley et al.
(2010) 8Milley (2010) 9Borovička et al. (2013a) 10Brown et al. (2013) 11Spurný
et al. (2016a) 12Brown et al. (2011) 13Halliday et al. (1978) 14Halliday et
al. (1981) 15Spurný et al. (2010) 16Borovička et al. (2013b) 17Borovička et
al. (2015b) 18McCrosky et al. (1971) 19Ceplecha (1996) 20Ceplecha and ReVelle
(2005) 21Keuer D and G (2009) 22Haak et al. (2010) 23Haak et al. (2011)
24Spurny et al. (2013) 25Spurný et al. (2012b) 26Borovička et al. (2003)
27Borovička and Kalenda (2003) 28Spurný et al. (2003) 29Spurný et al. (2002)
30Jenniskens et al. (2014) 31Brown et al. (2004) 32Brown et al. (1994)
33Ceplecha et al. (1996) 34Ceplecha (1961) 35Ceplecha (1977) 36Jenniskens et
al. (2012) 37Nishiizumi et al. (2014) 38Brown et al. (2001) 39Hildebrand et
al. (2006) 40Brown et al. (2002) 41Trigo-Rodriguez et al. (2006) 42Llorca et
al. (2005) 43Spurný (2015)

Table 2: Geophysical data for meteorite falls having instrumentally measured
orbits. This includes meteorite classification, bulk density and cosmic-ray
exposure age (CRE). All data are extracted from the associated references.

Meteorite name | Classification | Ref. | Bulk density | Ref. | CRE age | Ref.
---|---|---|---|---|---|---
|  |  | [kg m-3] |  | [Myr] |
Příbram | H5 | 73 | 3570 | 46 | 12 | 47
Lost City | H5 | 74 | – |  | 8 | 48
Innisfree | L5/LL5(?) | 75 | – |  | 26–28 | 49
Benešov | H5/LL3.5 | 76 | – |  | – |
Peekskill | H6 | 77 | – |  | 32 | 50
Tagish Lake | C2 | 40 | 1640 | 41 | >3 | 51
Morávka | H5 | 28 | 3590 | 28 | 5.7–7.7 | 28
Neuschwanstein | EL6 | 52 | 3500 | 53 | 43–51 | 52
Park Forest | L5 | 33 | 3370 | 54 | 12–16 | 55
Villalbeto de la Peña | L6 | 44 | 3420 | 44 | 43–53 | 44
Bunburra Rockhole | Euc-Anom | 56 | – |  | 22 | 57
Almahata Sitta | Ure-Anom | 1 | 2900–3300 | 58 | 16–22 | 59
Buzzard Coulee | H4 | 60 | 3370–3550 | 61 | – |
Maribo | CM2 | 62 | – |  | 0.8–1.4 | 62
Jesenice | L6 | 63 | – |  | 4 | 63
Grimsby | H5 | 64 | 3340–3370 | 64 | 21–26 | 13
Košice | H5 | 65 | 3320–3540 | 66 | 5–7 | 78
Mason Gully | H5 | 67 | 3280–3360 | 54 | – |
Križevci | H6 | 68 | – |  | – |
Sutter’s Mill | CM2 | 69 | 2156–2358 | 38 | 0.074–0.09 | 39
Novato | L6 | 31 | 3190–3350 | 31 | 8–10 | 31
Chelyabinsk | LL5 | 70 | 3321–3329 | 70 | 1 | 71
Annama | H5 | 72 | 3500 | 72 | 26–34 | 72
Žd’ár nad Sázavou | L3/L3.9 | 45 | 3050 | 45 | – |
Ejby | H5/6 | 11 | – |  | – |

  * 1.

1Jenniskens et al. (2009) 11Spurný et al. (2016a) 13Cartwright et al. (2010)
28Borovička and Kalenda (2003) 31Jenniskens et al. (2014) 33Simon et al.
(2004) 38Jenniskens et al. (2012) 39Nishiizumi et al. (2014) 40Brown et al.
(2001) 41Hildebrand et al. (2006) 44Llorca et al. (2005) 45Spurný (2015)
46Britt and Consolmagno (2003) 47Stauffer and Urey (1962) 48Baxter and
Funkhouser (1971) 49Goswami et al. (1978) 50Graf et al. (1997) 51Herzog and
Caffee (2014) 52Zipfel et al. (2010) 53Kohout et al. (2010) 54Macke (2010)
55Meier et al. (2017) 56Bland et al. (2009) 57Welten et al. (2012) 58Kohout et
al. (2011) 59Horstmann and Bischoff (2014) 60Hutson et al. (2009) 61Fry et al.
(2013) 62Haak et al. (2012) 63Bischoff et al. (2011) 64McCausland et al.
(2010) 65Ozdín et al. (2015) 66Kohout et al. (2014b) 67Dyl et al. (2016)
68Lyon et al. (2014) 69Zolensky et al. (2014) 70Kohout et al. (2014a)
71Righter et al. (2015) 72Kohout et al. (2016) 73Tucek (1961) 74Nava et al.
(1971) 75Kallemeyn et al. (1989) 76Spurný et al. (2014) 77Wlotzka (1993)
78Povinec et al. (2015)

##  4 Results and discussion

###  4.1 Orbits of known meteorite falls

We recomputed the orbits of known meteorite falls based on the observational
data presented in Sect. 3, using the original information from literature
sources as much as possible. In some cases we could not independently match
the published orbit with the radiant and speed given in the same reference. In
those cases we have tried to use the original trajectory information (and
stated errors) as much as possible to recompute the orbit from fundamental
measurements and propagate the uncertainties through to a final geocentric
radiant and orbit. Where this was not possible, we match the geocentric
radiant and geocentric velocity as published to produce the final orbital
elements, even if the final orbits differ slightly from published values. In
most cases these systematic differences are much smaller than the formal
uncertainties. In some cases, quoted errors represent only the uncertainty in
the mathematical model fit in the trajectory solution to data. This ignores
other uncertainties in the system such as centroid pick errors or differences
in calibration precision within the image as well as model assumptions of the
fit.

These differences are often due to ambiguities in the original reference, such
as whether apparent radiants refer to the beginning of the trajectory or the
mid-point (or end). We assume where this is not stated that apparent radiants
are computed for the beginning of the fireball.

In Table 1 we refer to an "equivalent" radiant and/or speed which produces the
literature values of the original apparent trajectory or geocentric
radiant/geocentric velocity. The final orbits are then found using our adopted
corrections as described above.

The resulting orbits are similar to typical NEO orbits with 20 falls having
nominal semimajor axes inside the 3:1J mean-motion resonance (MMR) with
Jupiter (J) and the remaining four having nominal semimajor axes suggesting an
origin in the outer main belt exterior to the 3:1J MMR but inside the 5:2J MMR
(Table 3). The 1-$\sigma$ uncertainty on the semimajor axis is typically
$\delta a<0.05\,\mathrm{au}$ but for the C and CM meteorite falls the
uncertainty is $\delta a\sim 0.3\,\mathrm{au}$ which immediately suggests that
the ER for C and CM meteorites cannot be accurately determined. The other
elements are well-constrained less two falls with essentially unconstrained
longitude of ascending node and argument of perihelion due to near zero-
inclination orbits.

Our recomputed orbits are generally in statistical agreement with those
reported in the original literature sources. However, some meteorite orbits do
show noticeable differences; for example in cases where complete initial state
vector information (like apparent radiant) are omitted (such as Lost City and
Annama). In other cases, these differences are due to the low inclination of
the orbits (e.g., Maribo and Villalbeto de la Peña) where small differences in
corrections will make large differences to the angular elements. For
Chelyabinsk, we have two independent literature estimates of the original
orbit and a low inclination which makes our independent recomputed orbital
elements differ slightly from both literature values. We have chosen to use
our recomputed values using uniform corrections (like average speed)
recognizing there may remain small systematic uncertainties due to lack of
consistency in reported state vector quantities. This is in addition to
quality differences resulting from the techniques used to make trajectory
measurements (cf. Borovička et al., 2015a).

