# Direct measurement of decimeter-sized rocky material in the Oort cloud

Denis Vida Peter G. Brown Hadrien A. R. Devillepoix Paul Wiegert Danielle E.
Moser Pavol Matlovič Christopher D. K. Herd Patrick J. A. Hill Eleanor K.
Sansom Martin C. Towner Juraj Tóth William J. Cooke Donald W. Hladiuk

## Abstract

The Oort cloud is thought to be a reservoir of icy planetesimals and the
source of long-period comets (LPCs) implanted from the outer Solar System
during the time of giant planet formation. The abundance of rocky ice-free
bodies is a key diagnostic of Solar System formation models as it can
distinguish between “massive” and “depleted” proto-asteroid belt scenarios and
thus disentangle competing planet formation models. Here we report a direct
observation of a decimeter-sized ($\sim 2$ kg) rocky meteoroid on a retrograde
LPC orbit ($e\approx 1.0$, i = $121^{\circ}$). During its flight, it
fragmented at dynamic pressures similar to fireballs dropping ordinary
chondrite meteorites. A numerical ablation model fit produces bulk density and
ablation properties also consistent with asteroidal meteoroids. We estimate
the flux of rocky objects impacting Earth from the Oort cloud to be
$1.08^{+2.81}_{-0.95}~{}\mathrm{meteoroids/10^{6}~{}km^{2}/yr}$ to a mass
limit of 10 g. This corresponds to an abundance of rocky meteoroids of $\sim
6^{+13}_{-5}$% of all objects originating in the Oort cloud and impacting
Earth to these masses. Our result gives support to migration-based dynamical
models of the formation of the Solar System which predict that significant
rocky material is implanted in the Oort cloud, a result not explained by
traditional Solar System formation models.

## Introduction

The sharp increase in the number of ground-based networks utilizing digital
cameras for observing fireballs [1, 2, 3, 4, 5] in recent years has resulted
in near continuous coverage of almost $2\%$ of the Earth’s atmosphere for
small impactors. Supplementing these ground-based instruments in fireball
detection is the Geostationary Lightning Mapper (GLM) instrument on board the
GOES-16 and 17 satellites. First deployed in 2016, GLM now observes a total of
$\sim 1/3$ of the Earth’s surface with a resolution of $\sim 10$ km at 500
frames per second in a narrow 1.1 nm pass band centered around the O I oxygen
triplet at 777.4 nm [6]. GLM is very efficient at detecting bright fireballs
which usually saturate ground-based cameras [7]. As camera saturation prevents
an accurate estimate of meteoroid properties during atmospheric entry, GLM
extends the usable measurement size range of bolides as compared to ground-
based cameras. The larger ground-based camera coverage, which provides
observations of fireball trajectories and orbits when fused with space-based
light curves, records larger numbers of the decimeter-sized meteoroid
population than previously possible and allows accurate estimates of their
physical properties.

Observations from earlier fireball networks [8, 9] have established that
decimeter-sized chondritic-like meteoroids which penetrate deeper into the
atmosphere predominantly come from asteroidal low-inclination orbits.
Similarly, most friable meteoroids which disrupt high in the atmosphere were
measured to be on Jupiter-family comet (JFC), Halley-type comet (HTC), or
long-period comet (LPC) orbits [10]. Minor cross-contamination of material
between asteroidal and JFC orbits is observed and can be explained by their
dynamical evolution [11], consistent with telescopic observations of comets
and asteroids [12]. In-situ measurements have found rocky (refractory)
materials in comets [13], but these are small, microscopic chondrules and CAI
fragments, presumed to be embedded during comet formation. However, the
presence of macroscopic (dm-sized) rocky material originating from the Oort
cloud (HTCs and LPCs) is much harder to explain. The abundance in the Oort
cloud of larger, refractory material which likely formed in the inner Solar
System would be a key diagnostic in distinguishing between dynamical models of
early Solar System formation [14, 15, 16].

Contemporary models which account for planetesimal collisions predict that a
significant number of rocky objects can only be implanted in the Oort cloud
during a Grand Tack dynamical instability episode caused by the radial
migration of the giant planets early in Solar System history [17]. The
dynamical instability causes removal of $50-90\%$ of rocky material in what is
now the asteroid belt in such a way as to reproduce the main-belt’s observed
orbital and compositional distribution [18, 19]. These migration models
necessitate a “massive” proto-asteroid belt scenario and predict the ratio of
icy to rocky planetesimals in the Oort cloud between 100:1 and 2000:1 [14, 20,
15, 16, 21, 17, 22]. Following this early and fast migration, a slower
dynamical diffusion process is postulated to further remove $\sim 70\%$ of the
main-belt leaving the mass we see today [23, 24]. Recent studies show that to
match the dynamical and geochemical evidence, the instability occurs as early
as $30-60$ Myr after the dissipation of gas in the protoplanetary disk [25,
26, 27].

The competing model of early Solar System formation, the pebble-accretion
model [28], eschews the migration scenario but allows for the rapid formation
of the giant planets before the solar gas nebula dissipates [29]. In the
pebble-accretion model, filaments of mm$-$ to cm-sized pebbles gravitationally
collapse quickly to form planetesimals [30]. The planetesimals in the
terrestrial region grow more efficiently than those beyond 1 au, so there is
no requirement to scatter rocky material to explain the small masses of Mars
and the asteroid belt [31]. As the initial mass of the proto-asteroid belt is
assumed to be small, the pebble-accretion model predicts that virtually no
scattered rocky objects are implanted into the Oort cloud. It predicts an
icy/rocky ratio of at least 10,000:1 [16].

The initial size of the proto-asteroid belt remains a contentious topic.
Recent work [32] suggests that the asteroid belt could have initially been
empty and later populated separately by S- and C-type objects. In this model,
S-type asteroids are implanted through simple gravitational diffusion as by-
products of terrestrial planet formation with C-types implanted during the
growth of the giant planets through aerodynamic drag destabilization [33].
This scenario is also compatible with an early onset of dynamical instability
and migration of the giant planets, which seems to be a necessary element in
the reproduction of observational constraints [34].