Table 3: Orbital elements for meteorite-dropping fireballs. Semimajor axis ($a$), eccentricity $e$, inclination $i$, longitude of ascending node $\Omega$, argument of perihelion $\omega$. Meteorite name |  $a$ [au] | $e$ |  $i$ [deg] |  $\Omega$ [deg] |  $\omega$ [deg] | MJD UTC
---|---|---|---|---|---|---
Příbram | $2.4050\pm 0.0043$ | $0.6717\pm 0.0006$ | $10.4841\pm 0.0086$ | $17.8019\pm 0.0000$ | $241.723\pm 0.020$ | 36665.812639
Lost City | $1.6486\pm 0.0037$ | $0.4133\pm 0.0013$ | $11.940\pm 0.025$ | $283.7568\pm 0.0000$ | $160.67\pm 0.14$ | 40590.093056
Innisfree | $1.866\pm 0.051$ | $0.472\pm 0.014$ | $12.250\pm 0.22$ | $317.5223\pm 0.0002$ | $177.97\pm 0.13$ | 43180.095579
Benešov | $2.4826\pm 0.0024$ | $0.6273\pm 0.0004$ | $23.9807\pm 0.0074$ | $47.0004\pm 0.0000$ | $218.369\pm 0.017$ | 48383.961030
Peekskill | $1.489\pm 0.015$ | $0.4052\pm 0.0055$ | $4.88\pm 0.15$ | $17.0289\pm 0.0001$ | $307.46\pm 0.61$ | 48904.991667
Tagish Lake | $1.98\pm 0.19$ | $0.554\pm 0.045$ | $2.06\pm 0.97$ | $297.9013\pm 0.0007$ | $224.3\pm 2.5$ | 51561.697014
Morávka | $1.851\pm 0.079$ | $0.469\pm 0.022$ | $32.28\pm 0.42$ | $46.2573\pm 0.0000$ | $203.5\pm 1.8$ | 51670.494329
Neuschwanstein | $2.398\pm 0.017$ | $0.6693\pm 0.0024$ | $11.416\pm 0.032$ | $16.8257\pm 0.0000$ | $241.185\pm 0.061$ | 52370.847431
Park Forest | $2.53\pm 0.21$ | $0.680\pm 0.025$ | $3.25\pm 0.66$ | $6.1153\pm 0.0003$ | $237.5\pm 2.0$ | 52725.243356
Villalbeto de la Peña | $2.30\pm 0.22$ | $0.627\pm 0.036$ | $0.02\pm 0.49$ | $282\pm 180$ | $134\pm 180$ | 53008.699132
Bunburra Rockhole | $0.8530\pm 0.0010$ | $0.2425\pm 0.0014$ | $8.937\pm 0.072$ | $297.5945\pm 0.0000$ | $210.04\pm 0.15$ | 54301.801296
Almahata Sitta | $1.3085\pm 0.0003$ | $0.3060\pm 0.0001$ | $2.4373\pm 0.0023$ | $194.0822\pm 0.0000$ | $232.405\pm 0.019$ | 54746.115046
Buzzard Coulee | $1.246\pm 0.029$ | $0.228\pm 0.018$ | $25.07\pm 0.78$ | $238.9374\pm 0.0001$ | $211.3\pm 1.5$ | 54791.018553
Maribo | $2.48\pm 0.27$ | $0.807\pm 0.015$ | $0.1\pm 1.3$ | $297\pm 48$ | $279\pm 49$ | 54848.797546
Jesenice | $1.744\pm 0.068$ | $0.429\pm 0.023$ | $9.58\pm 0.48$ | $19.1950\pm 0.0002$ | $190.49\pm 0.54$ | 54930.041435
Grimsby | $2.035\pm 0.048$ | $0.518\pm 0.011$ | $28.08\pm 0.28$ | $182.9560\pm 0.0000$ | $159.85\pm 0.24$ | 55100.043731
Košice | $2.73\pm 0.23$ | $0.650\pm 0.030$ | $1.99\pm 0.47$ | $340.0713\pm 0.0024$ | $204.2\pm 1.5$ | 55255.933866
Mason Gully | $2.5566\pm 0.0094$ | $0.6159\pm 0.0014$ | $0.895\pm 0.032$ | $203.2134\pm 0.0015$ | $19.01\pm 0.08$ | 55299.441817
Križevci | $1.5428\pm 0.0087$ | $0.5205\pm 0.0034$ | $0.638\pm 0.026$ | $315.5544\pm 0.0035$ | $254.383\pm 0.081$ | 55596.972685
Sutter’s Mill | $2.57\pm 0.38$ | $0.823\pm 0.022$ | $2.4\pm 1.5$ | $32.716\pm 0.015$ | $77.9\pm 3.3$ | 56039.608484
Novato | $2.091\pm 0.079$ | $0.528\pm 0.018$ | $5.52\pm 0.11$ | $24.9625\pm 0.0002$ | $347.36\pm 0.30$ | 56218.114236
Chelyabinsk | $1.770\pm 0.022$ | $0.5792\pm 0.0061$ | $4.78\pm 0.13$ | $326.4136\pm 0.0003$ | $109.22\pm 0.18$ | 56338.139120
Annama | $2.08\pm 0.13$ | $0.690\pm 0.021$ | $14.23\pm 0.49$ | $28.5990\pm 0.0001$ | $263.08\pm 0.74$ | 56765.926493
Žd’ár nad Sázavou | $2.1020\pm 0.0088$ | $0.6808\pm 0.0015$ | $2.809\pm 0.018$ | $257.2618\pm 0.0002$ | $257.748\pm 0.043$ | 57000.678356
Ejby | $2.805\pm 0.094$ | $0.655\pm 0.012$ | $0.958\pm 0.098$ | $317.2078\pm 0.0080$ | $197.75\pm 0.25$ | 57424.878125

None of the meteoroid orbits have perihelion distances $q\lesssim
0.4\,\mathrm{au}$, that is, within the orbit of Mercury (Table 4). A lack of
low-$q$ orbits has also been reported for fireballs produced by meter-scale
Earth impacting meteoroids in general (Brown et al., 2016). A similar lack of
objects having orbits with q < 0.4 AU is present in the collection of 57
fireballs reported by Halliday et al. (1996) having terminal masses in excess
of 100 g and therefore probable meteorite producers. Super-catastrophic
disruptions of asteroids at small $q$ was recently proposed by Granvik et al.
(2016) as an explanation for the lack of known NEOs at small $q$. As mentioned
in Sect. 2.2, the model by Granvik et al. (2016) was calibrated with the
observed distribution of NEOs with $17<H<25$, that is, diameters
$35\,\mathrm{m}\lesssim D\lesssim 1.4\,\mathrm{km}$ when assuming a geometric
albedo $p_{V}=0.14$. As shown in the same paper there is a linear correlation
between $H$ and the perihelion distance at which the disruption typically
happens, $q^{\star}$. A simple linear extrapolation in ($H$,$q^{\star}$) space
from the model’s lower diameter limit of about $D\approx 35\,\mathrm{m}$ down
to $D\approx 1\,\mathrm{m}$ ($H\approx 32$) suggests that for 1-meter-diameter
objects $q^{\star}\approx 0.38\,\mathrm{au}$. This is remarkably well in
agreement with the fireball data and suggest that the lack of meter-scale
meteoroids with $q\lesssim 0.4\,\mathrm{au}$ is real and that, similar to
larger asteroids, they are destroyed at non-trivial distances from the Sun. In
addition, whatever mechanism or mechanisms are destroying these objects, the
correlation between disruption distance and size is remarkably simple over a
size range covering more than three orders of magnitude.

The aphelion distances are all well within the perihelion distance of Jupiter
indicating that these objects are detached from Jupiter’s direct influence.
This suggests that they are of asteroidal rather than cometary origin. The
only border-line cases are those with $Q\gtrsim 4.5\,\mathrm{au}$, that is,
Košice, Ejby, Maribo, and Sutter’s Mill. Especially for the latter two the
probability for a cometary origin is increased because of their classification
as carbonaceous chondrites. The strong anticorrelation between strong,
probable meteorite-producing fireballs, and trans-Jovian orbits is apparent in
the larger set of Prairie Network (PN) fireball data as well (Wetherill and
ReVelle, 1982), indicating that very few obviously cometary fireballs yield
meteorites.

Table 4: Orbital parameters for meteorite-dropping fireballs computed from their apparent radiants. The epoch of osculation for $q$ and $Q$ is identical to that in Table 3. Here $v_{g}$ is the geocentric speed of the meteoroid prior to impact, that is, the speed it would have in the absence of gravitational acceleration, whereas $v_{h}$ is the heliocentic velocity of the meteorite at the epoch of impact. Meteorite name |  $q$ [au] |  $Q$ [au] |  $v_{g}$ [km/s] |  $v_{h}$ [km/s]
---|---|---|---|---
Příbram | $0.7896\pm 0.0001$ | $4.0204\pm 0.0087$ | $17.437\pm 0.012$ | $37.4600\pm 0.0089$
Lost City | $0.9672\pm 0.0002$ | $2.3300\pm 0.0074$ | $9.1984\pm 0.0018$ | $35.584\pm 0.017$
Innisfree | $0.9860\pm 0.0000$ | $2.75\pm 0.10$ | $9.40\pm 0.23$ | $36.38\pm 0.18$
Benešov | $0.9252\pm 0.0001$ | $4.0401\pm 0.0048$ | $18.0807\pm 0.0059$ | $37.4271\pm 0.0046$
Peekskill | $0.8856\pm 0.0018$ | $2.093\pm 0.029$ | $10.090\pm 0.075$ | $34.369\pm 0.087$
Tagish Lake | $0.884\pm 0.011$ | $3.08\pm 0.39$ | $11.31\pm 0.84$ | $36.82\pm 0.59$
Morávka | $0.9822\pm 0.0038$ | $2.72\pm 0.16$ | $19.60\pm 0.23$ | $35.77\pm 0.28$
Neuschwanstein | $0.7930\pm 0.0004$ | $4.003\pm 0.033$ | $17.506\pm 0.048$ | $37.453\pm 0.034$
Park Forest | $0.8107\pm 0.0098$ | $4.251\pm 0.419$ | $16.05\pm 0.37$ | $37.79\pm 0.39$
Villalbeto de la Peña | $0.8596\pm 0.0074$ | $3.75\pm 0.45$ | $12.92\pm 0.53$ | $37.67\pm 0.50$
Bunburra Rockhole | $0.6461\pm 0.0019$ | $1.0599\pm 0.0003$ | $6.735\pm 0.039$ | $26.571\pm 0.022$
Almahata Sitta | $0.9081\pm 0.0000$ | $1.7088\pm 0.0005$ | $6.8024\pm 0.0019$ | $33.1258\pm 0.0021$
Buzzard Coulee | $0.9612\pm 0.0015$ | $1.530\pm 0.058$ | $14.19\pm 0.51$ | $32.92\pm 0.25$
Maribo | $0.478\pm 0.018$ | $4.48\pm 0.52$ | $25.80\pm 0.22$ | $38.03\pm 0.51$
Jesenice | $0.9965\pm 0.0007$ | $2.49\pm 0.14$ | $8.28\pm 0.42$ | $35.54\pm 0.28$
Grimsby | $0.9817\pm 0.0003$ | $3.088\pm 0.096$ | $17.89\pm 0.22$ | $36.52\pm 0.14$
Košice | $0.9563\pm 0.0042$ | $4.50\pm 0.47$ | $10.31\pm 0.44$ | $38.29\pm 0.36$
Mason Gully | $0.9820\pm 0.0002$ | $4.131\pm 0.019$ | $9.324\pm 0.016$ | $37.715\pm 0.017$
Križevci | $0.7397\pm 0.0012$ | $2.346\pm 0.019$ | $14.456\pm 0.089$ | $34.995\pm 0.047$
Sutter’s Mill | $0.456\pm 0.022$ | $4.69\pm 0.74$ | $25.96\pm 0.65$ | $37.68\pm 0.67$
Novato | $0.9879\pm 0.0004$ | $3.19\pm 0.16$ | $8.22\pm 0.20$ | $36.83\pm 0.22$
Chelyabinsk | $0.7447\pm 0.0021$ | $2.795\pm 0.045$ | $15.14\pm 0.16$ | $35.99\pm 0.086$
Annama | $0.6436\pm 0.0054$ | $3.51\pm 0.26$ | $21.45\pm 0.56$ | $36.60\pm 0.36$
Žd’ár nad Sázavou | $0.6709\pm 0.0003$ | $3.533\pm 0.018$ | $18.607\pm 0.035$ | $37.141\pm 0.024$
Ejby | $0.9677\pm 0.0006$ | $4.64\pm 0.19$ | $9.44\pm 0.15$ | $38.51\pm 0.14$

###  4.2 Escape routes and source regions

Based on the orbits derived above we first estimate the likely ERs for these
meteorites. Table 5 provides estimates of each meteorite-producing fireball’s
probable ER based on its measured orbit using a debiased low-resolution model
for NEO ERs (see Sect. 2.2). The differences are negligible when using an 8
times higher resolution for the orbital distribution as shown in Table 6. The
insensitivity to the resolution of the orbital distribution suggests that even
the low resolution is able to reproduce the typical dynamical features in the
steady-state orbit distributions for each ER. It thus implies that estimates
of the most likely ERs will not become more accurate by increasing the
resolution of the orbit model (see discussion in Sect. 4.3).