Recently, it has been shown that the migration-induced dynamical instability
is also compatible with an enhanced version of the pebble accretion model
which uses realistic opacities [35]. In this model, the terrestrial planets
form fast in only $\sim 10$ Myr, and then planet migration is invoked as one
of the possibilities to explain the hafnium-tungsten anomaly in the Earth’s
mantle caused by the Theia impact [36]. Nevertheless, even though the 1.5 to 4
au region is assumed to be a divergence zone [37] (in between the terrestrial
and giant-planet convergence zones where growth occurs), planetesimals in the
divergence zone only slowly dissipate into neighbouring regions and are not
scattered into highly excited orbits.

The earliest evidence of macroscopic asteroidal material in the Oort cloud was
the discovery of asteroid 1996 PW [14]. Despite its highly eccentric orbit
(eccentricity $e=0.9907$, inclination $i=30.09$, semi-major axis
$a=269.5~{}\mathrm{au}$, and period $p=4424$ yr, solution date 2021-Apr-14),
it showed no cometary-like activity. It had a D-type asteroid reflectance
spectrum [38, 39, 40], also similar to bare cometary nuclei observed at large
solar distances; hence its origin as asteroid or an extinct cometary nucleus
was uncertain.

More such tailless comet “Manx” objects [41] have since been discovered,
having a wide variety of surface properties, including S-type spectra
consistent with anhydrous rocky material [42, 43]. For example, comet C/2014
S3 (PANSTARRS) has an S-type reflectance spectrum, however it shows activity
consistent with sublimation of water ice [16]. To explain the discovery of
Oort cloud S-type objects in the context of the Solar System formation models,
dynamical simulations of the evolution of the distribution of cometary and
asteroidal objects were performed by ref. [17]. Taking the collisional
evolution of asteroids into account, they found that the Grand Tack model [18]
is the only model which predicts a sufficient icy/rocky mass ratio of Oort
cloud objects (on the order of 100:1) to explain the detection of the comet
C/2014 S3.

Pan-STARRS1 observations of LPCs have found that there is a deficit of objects
with diameters $D\lesssim 1$ km [44], assuming the physical processes
producing cometary activity are size-independent. These data show a
significant change in the cumulative size-frequency distribution (SFD), where
Ncum $\propto$ D-α, for $D\sim 2.8$ km, with $\alpha=3.6$ for larger, and
$\alpha=0.5$ for smaller objects, consistent with comet formation models [45].
Pan-STARRS1 is able to detect LPC objects down to a size of $D\sim 100$ m[44].
This either means that the small objects are devoid of volatiles or they do
not exist.

As telescopic measurements of an object in an LPC orbit may be compromised by
space weathering [46, 47], a more direct way to probe bulk physical properties
of LPC material is desirable. One alternate method is to observe fireballs
associated with an LPC-type meteoroid entering the atmosphere [48, 49].
Nevertheless, such observations suffer from small atmospheric collection
areas, so detection of decimeter-sized objects on long-period comet orbits is
rare [50].

By using the observed light curves and dynamics of mm$-$ and cm-sized cometary
meteoroids, their ablation behaviour is well explained if they are modelled as
a highly porous ($\sim 90\%$) collection of $10-300~{}\mu$m sized silicate
grains [51, 52]. The grain size distribution derived from observations of
cometary meteoroids matches well to in-situ measurements of the JFC comet
67P/Churyumov–Gerasimenko [10, 53]. Similarly, observations of dm-sized
meteorite-dropping fireballs can be well explained by modelling them as rocky
objects which fragment deep in the atmosphere when aerodynamic loading exceeds
their global mechanical strength [54]. In most cases, global strengths of
meteorite-producing fireballs are found to be much lower than the compressive
strengths of their associated meteorites, a finding ascribed to internal
cracks [49].

Categorizing meteoroid strength relies on a relative comparison of atmospheric
ablation behaviour. Generally speaking, slower, more massive, and stronger
meteoroids penetrate deeper into the atmosphere. The PE criterion [48] removes
the speed and mass bias so that the strength can be directly compared among
observed meteoroids (see Methods). Meteoroids can be sorted into several
groups based on material strength: Type I fireballs having PE $>-4.6$ are
related to ordinary chondrites (strongest material), Type II with $-5.25\leq$
PE $\leq-4.6$ are related to carbonaceous chondrites, while Type III with PE
$<-5.25$ are cometary (weakest material).

The first observation of a multi-cm sized rocky meteoroid on an HTC orbit was
recorded in 1997 over the Czech Republic, called the Karlštejn fireball [55,
56]. The $\sim 30$ gram object was on a retrograde orbit, $a=3.5$ au,
$i=138^{\circ}$, $e=0.7$, and $T_{J}=0.62$ (where $T_{J}>3$ are asteroidal
orbits, $2<T_{J}<3$ are short period comet orbits, and $T_{J}<2$ are LPC
orbits). It entered the atmosphere at $65~{}\mathrm{km~{}s^{-1}}$ and
penetrated down to an end height of 65 km, about 25 km deeper than cometary
objects of similar speed and mass. It was classified as a Type I (rocky)
fireball based on its PE value. Its spectrum was highly depleted in volatile
elements, notably sodium, and distinct from cometary fireballs. It reached a
maximum dynamic pressure ($P_{\mathrm{dyn}}=v^{2}\rho_{\mathrm{air}}$) of 660
kPa before ablating away gradually, indicating that the true mechanical
strength of the body was not reached as there was no evidence of catastrophic
disruption. The dynamics of the body were consistent with a bulk density of
3700 $\mathrm{kg~{}m^{-3}}$. Nevertheless, the semi-major axis was smaller
than most long-period comets and the dynamic pressures lower than what
decimeter-sized chondritic meteorite-dropping fireballs survive, likely due to
the small mass of the body. The authors theorized it was a cm-sized rocky
component originally embedded in a comet, perhaps as part of an irradiated
crust [55].

Records from decades of meteor shower observations have not revealed any
macroscopic ($>$ cm-sized) lithic material mixed in with fragile HTC or LPC
meteoroids. Smaller inclusions have been documented, notably several
mm$-$sized Type I fragments of Leonid fireballs were observed during the 1998
Leonid fireball storm [57, 58, 59] as have some gram-sized Type I Taurids [1].
However, the Taurids are an unusual stream; they are on the dynamical boundary
between JFC and asteroidal orbits, are generally classified as Type II
material, can be difficult to separate from the sporadic background, and have
an origin likely related to fragmentation rather than gas drag sublimation
[60].

## Results

Here we report the direct observation of a decimeter-sized rocky meteoroid (PE
= -4.49, Type I) on a long-period comet orbit (i = $121^{\circ}$, $e\approx
1.0$, $T_{J}=-0.46$, see Table 1). This meteoroid reached dynamic pressures
similar to those of ordinary chondrites. The $\sim 2$ kg body entered the
atmosphere $\sim 100$ km north of Edmonton, Alberta, Canada on February 22,
2021 at 13:23:17 UTC. Its full atmospheric luminous path was recorded by two
Global Fireball Observatory (GFO) all-sky cameras [3] (see Figure 1) and over
200 security and dash cameras. In addition, it was detected by the
Geostationary Lightning Mapper (GLM) instruments on board the Geostationary
Operational Environment Satellites (GOES) 16 and 17, permitting measurement of
its unsaturated light curve (see the Photometric Calibration section in
Supplementary Information). We used the most recent astrometric calibration
methods [5] and computed the atmospheric trajectory (internal accuracy of 30
m) using the GFO data and using one additional security camera (accuracy 70 m)
(see the Astrometric Calibration section in Supplementary Information). The
fireball entered the atmosphere with a velocity of
$62.1~{}\mathrm{km~{}s^{-1}}$ and penetrated down to a height of 46.5 km,
about 20 km deeper than the Karlštejn event that had a similar velocity but a
$70\times$ smaller mass. The parent body search did not return any matches, an
expected result given the large orbital period.

Table 1: Geocentric radiant and heliocentric orbit (J2000.0). Description |  | Nominal value | 95% Confidence Interval
---|---|---|---
|  |  | Lower | Upper
Geocentric right ascension of radiant | $\alpha_{g}$ | $271.922^{\circ}$ | $271.856^{\circ}$ | $271.990^{\circ}$
Geocentric declination of radiant | $\delta_{g}$ | $+4.40^{\circ}$ | $+4.19^{\circ}$ | $+4.64^{\circ}$
Geocentric velocity ($\mathrm{km~{}s^{-1}}$) | $v_{g}$ | $60.97$ | 60.89 | 61.00
Semimajor axis (au) | $a$ | $104$ | 50 | 230
Eccentricity | $e$ | $0.9941$ | 0.9878 | 0.9973
Perihelion distance (au) | $q$ | $0.6150$ | 0.6126 | 0.6170
Argument of perihelion | $\omega$ | $103.95^{\circ}$ | $103.51^{\circ}$ | $104.25^{\circ}$
Longitude of ascending node | $\Omega$ | $333.857472^{\circ}$ | $333.857460^{\circ}$ | $333.857485^{\circ}$
Inclination | $i$ | $121.40^{\circ}$ | $120.98^{\circ}$ | $121.80^{\circ}$
Aphelion distance (au) | $Q$ | $207$ | 100 | 459
Period (yr) | $T$ | $1059$ | 357 | 3484
Last perihelion date |  | 2021-01-16.23 | 2021-01-16.06 | 2021-01-16.33
Tisserand parameter w.r.t. Jupiter | $T_{J}$ | $-0.46$ | -0.48 | -0.40
Figure 1: The fireball as seen from the two GFO stations. It was observed for
a total of 2.4 s with a path length of 148.5 km. Top: Miquelon Lake. Bottom:
Vermilion (the Big Dipper can be seen at the left side of the inset). The
fireball is moving left to right, and the periodic breaks in the fireball are
used to encode the absolute time to an accuracy of 1 ms.

### Ablation modelling

The dynamics, light curve, and the fragmentation behaviour were modelled using
a semi-empirical meteoroid ablation model [54] (see Methods) which has been
successfully applied to multiple meteorite-producing fireballs, as well as
cometary meteoroids. The comparison between observations and the model fit is
shown in Figure 2; the modelling details are given in the Modelling Results
section in Supplementary Information. A bulk density of
$\rho_{\mathrm{m}}=3300~{}\mathrm{kg~{}m^{-3}}$, as appropriate for chondritic
meteorite-dropping fireballs [9], fits the observed dynamics well.

Figure 2: Left: Observed and simulated light curve. The solid black line is
the nominal fit with the parameters and fragmentation behaviour given in the
Supplementary Materials (Supplementary Tables 9 and 8). A no-fragmentation
solution for Type I (black), II (green), and III (red) objects is also shown.
The GLM light curve was calibrated to an accuracy of $\pm 0.1$ mag using three
independent high speed fireballs where GLM light curves and ground-based
records were available. The GoPro light curve was calibrated to an accuracy of
$\pm 0.3$ mag. Right: Observed and simulated deceleration profile (lag) for
various simulation scenarios. The lag is the distance a decelerating meteoroid
falls behind a hypothetical non-decelerating meteoroid moving at the initially
observed velocity. As the fireball showed a wake, it was not possible to
determine the along the trajectory positions of the leading fragment to the
same accuracy as the transverse positions. The lag measurement errors are
reflected in the scatter around the zero lag axis which is on the order of
$\pm 200$ m. The Cochrane security camera was not used for velocity
measurement due to lower accuracy.

As a demonstration of how improbable that this was a weak, cometary-like body,
we modelled a non-fragmenting fireball using physical properties appropriate
for cometary meteoroids (ablation coefficient
$\sigma=0.08~{}\mathrm{kg~{}MJ^{-1}}$,
$\rho_{\mathrm{m}}=1000~{}\mathrm{kg~{}m^{-3}}$, and luminous efficiency
$\tau$ for Type III bodies [61, 62]), with a $10\times$ larger pre-atmospheric
mass (20 kg) than the Alberta fireball keeping the same trajectory parameters.
The hypothetical cometary meteoroid only penetrated down to a height of $\sim
60$ km.