Table 5: Probabilities of different escape regions for meteorite falls based on the low-resolution NEO orbit model. Meteorite classification has been included to help interpretation. Meteorite name | Classification | Hungaria | $\nu_{6}$ | Phocaea | 3:1J | 5:2J | 2:1J | JFC
---|---|---|---|---|---|---|---|---
|  | [%] | [%] | [%] | [%] | [%] | [%] | [%]
Příbram | H5 | $0.8\pm 0.4$ | $15\pm 7$ | $0.0\pm 0.3$ | $70\pm 20$ | $10\pm 9$ | $0.0\pm 0.2$ | $2\pm 2$
Lost City | H5 | $24\pm 7$ | $69\pm 8$ | $0.0\pm 0.2$ | $7\pm 2$ | $0.3\pm 0.2$ | $0.02\pm 0.06$ | $0\pm 0$
Innisfree | L5/LL5? | $28\pm 4$ | $60\pm 4$ | $0.0\pm 0.5$ | $11\pm 2$ | $1.1\pm 0.5$ | $0.0\pm 0.1$ | $0\pm 0$
Benešov | H5/LL3.5 | $0.8\pm 0.4$ | $5\pm 2$ | $0\pm 7$ | $80\pm 30$ | $9\pm 9$ | $0.1\pm 0.3$ | $2\pm 3$
Peekskill | H6 | $20\pm 3$ | $72\pm 4$ | $0.00\pm 0.07$ | $7\pm 1$ | $0.17\pm 0.08$ | $0.0\pm 0.1$ | $0\pm 0$
Tagish Lake | C2 | $6.7\pm 0.6$ | $82\pm 2$ | $0.00\pm 0.01$ | $11\pm 1$ | $0.28\pm 0.09$ | $0.004\pm 0.006$ | $0.2\pm 0.1$
Morávka | H5 | $61\pm 5$ | $27\pm 3$ | $0\pm 2$ | $10\pm 1$ | $1.2\pm 0.4$ | $0.04\pm 0.05$ | $0\pm 0$
Neuschwanstein | EL6 | $1.4\pm 0.4$ | $26\pm 6$ | $0.0\pm 0.2$ | $63\pm 13$ | $9\pm 6$ | $0.0\pm 0.1$ | $1\pm 1$
Park Forest | L5 | $1.6\pm 0.2$ | $25\pm 3$ | $0.001\pm 0.006$ | $48\pm 5$ | $11\pm 4$ | $0.1\pm 0.1$ | $15\pm 5$
Villalbeto de la Peña | L6 | $3.4\pm 0.3$ | $50\pm 2$ | $0.001\pm 0.006$ | $41\pm 3$ | $2.7\pm 0.8$ | $0.03\pm 0.04$ | $3\pm 1$
Bunburra Rockhole | Euc- Anom | $24\pm 7$ | $68\pm 9$ | $0.00\pm 0.04$ | $7\pm 3$ | $0\pm 0$ | $0.1\pm 0.5$ | $0\pm 0$
Almahata Sitta | Ure - Anom | $25\pm 7$ | $70\pm 9$ | $0.0\pm 0.2$ | $5\pm 2$ | $0\pm 0$ | $0\pm 1$ | $0\pm 0$
Buzzard Coulee | H4 | $38\pm 7$ | $55\pm 7$ | $0.0\pm 0.7$ | $5\pm 1$ | $2\pm 2$ | $0\pm 0$ | $0\pm 0$
Maribo | CM2 | $2.3\pm 0.3$ | $33\pm 3$ | $0.000\pm 0.006$ | $36\pm 4$ | $6\pm 2$ | $0.07\pm 0.09$ | $22\pm 8$
Jesenice | L6 | $21\pm 31$ | $70\pm 3$ | $0.00\pm 0.06$ | $9\pm 1$ | $0.5\pm 0.2$ | $0.01\pm 0.03$ | $0\pm 0$
Grimsby | H5 | $45\pm 6$ | $23\pm 3$ | $0\pm 5$ | $25\pm 4$ | $7\pm 2$ | $0.1\pm 0.1$ | $0.0010\pm 0.0008$
Košice | H5 | $0.7\pm 0.1$ | $13\pm 2$ | $0.000\pm 0.003$ | $37\pm 4$ | $16\pm 5$ | $0.08\pm 0.09$ | $33\pm 11$
Mason Gully | H5 | $1.1\pm 0.5$ | $21\pm 8$ | $0\pm 0$ | $64\pm 18$ | $7\pm 7$ | $0.0\pm 0.2$ | $7\pm 9$
Križevci | H6 | $10\pm 2$ | $73\pm 6$ | $0.00\pm 0.05$ | $17\pm 4$ | $0.6\pm 0.4$ | $0\pm 0$ | $0\pm 0$
Sutter’s Mill | CM2 | $2.6\pm 0.3$ | $36\pm 3$ | $0.001\pm 0.006$ | $31\pm 3$ | $5\pm 1$ | $0.07\pm 0.08$ | $26\pm 11$
Novato | L6 | $4.6\pm 0.9$ | $89\pm 5$ | $0.000\pm 0.006$ | $6\pm 1$ | $0.3\pm 0.2$ | $0.0004\pm 0.0006$ | $0.08\pm 0.08$
Chelyabinsk | LL5 | $8\pm 3$ | $80\pm 8$ | $0.0\pm 0.1$ | $11\pm 4$ | $0.7\pm 0.7$ | $0.01\pm 0.02$ | $0\pm 0$
Annama | H5 | $6.8\pm 0.9$ | $62\pm 3$ | $0.0\pm 0.3$ | $25\pm 3$ | $5\pm 2$ | $0.04\pm 0.07$ | $0.3\pm 0.2$
Žd’ár nad Sázavou | L3/L3.9 | $6\pm 1$ | $72\pm 5$ | $0.00\pm 0.02$ | $19\pm 3$ | $1.0\pm 0.5$ | $0.002\pm 0.007$ | $1\pm 1$
Ejby | H5/6 | $0.3\pm 0.1$ | $5\pm 2$ | $0\pm 0$ | $15\pm 7$ | $32\pm 24$ | $0.1\pm 0.3$ | $50\pm 30$

Table 6: Probabilities of different escape regions for meteorite falls based on the high-resolution NEO orbit model. Meteorite classification has been included to help interpretation. Meteorite name | Classification | Hungaria | $\nu_{6}$ | Phocaea | 3:1J | 5:2J | 2:1J | JFC
---|---|---|---|---|---|---|---|---
|  | [%] | [%] | [%] | [%] | [%] | [%] | [%]
Příbram | H5 | $1.0\pm 0.5$ | $18\pm 8$ | $0.0\pm 0.3$ | $70\pm 20$ | $10\pm 10$ | $0.0\pm 0.2$ | $2\pm 3$
Lost City | H5 | $27\pm 5$ | $65\pm 6$ | $0.0\pm 0.1$ | $7\pm 2$ | $0.1\pm 0.1$ | $0.01\pm 0.04$ | $0\pm 0$
Innisfree | L5/LL5? | $26\pm 2$ | $61\pm 3$ | $0.0\pm 0.2$ | $12\pm 1$ | $0.9\pm 0.3$ | $0.03\pm 0.05$ | $0\pm 0$
Benešov | H5/LL3.5 | $0.5\pm 0.3$ | $3\pm 2$ | $0\pm 6$ | $90\pm 30$ | $9\pm 9$ | $0.1\pm 0.3$ | $2\pm 3$
Peekskill | H6 | $20\pm 3$ | $72\pm 4$ | $0.00\pm 0.06$ | $8\pm 1$ | $0.2\pm 0.1$ | $0.02\pm 0.06$ | $0\pm 0$
Tagish Lake | C2 | $6.7\pm 0.3$ | $81\pm 1$ | $0.001\pm 0.005$ | $11.7\pm 0.5$ | $0.28\pm 0.04$ | $0.004\pm 0.005$ | $0.22\pm 0.06$
Morávka | H5 | $62\pm 3$ | $28\pm 2$ | $0\pm 1$ | $9.5\pm 0.9$ | $0.9\pm 0.2$ | $0.03\pm 0.03$ | $0\pm 0$
Neuschwanstein | EL6 | $1.4\pm 0.4$ | $24\pm 6$ | $0.0\pm 0.2$ | $60\pm 10$ | $10\pm 7$ | $0.0\pm 0.1$ | $1\pm 2$
Park Forest | L5 | $1.6\pm 0.1$ | $27\pm 2$ | $0.001\pm 0.004$ | $53\pm 3$ | $9\pm 2$ | $0.08\pm 0.06$ | $9\pm 2$
Villalbeto de la Peña | L6 | $3.4\pm 0.2$ | $46\pm 1$ | $0.001\pm 0.004$ | $42\pm 2$ | $2.6\pm 0.4$ | $0.05\pm 0.04$ | $6\pm 1$
Bunburra Rockhole | Euc - Anom | $24\pm 7$ | $71\pm 9$ | $0.00\pm 0.03$ | $5\pm 2$ | $0\pm 0$ | $0.2\pm 0.9$ | $0\pm 0$
Almahata Sitta | Ure - Anom | $24\pm 7$ | $71\pm 9$ | $0.0\pm 0.3$ | $5\pm 2$ | $0\pm 0$ | $0\pm 2$ | $0\pm 0$
Buzzard Coulee | H4 | $41\pm 4$ | $54\pm 4$ | $0.0\pm 0.4$ | $3.8\pm 0.6$ | $1.0\pm 0.6$ | $0\pm 0$ | $0\pm 0$
Maribo | CM2 | $2.2\pm 0.2$ | $29\pm 2$ | $0.000\pm 0.003$ | $29\pm 3$ | $5\pm 1$ | $0.07\pm 0.06$ | $35\pm 6$
Jesenice | L6 | $23\pm 1$ | $68\pm 2$ | $0.00\pm 0.03$ | $8.0\pm 0.6$ | $0.6\pm 0.1$ | $0.01\pm 0.02$ | $0\pm 0$
Grimsby | H5 | $41\pm 5$ | $20\pm 2$ | $1\pm 4$ | $29\pm 4$ | $9\pm 3$ | $0.1\pm 0.1$ | $0\pm 0$
Košice | H5 | $0.62\pm 0.04$ | $11.5\pm 0.7$ | $0.000\pm 0.001$ | $35\pm 2$ | $18\pm 3$ | $0.09\pm 0.05$ | $35\pm 5$
Mason Gully | H5 | $1.2\pm 0.4$ | $20\pm 5$ | $0.00\pm 0.01$ | $60\pm 10$ | $7\pm 5$ | $0.0\pm 0.2$ | $13\pm 9$
Križevci | H6 | $9\pm 2$ | $71\pm 5$ | $0.00\pm 0.02$ | $20\pm 3$ | $0.05\pm 0.05$ | $0\pm 0$ | $0\pm 0$
Sutter’s Mill | CM2 | $2.4\pm 0.1$ | $34\pm 1$ | $0.001\pm 0.003$ | $32\pm 2$ | $5.4\pm 0.8$ | $0.07\pm 0.04$ | $26\pm 5$
Novato | L6 | $5.1\pm 0.6$ | $87\pm 3$ | $0.000\pm 0.003$ | $7.5\pm 0.8$ | $0.4\pm 0.1$ | $0.0001\pm 0.0003$ | $0.11\pm 0.06$
Chelyabinsk | LL5 | $8\pm 1$ | $79\pm 4$ | $0.00\pm 0.05$ | $12\pm 2$ | $0.5\pm 0.2$ | $0.0003\pm 0.0008$ | $0\pm 0$
Annama | H5 | $7.0\pm 0.4$ | $64\pm 1$ | $0.0\pm 0.1$ | $24\pm 1$ | $4.9\pm 0.7$ | $0.05\pm 0.04$ | $0.27\pm 0.07$
Žd’ár nad Sázavou | L3/L3.9 | $6\pm 1$ | $74\pm 5$ | $0.00\pm 0.02$ | $18\pm 3$ | $0.9\pm 0.4$ | $0\pm 0$ | $0.9\pm 0.7$
Ejby | H5/6 | $0.21\pm 0.06$ | $4\pm 1$ | $0\pm 0$ | $11\pm 4$ | $21\pm 9$ | $0.1\pm 0.1$ | $60\pm 30$

When correlating meteorite types with their likely ERs it becomes clear that
the inner main belt and the Hungaria group are the likely ERs for almost all
known meteorite falls (Fig. 1). However, for meteorites (or their parent
bodies) escaping the main belt through the 3:1J MMR, we cannot rule out an
origin in the middle belt combined with subsequent orbital evolution to a
smaller semimajor axis, such as through Yarkovsky drift. There is,
nevertheless, substantial evidence from current meteorite orbits and the
present delivery model that few meteorite falls directly originate in the
outer main belt or from the immediate JFC population. The bias is largely
explained by orbital dynamics as asteroids from the outer main belt have a
small contribution to the part of NEO orbital-element phase space that harbor
the most likely Earth-impacting orbits, that is, those with $a\sim
1\,\mathrm{au}$, $e\sim 0$, and $i\sim 0^{\circ}$.

Figure 1: Escape regions for different meteorite groups. The area of the
filled circle is proportional to the probability that the meteorite originates
in that source region or escapes the main asteroid belt through that escape
route. Note that Benešov and Innisfree have mixed classifications as shown in
Table 2 of LL3 and LL5, respectively.

The material strength of meteoroids can be expected to also cause (a part of)
this bias, particularly assuming outer belt asteroids and JFCs are composed of
weaker material which is much more easily destroyed upon impact with the
Earth’s atmosphere leaving no macroscopic meteorites to be found. This notion
is consistent with the fireball record (Flynn et al., 2017) where most
fireballs having comet-like orbits also have lower penetrating ability on
average, indicative of more fragile structure, than fireballs on more
asteroid-like orbits, a long established result (Wetherill and ReVelle, 1982;
Borovička, 2007).

Asteroid types with weaker material strength are also expected to be fairly
common in the inner belt in the size range of meteorite parent bodies (DeMeo
and Carry, 2014). While there are 3 carbonaceous chondrites among the known
meteorite producing falls with orbits, this still amounts to only about 13% of
the entire sample, almost an order of magnitude higher than the relative
abundance of carbonaceous chondrites among all recovered meteorites (3.5%).

In contrast, approximately 1/3 of asteroids with diameters
$5\,\mathrm{km}<D<20\,\mathrm{km}$ in the inner main-belt are C types, while
the fraction of NEOs which are C-types is in the 20-35% range (Binzel et al.,
2015). It is notable, that these three meteorite producing fireballs are also
extraordinary in that they were all produced by comparatively large impactors,
ranging from 1.5 tonnes for Maribo to 56 tonnes for Tagish Lake (Borovička et
al., 2015a). Taken together, this suggests a material strength bias is
present.

The essentially complete lack of falls connected to the Phocaea group and to
asteroids escaping the belt through the 2:1 mean-motion resonance with Jupiter
can be explained by both dynamical and material-strength arguments. In terms
of dynamical arguments these groups have a factor of several smaller impact
probabilities with the Earth compared to other asteroidal sources (Granvik et
al., 2018), and hence a collision with the Earth is less likely. As for
material strength, the outer asteroid belt is well-known to be mass dominated
in carbonaceous asteroids that are assumed to produce weak meteoroids(DeMeo
and Carry, 2014). Recently a low albedo (and hence likely carbonaceous)
asteroid family was found in the Phocaea region, likely dominating the size
distribution of Phocaeas at scales akin to meteoroid parent bodies (Novaković
et al., 2017).

CM meteorites have been linked to B-type asteroids (de León et al., 2012) and
Ch/Cgh-type asteroids (Vernazza et al., 2016). Ch-like asteroids with a
0.7-$\mu$m hydration band are found across the asteroid belt with a minor
preference for the middle belt ($2.5\,\mathrm{au}<a<2.8\,\mathrm{au}$)
(Rivkin, 2012). B-type asteroids (SMASS II) are also found across the belt
with a slight preference for the middle belt. C-type asteroids that lack the
0.7-$\mu$m hydration band are expected to typically be found closer to the Sun
where temperatures are high enough to drive out volatiles. Our results show
that Tagish Lake, an ungrouped C meteorite, is very likely a sample of such a
C-type asteroid as it likely originates in the inner part of the main belt and
does not show signs of water. This is in contrast to earlier work (Hildebrand
et al., 2006) which suggested a comparatively large probability (1/4) that
Tagish Lake originated directly from the outer part of the main belt.