The simulation was repeated for a hypothetical carbonaceous chondrite
meteoroid ($\sigma=0.042~{}\mathrm{kg~{}MJ^{-1}}$,
$\rho_{\mathrm{m}}=2000~{}\mathrm{kg~{}m^{-3}}$, $\tau$ for Type II bodies
[61, 62]) with the same 20 kg mass. In this case, the meteoroid only
penetrated to a height of 53 km while the simulated light curve was $\sim 2.5$
magnitudes brighter than observed.

We found no combination of model parameters for carbonaceous-chondrite or
cometary-like material which could fit the observations. If these hypothetical
Type II and III objects had the same mass as our Type I rocky object, their
end heights would have been a further 8 km higher than these values. From
other fireball measurements, a cometary body at these speeds and masses is not
expected to withstand the aerodynamic loading below $\sim 80$ km without
fragmenting [60].

The fireball fragmented under dynamic pressures similar to those observed for
rocky meteoroids. Ref. [49] analyzed the fragmentation behaviour of several
instrumentally observed ordinary chondrite (OC) meteorite dropping fireballs.
They found that OC meteoroids do not fragment randomly but follow a specific
pattern. The first phase of fragmentations occurs at dynamic pressures between
0.04–0.12 MPa, interpreted as being caused by detaching of weakly cemented
fragments from the surface. The second phase occurs between 0.5-5 MPa,
presumably due to weaknesses associated with internal cracks.

Figure 3 shows their measurements of relative fragmentation mass loss versus
the dynamic pressure for a collection of fireballs with recovered OC
meteorites and fireballs of OC physical properties that were too small to
produce meteorites. The dynamic pressure at fragmentation measured for the
Alberta fireball matches well to the chondritic fragmentation profile.

Figure 3: Observed fragmentations of the Alberta meteoroid (vertical dashed
lines) compared to previously observed fragmentation behaviour of ordinary
chondrite (OC) fireballs. The dynamic pressure
($\Gamma\rho_{\mathrm{air}}v^{2}$) is computed using the drag coefficient of
$\Gamma=1.0$ to be consistent with values from ref. [49]. The uncertainty in
the dynamic pressure due to short-term variations in the air mass density
which are not captured by the NRLMSISE-00 model [63] is about 25%. However,
uncertainties due to the unknown values of $\Gamma$ in the flow regime of this
meteoroid are not quantified. The gray bars show the sum of relative mass loss
at the given dynamic pressure for fireballs with recovered meteorites, and
white bars are for (OC) fireballs with currently unrecovered meteorites, or
which were too small to produce meteorites

.

### Flux of rocky meteoroids from the Oort cloud

It is possible to estimate the flux and the ratio of Type I (rocky) objects in
comparison to weaker Type II/III from the Oort cloud at the limiting mass
appropriate for fast fireballs. The only published source for which there are
reliable mass and time-area product estimates is the fireball data set of the
Meteorite Observation and Recovery Project (MORP)[64]. MORP is the the only
unbiased “clear sky” survey of fireballs. There are a total of 30 fireballs
with $T_{J}<2$, speed $>50~{}\mathrm{km~{}s^{-1}}$, and a mass larger than 10
g in the MORP data set. The speed limit removes the speed-dependent mass
sensitivity [61], allowing us to set consistent limiting mass for the flux. We
set the mass limit to 10 g (in the contemporary mass scale following ref.
[49]), for which the data set is complete. This mass is also significantly
larger than any previously observed refractory inclusions in cometary
material; the largest Type I Taurids are an order of magnitude smaller [1].

Among the population of 30 fireballs with $T_{J}<2$, only one is a Type I
object (MORP catalog #441 with $m=20$ g), which was also on a retrograde orbit
($e=0.969$, $i=159.7^{\circ}$). This additional fireball, together with
Karlštejn and the Alberta event, forms an isolated group among all published
fireballs: they have $T_{J}<1$, retrograde orbits, and are quite far from the
PE dividing line for Type II objects (see Figure 4 and Table 2).

Figure 4: All published fireball data showing PE as a function of Tisserand’s parameter ($T_{J}$) with respect to Jupiter for $T_{J}<2$ fireballs in the MORP data set [64]. PE is a meteoroid strength factor, see the Methods section for more details. The Type I (rocky) objects of interest above the PE = -4.6 dividing line between Type I/II fireballs form a clearly separate grouping. The blue arrow points to the Alberta event. The MORP data set does not contain formal uncertainties, but they are of the same order as for the Alberta event.  Table 2: Table of all $T_{J}<2$ Type I objects in the literature satisfying our criteria. The errors for Karlštejn and the Alberta event are the 95% confidence intervals. We assumed a conservative uncertainty in the mass of the Alberta event of a factor of 2, due to possible variations in the luminous efficiency [65]. Karlštejn has larger uncertainties as the mass was only derived dynamically (0.003 to 0.1 kg), which we converted to the contemporary mass scale (from ref. [48] to ref. [49]). The orbital uncertainties for the Karlštejn fireball are symmetric and taken from the original publication[55]. The MORP data set does not contain any uncertainties. The uncertainty of the ascending node is near zero as it reflects the time of the meteoroid intersecting Earth’s orbit (i.e. entering the atmosphere) which is accurately known. However for MORP, the uncertainty in the timing for some fireballs is on the order of tens of minutes ($\pm 10^{-5\circ}$ in the ascending node).  Name | PE | $T_{J}$ | Mass | a | q | e | i | $\omega$ | $\Omega$
---|---|---|---|---|---|---|---|---|---
|  |  | (kg) | (au) | (au) |  | (deg) | (deg) | (deg)
Alberta (this work) | $-4.49^{+0.12}_{-0.13}$ | $-0.46^{+0.06}_{-0.02}$ | $1.8^{+1.8}_{-0.9}$ | $104^{+126}_{-54}$ | $0.615^{+0.002}_{-0.002}$ | $0.994^{+0.003}_{-0.006}$ | $121.40^{+0.4}_{-0.4}$ | $104.0^{+0.3}_{-0.4}$ | 333.86
Karlštejn[55] | $-4.53^{+0.42}_{-0.23}$ | $0.64^{+0.12}_{-0.18}$ | $0.033^{+0.082}_{-0.030}$ | $3.5^{+0.18}_{-0.18}$ | $1.012^{+0.0002}_{-0.0002}$ | $0.710^{+0.016}_{-0.016}$ | $137.90^{+0.10}_{-0.10}$ | $174.60^{+0.14}_{-0.14}$ | 71.55
MORP #441[64] | -4.04 | -0.78 | 0.020 | 24.7 | 0.765 | 0.969 | 159.7 | 56.7 | 103.8

The total time-area product for the MORP clear-sky survey was $1.51\times
10^{10}$ $\mathrm{km^{2}~{}h}$ [64]. Given the 29 MORP fireballs satisfying
our orbital criteria, the total flux of carbonaceous and cometary (Type II and
III) objects can be computed. Assuming that times of meteor events are
distributed according to the Poisson distribution [66], the 95% confidence
interval is computed using the exact method [67] as
$[\mathrm{Pr}(\alpha/2,2x),\mathrm{Pr}(1-\alpha/2,2(x+1))]$, where
$\mathrm{Pr}$ is the percent point function of the $\chi^{2}$ distribution,
$x=29$ is the number of observed events, and $\alpha=0.05$ (i.e. the 95%
confidence interval). The corresponding range of observed events is
$[19.4,41.7]$, producing a flux of
$16.8^{+7.3}_{-5.6}~{}\mathrm{meteoroids/10^{6}km^{2}/yr}$ to a mass limit of
10 g.

As a check on the flux values and ranges we derive, we use data from the
Global Fireball Observatory cameras in Alberta. These were gradually deployed
starting with three cameras in July 2018, completing deployment with five
cameras in November 2018. We used known deployment times and atmospheric
coverage to compute a time-series of common collecting area for the network;
$0.24\times 10^{6}$ $\mathrm{km^{2}}$ for the three and $0.45\times 10^{6}$
$\mathrm{km^{2}}$ for the five camera configuration. The common area was
computed as an intersection of at least two camera fields of view at the
height of 70 km and within a radius of 300 km from an individual camera [3].
Given that the average daily effective collection time is $3~{}\mathrm{h/day}$
in Alberta [68], we estimate that the time-area product for the network up
until February 2021 is $1.2\times 10^{9}$ $\mathrm{km^{2}~{}h}$. This network
has yet to record a single Type II or III object on an LPC orbit in that time
period, although it should have observed $\sim 2$ given the MORP flux. Using
Poisson statistics, the probability for this non-observation is 10%, which is
within statistical significance.

The total time-area product for $T_{J}<2$ rocky Type I events is $1.63\times
10^{10}$ $\mathrm{km^{2}~{}h}$, derived by combining the values from the two
networks. Note that the product is entirely dominated by the MORP survey,
making up 90% of the total. We only include the Alberta event and the MORP
#441 fireball in the flux estimate. To include the Karlštejn fireball we would
need an accurate estimate of the completeness and the time-area product for
the contemporary European Network [68], which is not available.

Given that only two events were observed, the 95% Poisson confidence interval
is $[0.24,7.22]$ for the number of events. The total flux of rocky Type I
objects on LPC orbits is thus
$1.08^{+2.81}_{-0.95}~{}\mathrm{meteoroids/10^{6}~{}km^{2}/yr}$ for a mass
limit of 10 g, or $6.0^{+12.8}_{-5.2}$% of the total flux of all meteoroids
impacting Earth on LPC orbits. This suggests of order 1–20% (about one in five
to about one in a hundred) of LPC meteoroids at tens of gram sizes or larger
are rocky.

## Discussion

The confirmation of the existence and a comparatively high abundance of
macroscopic lithic objects in the Oort cloud, constraining the ratio of
icy/rocky objects to between 130:1 and 5:1 for masses $>10$ g (95% CI),
supports the need for a mechanism of ejection of inner Solar System material
into nearly hyperbolic orbits. Even in a scenario where most of the Oort cloud
objects are captured from other star systems [69], an ejection mechanism still
needs to be present to explain the radial mixing of material.

We interpret the icy/rocky ratio as an intrinsic parameter of the population,
assuming that it has remained unchanged in the Oort cloud since its
implantation during the formation of the Solar System, as it is consistent
with reflectance spectra surveys of large Oort cloud objects [17] which
predict an icy/rocky ratio on the order of 100:1.

Was the Alberta fireball itself a primordial object? Collisions between
similarly-sized Oort cloud objects are very rare across the range of sizes
[70, 71], however $>100$ m bodies are known to experience surface processing
due to impacts of m-sized and smaller objects. Surface gardening and erosion
due to $\mathrm{\mu}$m-sized dust impacts from the interstellar medium (ISM)
[72] is generally experienced by objects of all sizes. The ISM erosion model
predicts that all primordial objects smaller than a few meters should have
been eroded away [73], indicating that the Alberta fireball possibly
originated from a larger parent asteroid.

Our findings support a massive proto-asteroid belt scenario as the source of
rocky objects. Recent work [17] shows that the Grand Tack dynamical
instability model is the only one able the reproduce the observed abundance of
rocky material in the Oort cloud predicting that the total icy/rocky ratio
depends on the duration of the instability. As the model predicts more rocky
material is implanted if the instability occurs faster, direct measurement of
the icy/rocky fraction can be used to constrain the duration of the early
instability. These findings challenge Solar System formation models based on
pebble accretion alone, which currently cannot explain the high observed
abundance of rocky material in the Oort cloud as derived from fireball
measurements and telescopic reflectance spectra data.