Sutter’s Mill and Maribo, the two CM2 meteorites in our sample, have very
similar orbits and ER source probabilities. Both have relatively high ER
affinities with the JFC population but, even within the upper bounds of
uncertainty, are more likely to be from the inner to middle main belt. It is
most likely these are from middle belt Ch/Cgh-type or B-type asteroids.

The likely source region for Chelyabinsk, an LL5 meteorite, is in the inner
main belt with an escape through $\nu_{6}$ as has also previously been shown
(Popova et al., ). There is some controversy over the classification of
Innisfree as either an L5 (generally accepted; Rubin, 1990) or LL5 (Smith,
1980). If Innisfree belongs to the LL5 group it implies that we would have two
LL5 meteorites with associated orbits and both indicate a likely origin in the
inner main belt with an escape through $\nu_{6}$. This could indicate that
these meteorites were originally part of a common parent body. The spectral
similarity of LL chondrites and (8) Flora as well as the proximity of the
Flora family to $\nu_{6}$ has been suggested as evidence for Flora being the
parent body of LL chondrites (Vernazza et al., 2008; Dunn et al., 2013). A
modern re-analysis could reduce the uncertainty on the classification of
Innisfree, but to the best of our knowledge such a re-analysis has not been
performed. We note that Stubenberg, which we do not include in our study as
the lack of complete published primary trajectory data does not permit us to
do an independent computation consistent with other published events, is an
LL6 chondrite. The currently published orbital elements (Spurný et al., 2016b)
suggest a high ER-likelihood for $\nu_{6}$ (70%) and lesser likelihood for
3:1J and Phocaea (23% and 6%, respectively). Interestingly, Stubenberg’s orbit
has the largest probability of originating from the Phocaea group among all
our examined cases.

H chondrites comprise almost half our total sample. In most cases an ER from
either the 3:1J MMR or the $\nu_{6}$ is indicated. This is consistent with
some of the H-chondrite’s being from in the inner main belt (Trigo-Rodríguez
et al., 2015), potentially linked to (6) Hebe (Gaffey and Gilbert, 1998) or
smaller parents located in this zone (Binzel et al., 2015). However, two of
the H5 chondrites with measured orbits (Ejby and Košice) show comparatively
strong probabilities (with large error) as being from JFCs, a surprising
result. This may simply reflect the mixing between main belt asteroids and
JFCs which occurs near the $T_{j}\approx$ 3 region as noted by Tancredi
(2014).

The five measured L chondrite orbits are strongly associated with ERs in the
inner main belt, in particular the $\nu_{6}$ and to a lesser degree the 3:1J
MMR. These remain small number statistics, but this is somewhat at odds with
an origin from the Gefion family (Nesvorný et al., 2009; Jenniskens et al.,
2014) in the outer belt which would require an escape predominantly from the
5:2J or, less likely, the 3:1J MMR.

Our predictions for the ERs of Almahata Sitta and Bunburra Rockhole, both
primarily $\nu_{6}$, are in agreement with previous studies (Gayon-Markt et
al., 2012; Bland et al., 2009).

Figure 2: CRE age and bulk density for meteorites for which both have been
measured. The error bars show the range of possible values with the nominal
value equal to the midpoint of the range. Note that only the nominal value has
been reported for many measurements (Table 2). The meteorite with the lowest
measured density (Tagish Lake) only has a measured lower limit for the CRE
age, but for plotting reasons we have here used an (artificial) upper limit of
6 Myr.

The CRE age and bulk density are correlated in the sense that low densities
are only measured for meteorites with short CRE ages (Fig. 2). In principle,
the correlation could be due to either material properties (low-density
materials are more fragile and therefore CRE ages are typically short) or
dynamical reasons (low-density materials are more common in the outer asteroid
belt and dynamical lifetimes for objects originating in the outer belt are
shorter than for objects originating in the inner belt). The latter mechanism
is likely to be less important, because $\nu_{6}$ is the most likely ER for
the meteorites with the lowest densities and short CRE ages (Tagish Lake and
Sutter’s Mill). The interpretation is currently based on the measurements of
only 13 meteorites, but it can be tested by measuring CRE age and/or bulk
density for the remaining 12 meteorites.

Additional insight to the origins of meteorites can be obtained by comparing
the CRE age to the dynamical age typical for objects originating in a specific
ER. A particular question is whether meteorites separated from their parent
bodies while still in the asteroid belt or if they separated later from NEOs.
We estimated the dynamical age of the meteorites by calculating the time it
takes for test asteroids in orbital integrations carried out by Granvik et al.
(2016) to evolve from a $q=1.3\,\mathrm{au}$ orbit to the orbit of the
meteorite immediately prior to the impact with the Earth (Table 7). For
orbital similarity we required the test asteroid’s orbital elements to
reproduce the meteorite orbit to within the latter orbit’s uncertainty. The
relatively small uncertainties implied that only a limited number of test
asteroids, out of the more than 90 thousand integrated, ever reached orbits
similar to those of the meteorites considered here, and hence the
uncertainties are substantial.