## Methods

### Ablation and fragmentation model

The dynamics and light curve of the fireball were simulated using the
established semi-empirical model [54] which was successfully applied to
reconstruct the fragmentation behaviour and physical properties of many
meteorite dropping fireballs [74, 75, 76, 49] and fainter meteors [51, 10]. In
this model, the meteoroid is initially treated as a single body, but increases
in brightness and sudden deceleration are explained by fragmentation. Previous
works established several main modes of fragmentation: splitting into several
single-body fragments, steady erosion of 10 $\mu$m $-$ 1 mm sized refractory
constituent grains from the meteoroid’s surface, ejection of an eroding
fragment, and a sudden release of dust (i.e. a large number of constituent
grains)[54].

All fragments and grains are modelled using the classical equations of single-
body ablation [61]:

$\frac{dv}{dt}=-Km^{-1/3}\rho_{\mathrm{air}}v^{2}\,,$ (1)

$\frac{dm_{a}}{dt}=-K\sigma m^{2/3}\rho_{\mathrm{air}}v^{3}\,,$ (2)

where $K$ is the shape density coefficient, $m$ the meteoroid mass ($m_{a}$ is
the ablated mass), $v$ the velocity, $\rho_{\mathrm{air}}$ the atmosphere bulk
density (NRLMSISE-00 model [77]), and $\sigma$ is the ablation coefficient.
The ablation coefficient regulates how much mass is removed from the meteoroid
per unit energy, and is usually expressed in $\mathrm{kg~{}MJ^{-1}}$
($\mathrm{s^{2}~{}km^{-2}}$ is also often found in the literature). The
parameter $K$ is used because the meteoroid density and shape cannot be
measured separately:

$K=\Gamma A\rho_{\mathrm{m}}^{-2/3}\,,$ (3)

where $\Gamma$ is the drag coefficient, $A$ is the shape coefficient (1.21 for
spheres which we adopt), and $\rho_{\mathrm{m}}$ is the meteoroid (or grain)
bulk density. The equations were numerically integrated using a
$\mathrm{4^{th}}$ order Runge-Kutta method and a time step of 2 ms. The
integration of individual fragments is stopped if their mass falls below
$10^{-14}$ kg or the speed below $3~{}\mathrm{km~{}s^{-1}}$, which is the
ablation limit [61].

The luminosity produced by ablation is computed as:

$I=-\tau\frac{v^{2}}{2}\frac{dm_{a}}{dt}+mv\frac{dv}{dt}\,,$ (4)

where $\tau$ is the luminous efficiency. In this work we use the modern
luminous efficiency function of ref. [49] to model the observed event.

If the meteoroid or an ejected fragment is set to erode at a given time in the
model, the total mass lost in erosion is regulated by the erosion coefficient
$\eta$ which is applied in the same manner as the ablation coefficient in
equation 2:

$\frac{dm_{e}}{dt}=-K\eta m^{2/3}\rho_{\mathrm{air}}v^{3}\,.$ (5)

For grain bulk density, we use $3500~{}\mathrm{kg~{}m^{-3}}$, appropriate for
refractory silicate grains. The total mass loss at a given time is then the
sum of the ablation and erosion mass loss:

$\frac{dm}{dt}=\frac{dm_{a}}{dt}+\frac{dm_{e}}{dt}\,.$ (6)

Inspired by in-situ observations of the mass distribution of cometary dust
[53], the masses of eroded grains are distributed according to a power-law
$n(m)\sim m^{-s}$ [78] where $n(m)$ is the number of grains of a given mass
$m$, and $s$ is the differential mass distribution index. An upper ($m_{u}$)
and a lower ($m_{l}$) grain mass limit is set during the modelling. To speed
up computation, this mass range is binned into $z$ bins per order of
magnitude, thus the integration of ablation equations is done only once for
every mass bin instead for every fragment. A mass sorting parameter can be
defined as $p=10^{1/z}$ and it follows that the total number of grain mass
bins within a range of masses is $k=\lceil\log(m_{l}/m_{u})/\log p\rceil$. The
total number of grains having a mass equal to the upper mass limit is then:

$n_{u}=\left\\{\begin{array}[]{ll}\frac{m_{e}}{km_{u}},&\text{for }s=2\\\
\frac{m_{e}}{m_{u}}\frac{1-p^{(2-s)}}{1-p^{k(2-s)}},&\text{for }s\neq
2\,,\end{array}\right.$ (7)

where $m_{e}$ is the total eroded mass at the given time step. The mass of
every bin $i$ is then $m_{i}=m_{u}p^{i}$ for $i=0,1,...,k-1$. The number of
discrete grains $N_{i}$ in every bin can be computed as:

$n_{i}=n_{u}(m_{u}/m_{i})^{(s-1)}+\frac{\Delta m_{i-1}}{m_{i}}\,,$ (8)

$N_{i}=\lfloor n_{i}\rfloor\,,$ (9)

where $\Delta m_{i}=m_{i}(n_{i}-N_{i})$ is the leftover mass in the mass bin
after making the number of grains discrete ($\Delta m_{0}=0$). The leftover
mass from the larger mass bins is distributed into smaller mass bins to ensure
that there is no ”virtual” mass loss due to numerical rounding. The grains are
then ablated as single bodies until exhaustion following equations 1 and 2. A
separate luminosity $I_{i}$ is computed for every mass bin, and the total
luminosity produced by all grains at a given time is simply
$\sum_{i=0}^{k-1}N_{i}I_{i}$.

Finally, after all fragments and grains have been fully integrated and their
masses depleted, the magnitude $M$ of the fireball as it would have be seen at
a distance of 100 km is computed as:

$M=-2.5\log\frac{I}{P_{\mathrm{0m}}}\,,$ (10)

where $P_{\mathrm{0m}}$ is the power that a meteor needs to radiate in the
camera’s spectral band-pass so that it has an apparent magnitude of $0$ mag at
a range of 100 km. In this work, we use a value of 1300 W, as appropriate for
a high-speed meteor in the spectral band-pass of CMOS/CCD sensors [79].

### Meteoroid strength and dynamic pressure

From decades of observations, it is now well established that there is a
strong correlation between meteoroid material type and bulk strength [80].
Cometary meteoroids are weak and disrupt under dynamic pressures of $\sim$ 1
kPa [61] upon entering the atmosphere, while asteroidal meteoroids can
withstand pressures of 100 kPa prior to any fragmentation [49], with their
strongest components withstanding pressures of up to $1-10$ MPa without
catastrophic disruption [81]. These differing strengths explain why cometary
fireballs break up at heights above 70 km [1], while meteorite dropping
fireballs break up typically below 40 km [49]. For cometary meteoroids, the
strength of constituent $10-300~{}\mu$m silicate grains is on the order of 10s
of MPa [82], but high porosity significantly reduces the strength of larger
grain aggregates [83].

Meteoroid fragmentation is commonly assumed to occur when the dynamic pressure
$P_{\mathrm{dyn}}=\Gamma\rho_{\mathrm{air}}v^{2}$ exceeds the mechanical
strength of the body [78]. In most cases, meteorite-dropping fireballs of
asteroidal origin fragment in two phases: the first from 0.04–0.12 MPa and the
second from 0.5–5 MPa [49]. These are significantly lower than the tensile
strengths of ordinary chondrites which survive atmospheric flight and are
recovered, which are measured to be between $20-40$ MPa [9]. Rarely,
meteoroids act like monoliths and show no evidence of fragmentation [84],
possibly due to a lack of internal cracking which is commonly invoked as the
mechanism which causes fragmentation at lower strengths [80]. As we model
fragmentation directly and use both the light curve and the dynamics as a
constraint, the derived values should be accurate to within $\pm 25\%$, which
is the short-term variation in the atmosphere mass density that is not
captured by current atmosphere models [63].

### Computing PE

The PE criterion was derived as an empirical tool to help easily differentiate
between different material types [48] without the complexity of full numerical
ablation modelling. It was based on well understood relationships between
physical properties of meteoroids and their observed behaviour as they enter
the atmosphere.

It is defined as:

$PE=\log\rho_{E}-0.42\log m_{0}+1.49\log v_{0}-1.29\log\cos Z_{C}$ (11)

where $\rho_{E}$ is the atmosphere mass density at the end height of the
fireball in $\mathrm{g~{}cm^{-3}}$, $m_{0}$ is the initial mass in grams,
$v_{0}$ the initial velocity in $\mathrm{km~{}s^{-1}}$, and $Z_{C}$ is the
zenith angle.

Note that for the PE criterion to be properly computed, the correct mass scale
(as outlined in refs. [48] and [8]) needs to be used. In general, initial
meteoroid mass is computed by integrating the total observed light production,
assuming a spectral distribution $P_{\mathrm{0m}}$ and a luminous efficiency
$\tau$ [85]:

$m=\frac{2P_{\mathrm{0m}}}{\tau v^{2}}\int_{0}^{t}10^{-0.4M(t)}$ (12)

where $M(t)$ is the observed magnitude. As it enters the atmosphere, a
meteoroid only possesses kinetic energy. The luminous efficiency measures how
much of that kinetic energy gets converted into light and is usually on the
order of a few percent.

PE was originally derived using the following luminous efficiency which should
always be used for PE computation:

$\tau=\left\\{\begin{array}[]{ll}1.5\times 10^{-2.75},&\text{for }v_{0}\leq
9.3\mathrm{km~{}s^{-}{1}}\\\ 1.5\times 10^{-5.60+2.92\log v_{0}},&\text{for
}9.3<v_{0}\leq 12.5~{}\mathrm{km~{}s^{-1}}\\\ 1.5\times 10^{-3.24+0.77\log
v_{0}},&\text{for }12.5<v_{0}\leq 17.0~{}\mathrm{km~{}s^{-1}}\\\ 1.5\times
10^{-2.50+0.17\log v_{0}},&\text{for }17.0<v_{0}\leq
27.0~{}\mathrm{km~{}s^{-1}}\\\ 1.5\times 10^{-3.69+1.00\log
v_{0}},&\text{otherwise}\\\ \end{array}\right.$ (13)

where $\tau$ is the dimensionless luminous efficiency as a fraction (not
percentage), and $v_{0}$ the initial velocity in $\mathrm{km~{}s^{-1}}$.

These values of luminous efficiency are considered to be underestimated
compared to contemporary models. For example, for the Alberta fireball with
$v_{0}=62.1\mathrm{km~{}s^{-1}}$ the luminous efficiency according to equation
13 is $\tau=1.9\%$, while in the modelling we used values between $10\%$ and
$14\%$ (depending on the mass). To scale contemporary mass values to the
appropriate values for PE computation, we simply scale the mass by the ratio
of the historic (eq. 13) and modern [49] luminous efficiencies.

### Strength of Cometary Material and Cometary Refractory Inclusions

In-situ measurement of the nucleus of comet 67P by the Philae lander found a
surface compressive strength of $1-3$ kPa [86], a value consistent with in-
atmosphere measurements of cometary meteoroid strength [63]. The probe stopped
bouncing when it hit an area of crushing strength $>4$ MPa, possibly a
processed, tightly packed “sintered” surface layer [87] created by space
weathering. Despite having a high crushing strength, the surface layer was
also found to have a high porosity of 30 to 65%. The best fit to data was
found by using a surface bulk density of $470\pm 45~{}\mathrm{kg~{}m^{-3}}$
[88].

To explain Philae lander measurements, modelling of sintering for the comet
67P has shown that a hardened surface layer (compressive strength 8 MPa)
several meters thick can be formed due to space weathering [89]. However, the
model found that the tensile strength (what is traditionally measured during
atmospheric entry of meteoroids [90]) of this layer is an order of magnitude
lower.

The possibility of meteorite delivery from the outer Solar System was
discussed in detail by ref. [91]. Using a numerical model which included
radioactive decay of short-lived nuclides and exothermic crystallization of
amorphous water ice to crystalline ice as sources of heat, they explored if it
was possible to sustain liquid water in comets for 1 kyr$-$1 Myr shortly after
the formation of the Solar System, long enough for the hydrothermal alteration
to produce CI chondritic material. They concluded that the transformation was
possible, but discuss no possibility of forming ordinary chondritic material.
We are unaware of any proposed physical process in the literature which can
transform soft cometary material into material of similar bulk density and
strength to ordinary chondrites.