Table 7: Dynamical age of meteorites assuming an origin in the asteroid belt. The dynamical age is calculated as the time it takes to evolve from an asteroidal ER (at the NEO-MBO border) to the orbit just before impact with the Earth’s atmosphere. We only consider test asteroids whose orbits ($a$,$e$,$i$) reproduce the meteorite orbits to better than 1-$\sigma$ as reported in Table 3. The estimates are based on the orbital integration of more than 90 thousand test asteroids as reported by Granvik et al. (2016). The numbers given for each meteorite and ER are median dynamical age in Myr, range of dynamical ages in Myr, and the number of test asteroids that reproduce the meteorite orbit. Dynamical ages corresponding to the most likely ERs are highlighted in boldface font. Note that Maribo and Ejby are likely to originate from the JFC population. Note also that the orbit of Almahata Sitta is known so accurately that none of the test asteroids available to us reproduce its orbital elements to within the orbital uncertainty. Meteorite name | Hungaria | $\nu_{6}$ | Phocaea | 3:1J | 5:2J | 2:1J
---|---|---|---|---|---|---
Příbram | – | 5.9/0.9–11.0/2 | 1.5/1.5–1.5/1 | 0.1/0.1–0.1/1 | – | –
Lost City | 2.3/2.3–2.3/1 | 3.7/1.9–11.4/6 | – | 13.2/13.2–13.2/1 | – | –
Innisfree | 47.1/47.1–47.1/1 | 3.6/0.8–22.8/7 | 53.8/53.8–53.8/1 | 16.6/9.5–23.2/5 | 6.3/1.6–8.3/3 | 7.1/3.6–10.6/2
Benešov | – | – | – | 0.3/0.3–0.3/1 | – | –
Peekskill | 60.7/60.7–60.7/1 | 8.1/3.7–16.8/7 | 167.0/167.0–167.0/1 | 19.1/3.4–24.3/3 | – | –
Tagish Lake | 74.7/74.7–74.7/1 | 1.8/0.0–16.4/7 | 115.8/115.8–115.8/1 | 2.3/0.8–7.2/4 | 11.2/1.6–20.9/2 | 0.4/0.4–0.4/1
Morávka | 15.8/15.8–15.8/1 | 22.4/4.4–167.5/7 | 79.1/79.1–79.1/1 | 10.1/2.1–17.6/4 | 8.7/5.0–12.4/2 | 12.6/12.6–12.6/1
Neuschwanstein | 553.7/553.7–553.7/1 | 3.0/0.8–39.5/7 | 1.0/1.0–1.0/1 | 0.8/0.2–4.3/5 | 7.6/1.8–13.4/2 | –
Park Forest | 74.9/74.9–74.9/1 | 7.4/1.4–22.0/7 | 55.4/55.4–55.4/1 | 1.2/0.0–6.0/5 | 1.0/0.0–5.8/3 | 0.6/0.1–0.9/3
Villalbeto de la Peña | 74.8/74.8–74.8/1 | 3.8/1.1–31.6/7 | 185.6/185.6–185.6/1 | 0.9/0.0–1.7/4 | 0.7/0.1–1.5/3 | 0.1/0.1–0.1/1
Bunburra Rockhole | 99.3/99.3–99.3/1 | 10.0/4.6–18.3/3 | – | – | – | –
Almahata Sitta | – | – | – | – | – | –
Buzzard Coulee | 28.6/28.6–28.6/1 | 13.8/5.8–145.2/7 | 122.3/122.3–122.3/1 | 26.3/17.8–46.7/3 | 45.6/21.8–69.3/2 | –
Maribo | 74.9/74.9–74.9/1 | 3.7/1.8–24.1/7 | 185.8/185.8–185.8/1 | 1.0/0.0–1.9/4 | 0.4/0.2–1.0/3 | 1.5/0.7–6.3/3
Jesenice | 296.9/296.9–296.9/1 | 4.9/0.4–38.3/7 | 53.0/53.0–53.0/1 | 16.6/6.3–24.4/5 | 11.3/9.5–13.0/2 | 10.7/10.7–10.7/1
Grimsby | 43.3/43.3–43.3/1 | 56.2/4.0–172.4/7 | 12.8/12.8–12.8/1 | 3.5/1.6–26.6/5 | 4.7/2.9–6.6/2 | 12.4/1.5–23.3/2
Košice | 74.9/74.9–74.9/1 | 3.5/0.8–22.6/7 | 55.5/55.5–55.5/1 | 1.0/0.0–6.5/5 | 1.0/0.0–5.8/3 | 0.3/0.2–0.8/3
Mason Gully | 0.4/0.4–0.4/1 | 15.4/2.7–20.7/4 | – | 0.2/0.1–3.6/3 | – | –
Križevci | 1.1/1.1–1.1/1 | 10.4/1.7–18.2/4 | – | – | – | –
Sutter’s Mill | 74.9/74.9–74.9/1 | 2.8/0.4–21.9/7 | 50.7/50.7–50.7/1 | 0.3/0.0–23.8/5 | 0.3/0.0–6.2/3 | 0.4/0.2–1.0/4
Novato | 950.3/950.3–950.3/1 | 5.5/0.0–19.1/7 | 115.8/115.8–115.8/1 | 18.0/0.8–35.2/4 | 8.0/0.5–15.5/2 | –
Chelyabinsk | 60.9/60.9–60.9/1 | 5.6/2.2–27.8/7 | 1.9/1.9–1.9/1 | 2.1/1.3–3.3/3 | 7.3/1.9–12.6/2 | –
Annama | 54.9/54.9–54.9/1 | 4.3/0.3–58.1/7 | 24.3/24.3–24.3/1 | 11.0/0.5–129.5/5 | 1.3/0.6–1.6/3 | 8.0/1.7–14.3/2
Zd’nar nad Sazavou | 1.0/1.0–1.0/1 | 8.2/2.0–48.9/7 | – | 1.5/0.5–3.4/3 | – | –
Ejby | 0.7/0.7–0.7/1 | 21.0/0.7–30.4/7 | 53.5/53.5–53.5/1 | 0.8/0.4–5.1/4 | 0.1/0.1–0.3/3 | 0.3/0.3–0.3/1

By comparing the reported CRE ages to the dynamical ages we find that most
meteorites considered here were released from their parent bodies prior to
entering their most likely ERs (Fig. 3). This is particularly evident for
meteorites with the largest CRE ages. The two apparent outliers that are below
the dashed line (Morávka and Grimsby) suffer from small number statistics and
the range of dynamical ages cannot be estimated. Hence it is possible that
improved statistics in the dynamical analysis would shorten their likely
dynamical ages. Given the relatively slow dynamical evolution prior to
entering a resonance we find it reasonable to assume that the CRE ages are
typically reset at the time of the catastrophic impacts in the main asteroid
belt that sends fragments towards planet-crossing orbits. This picture is
consistent with the apparent lack of "meteorite-streams" (Pauls and Gladman,
2005) and is further supported by the apparent lack of near-Earth asteroid
streams (Schunová et al., 2012). It is broadly consistent with the notion that
most of the parent meteoroid’s time spent as a meter-sized object is in the
main belt undergoing Yarkovsky drift to one of the ERs (Vokrouhlický and
Farinella, 2000).

Figure 3: Comparison of dynamical age corresponding to the most likely ER
(Table 7) and the reported CRE age (Table 2). The dashed line corresponds to
an equal dynamical and CRE age with points above (below) the line implying
shorter (longer) dynamical ages than CRE age.

###  4.3 Sensitivity of ER prediction to accuracy of fireball velocity

In this section we will quantitatively assess the impact that improving the
determination of fireball velocity would have on our knowledge of meteorite
ERs. We start with the observed atmospheric trajectories for the 25 fireballs
discussed above, but rather than using the nominal published values for the
velocity uncertainty, we then calculate their heliocentric orbits using 8
different assumptions for the pre-atmosphere velocity uncertainty:
$0.001\,\mathrm{km}\,\mathrm{s}^{-1}$, $0.003\,\mathrm{km}\,\mathrm{s}^{-1}$,
$0.01\,\mathrm{km}\,\mathrm{s}^{-1}$, $0.03\,\mathrm{km}\,\mathrm{s}^{-1}$,
$0.1\,\mathrm{km}\,\mathrm{s}^{-1}$,
$0.3\,\mathrm{km}\,\mathrm{s}^{-1}$, $1\,\mathrm{km}\,\mathrm{s}^{-1}$, and
$3\,\mathrm{km}\,\mathrm{s}^{-1}$. Note that the two last velocity
uncertainties are larger than reported for any of these events.

As expected, the uncertainty on the orbital elements is reduced when the
velocity uncertainty becomes smaller and the radiant uncertainty remains
constant (left column in Fig. 4). The apparent insensitivity to velocity
uncertainties below about $0.1\,\mathrm{km}\,\mathrm{s}^{-1}$ is explained as
a consequence of a relatively large radiant uncertainty, which is kept at the
nominal observed value. At some point the velocity uncertainty becomes
negligible compared to the radiant uncertainty which now dominates the total
uncertainty budget. An improvement in the orbital uncertainty can thus no
longer be obtained by reducing the velocity uncertainty. For example, all but
one of the cases that show $\Delta a>0.01\,\mathrm{au}$ for a velocity
uncertainty of $0.001\,\mathrm{km}\,\mathrm{s}^{-1}$ have radiant
uncertainties $\geq 0.3^{\circ}$ whereas the ones that show $\Delta
a<0.01\,\mathrm{au}$ have radiant uncertainties $\leq 0.3^{\circ}$. The only
exception to this rule is Příbram which has a radiant uncertainty of only
$0.01^{\circ}$ and for which a velocity uncertainty of
$0.001\,\mathrm{km}\,\mathrm{s}^{-1}$ results in $\Delta a\approx
0.013\,\mathrm{au}$.

Figure 4: Resulting orbital-element uncertainty as a function of assumed
velocity uncertainty when using a fixed radiant uncertainty (left) and a
radiant uncertainty correlated with the velocity uncertainty (right).

Considering the substantial reduction in orbital uncertainty when reducing the
velocity uncertainty, it is somewhat surprising that the determination of
meteorite ERs—the primary scientific motivation for setting up fireball
networks—is much less improved (left column in Figs. 5–8). In all but a few
cases the largest improvement takes place when the velocity uncertainty is
pushed down to about $1\,\mathrm{km}\,\mathrm{s}^{-1}$. It is reassuring to
see that in most cases the primary ERs coincide with $\nu_{6}$ and 3:1J, the
most important NEO ERs. Note also that in all cases the predicted
probabilities are substantially different from the prior distribution, i.e.,
the limiting case in which the observations would provide no constraints on
the meteoroid orbit and, further, the ER.

Figure 5: ER prediction corresponding to different speed uncertainties
(defined in the legend) based on low-resolution model with fixed radiant
uncertainty for the meteor (left), high-resolution model with fixed radiant
uncertainty for the meteor (middle), and high-resolution model when assuming
linear correlation between radiant uncertainty and velocity uncertainty
(right). The gray line refers to the prior distribution, that is, the
predicted ER ratios in the absence of orbital information or, equivalently,
infinite orbital uncertainty. See Sect. 4.3 for a detailed discussion of these
plots.

Figure 6: As Fig. 5.

Figure 7: As Fig. 5.

Figure 8: As Fig. 5.

The results change only marginally when the resolution of the NEO model is
increased by a factor of 8 (left versus middle column in Figs. 5–8). The
explanation for the insensitivity to model resolution is that the model itself
is probabilistic. Increasing the model resolution can never result in a unique
determination of ER in the volumes of orbital space that harbour most NEOs,
because those volumes are fed by multiple ERs. As explained in the
Introduction, the physical reason for the non-determinism is the chaotic long-
term orbital evolution of NEOs. The chaotic orbital evolution leads to
overlapping but statistically distinct steady-state orbit distributions for
NEOs originating in different ERs. A comparison of the left and middle columns
in Figs. 5–8 suggests that the low-resolution model accurately captures the
overall picture and the high-resolution model provides little added value.

The assumption that the radiant uncertainty would not be reduced when the
velocity uncertainty is reduced is not entirely correct (Fig. 9). An accurate
treatment of the correlation would require detailed consideration of the
hardware and trajectory-computation approach for each case; this is not within
the scope of this paper, nor is it possible in most cases given the lack of
primary published data for each fireball producing meteorite fall.

Instead we take a simplistic approach and assume a linear correlation between
the radiant uncertainty and the velocity uncertainty. Based on a linear
regression we find that the radiant uncertainty (in degrees) can be
approximated as $3.9\delta v_{\infty}$ where the constant $b$ is statistically
indistinguishable from zero and hence omitted, and $\delta v_{\infty}$ is
provided in $\,\mathrm{km}\,\mathrm{s}^{-1}$ (Fig. 9). Given the velocity
uncertainties used above the radiant uncertainties are approximately
$0.004^{\circ}$, $0.012^{\circ}$, $0.04^{\circ}$, $0.12^{\circ}$,
$0.4^{\circ}$, $1.2^{\circ}$, $4^{\circ}$, $12^{\circ}$, respectively. Again,
note that the two last radiant uncertainties are larger than reported for any
of these events.

Figure 9: The observed correlation between velocity uncertainty and radiant
uncertainty ($\sqrt{(\Delta{\rm RA}\cos({\rm Dec}))^{2}+(\Delta{\rm
Dec})^{2}}$) for meteorite-producing fireballs. The black line is a linear fit
($y=ax+b$) to the data with $a=(3.9\pm
0.8)^{\circ}\,\mathrm{s}\,\mathrm{km}^{-1}$ and $b=(-0.02\pm 0.22)^{\circ}$.

In this simple model, the reduced radiant uncertainties that correspond to
small velocity uncertainties, lead to orbital uncertainties which are also
much reduced (right column in Fig. 4). The reduction of both velocity and
radiant uncertainty leads to a corresponding reduction in orbital uncertainty,
and for most cases there is no indication across the range of uncertainties
considered here that the orbital uncertainty would reach a plateau. There are
only two events that have clearly different behaviour compared to the rest:
Ejby and Sutter’s Mill. The orbital uncertainty for these two reaches a
plateau at some hundreds of meters per second.

The ER probabilities estimated with the correlated radiant uncertainties
hardly show variation when compared to the ER probabilities estimated using
fixed radiant uncertainties, particularly for $\delta v_{\infty}\lesssim
0.03\,\mathrm{km}\,\mathrm{s}^{-1}$ (middle versus right column in Figs. 5–8).
This is explained by the fact that the more accurate trajectories typically
correspond to orbital-element uncertainties smaller than the resolution of the
NEO model. Hence an improvement in the orbital accuracy does not directly
translate to an improvement in the source probabilities.

Figure 10: The average range in source probability as a function of
uncertainty on measured meteor speed.

To summarize the effect of the correlated radiant and speed uncertainty on the
ER prediction uncertainty, we consider the sample average of the maximum range
of ER probability (a proxy for the uncertainty) for each ER, and speed and
radiant uncertainty value (Fig. 10). The maximum range of ER probabilities for
a particular orbit solution is computed by finding the minimum and maximum ER
probabilities among the cells in the high-resolution model that are within the
orbital-uncertainty volume. The sample averages show a steep reduction in ER-
probability uncertainty when reducing the speed uncertainty (and the
correlated radiant uncertainty) from 3 km/s to about 0.1–0.3 km/s. Reducing
the speed uncertainty to below 0.1 km/s will only have a marginal impact on
the uncertainty of the ER probability. We also note that the JFC source will
always have an uncertainty greater than 10%.

##  5 Conclusions

In this work, we first computed heliocentric orbits for 25 meteorite falls
based on the trajectory information reported in the literature. For several
meteorite falls the trajectory information has only been reported in
conference abstracts. We urge members of the community to have their
trajectory analysis peer-reviewed, and published with enough supporting data
to allow colleagues to reproduce their results.

We then used the orbits (including the orbital uncertainties) and the NEO
model by Granvik et al. (2016) to estimate the most likely entrance routes
(ERs) for the falls. Both for orbits and ERs our results broadly agree with
previously published results in that most meteorite falls originate in the
inner main asteroid belt and escape through the 3:1J mean-motion resonance or
the $\nu_{6}$ secular resonance.

We then proceeded to test how the velocity uncertainty affects the results for
both orbits and ER probabilities. We found that pushing the velocity
uncertainty below some tens of meters per second does not lead to a
substantial reduction of uncertainties related to ER probabilities. Similarly,
increasing the resolution of the steady-state orbit distribution of the NEO
model also had a limited effect on the uncertainties related to ER
probabilities.

For the purpose of more accurately identifying meteorite ERs it would thus be
more useful to increase the number of ERs that go into the NEO model rather
than determining the meteoroid velocity more accurately or increasing the
resolution of the NEO orbit model. That is, if the fairly extensive ER
complexes used currently would be divided into their sub-components, it would
become possible to provide more specific (but still probabilistic) estimates
for the most likely ERs. Such an improvement primarily depends on the amount
of NEO data available — the current choice to use 7 ERs in the state-of-the-
art NEO model is dictated by the need to ensure that the model is not
degenerate (Granvik et al., 2016).

Finally, we may apply our results in terms of the optimal approaches to
designing and operating fireball camera networks. In particular, our results
suggest that a larger number of moderately precise meteorite recoveries, with
speed precision of order a few hundred meters/sec will provide the most
information regarding meteorite ERs and, ultimately, source regions.

## Acknowledgements

The authors wish to thank the two anonymous reviewers for their constructive
suggestions that helped improve the paper. MG is grateful for the kind
hospitality and financial support when visiting the University of Western
Ontario’s Meteor Physics Group. MG acknowledges funding from the Academy of
Finland (grant #299543) and the Ruth and Nils-Erik Stenbäck foundation. PGB
was supported by funding from the Meteoroid Environment Office through NASA
co-operative agreement NNX15AC94A, the Natural Sciences Research Council and
the Canada Research Chairs program.

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