Based on all of the foregoing considerations, macroscopic samples of cometary
surface layers are expected to have smaller bulk densities than monolithic
silicate material. Nevertheless, cometary material can have mm$-$sized
inclusions of a stronger material such as calcium-aluminum-rich inclusions
(CAIs), as found in the dust of comets Wild 2 [92] and 67P [93]. In addition,
some mm-sized components of Taurid meteoroids (from 2P/Encke) were found to
withstand pressures of up to 300 kPa [94, 60], and strong mm-sized inclusions
have been found in Leonid meteoroids (from an HTC 55P/Tempel-Tuttle)[57].

Most recently, a survey [10] of mm-sized meteoroids which analyzed their
spectral and fragmentation properties, identified two iron meteoroids on HTC
orbits (out of a total of 64 HTC meteors). The authors suggested these were
ejected during the formation of the Solar Solar due to the dynamical
instability caused by Jupiter’s migration.

### Astrometric Calibration

The most critical measurement leading to the core result in this work (the
unusually low end height for such a high velocity fireball) is directly
derived from optical observations of the event. Thus, the quality of the
astrometric calibration and measurements is of paramount importance. In this
section, we present the calibration details for each of the three optical
instruments used to derive the trajectory. These include two dedicated high
resolution Global Fireball Observatory (GFO) fireball cameras (one at Miquelon
Lake and the other near Vermilion, Alberta) and one security camera (located
in Cochrane, Alberta, outside of Calgary). The camera locations are given in
Table 3 and shown in relation to the fireball in Figure 5.

Table 3: Geographical coordinates of optical cameras used in this work. Name | Field of view | Latitude (+N) | Longitude (+E) | Elevation (mean sea level)
---|---|---|---|---
GFO Miquelon Lake | all-sky |  53.239340∘ |  -112.889855∘ | 785 m
GFO Vermilion | all-sky |  53.338975∘ |  -110.884085∘ | 624 m
Cochrane | $134^{\circ}\times 105^{\circ}$ |  51.224138∘ |  -114.706921∘ | 1213 m
GoPro (photometry) | $140^{\circ}\times 90^{\circ}$ |  50.910076∘ |  -114.038749∘ | 1040 m
Figure 5: Map showing the location of the fireball trajectory (red line),
cameras, and major population centers in Calgary and Edmonton. The GoPro
camera was located in Calgary.

#### Global Fireball Observatory Data

The GFO all-sky cameras operated by the MORP2.0 project produce $7340\times
4930$ px color images with an exposure time of 27 s and 14 bits of depth.
Electronic liquid crystal shutters are toggled to encode the timing
information into the image. The shutters produce 20 segments per second, and
the segments are encoded as a de Brujin sequence of ones and zeros [95] so
that the absolute time of every segment can be derived to an accuracy of 1 ms.
In combination with the Samyang 8 mm f/3.5 fish-eye lens, the images have a
plate scale of $\mathrm{2~{}arcmin~{}px^{-1}}$. The data produced by these
cameras are of similar quality and have a similar sensitivity limit as
compared to other fireball networks.

The astrometric fit was performed with a radial distortion model [5] using odd
polynomial coefficients up to the 7th order, asymmetry correction, and a fixed
aspect ratio. Including the pointing direction (reference right ascension,
declination, position angle, and the plate scale), the fit uses a total of 11
free parameters.

Figure 6 shows the fit residuals for the Miquelon Lake camera. The mean
angular forward mapping (image to sky) error was 0.49 arcmin, with a fit
showing no trends in residuals with radius from the centre of the image but a
slight systematic trend in the azimuth. We believe that the main cause of the
trend is a higher order component of asymmetry in the optics not captured by
the distortion model, as the point-spread function significantly varied across
the field of view. Nevertheless, this offset is only on the order of 0.5
arcmin, i.e. 20 m at the range of the fireball from the station, and does not
significantly influence the final result. The fireball covered azimuths from
$30^{\circ}$ to $350^{\circ}$ (counter-clockwise) and elevations from
$54^{\circ}$ to $15.7^{\circ}$, ranges well covered by available calibration
stars.

Figure 6: Astrometric calibration fit using a 7th order polynomial (odd-terms
only) radial distortion model for the Miquelon Lake camera. Forward mapping
(image to sky) errors.

The astrometric fit for the Vermilion GFO station was not as good, having root
mean square fit residuals of 1.37 arcmin, as shown in Figure 7. This decrease
in accuracy was caused by a more non-Gaussian point-spread function than for
the Miquelon Lake camera. However, the absolute accuracy remained high $-$ the
corresponding linear error was only 65 m at the range of the fireball. The
fireball had a nearly constant azimuth of $310^{\circ}$ and covered elevations
from $43^{\circ}$ to $11^{\circ}$, ranges for which there were many stars in
the calibration.

Figure 7: Astrometric calibration fit for the Vermillion camera. Forward
mapping (image to sky) errors.

### Security Camera Calibration

Despite the good geometry and high accuracy of GFO measurements (convergence
angle of $46.5^{\circ}$ and spatial trajectory fit residuals of $\sim 30$ m),
a two-station trajectory solution can suffer from systematic biases due to
meteor-station geometry [96, 97]. As a further constraint, we included
additional measurements from a Google Nest doorbell camera in Cochrane,
Alberta, 50 km west of Calgary.

The radial distortion model with odd terms up to the fifth order was used for
calibration [5]. The model has a total of eight parameters and eight stars
were used in the fit (Figure 8). The average fit error was 4 arcmin. Only the
first half of the fireball was used in the trajectory solution as the camera
saturated and skipped frames during the brightest phase. The difference in the
geocentric radiant with and without the security camera measurements was only
$0.03^{\circ}$, and $0.14~{}\mathrm{km~{}s^{-1}}$ in geocentric speed,
indicating that the GFO-only solution had no major systematic errors.

Figure 8: Composite of frames from the Cochrane security camera video showing
the fireball and the calibration stars (marked with a white letter C), four of
which were in Cassiopeia. An equatorial grid is laid over the video with
catalog stars shown as yellow crosshairs. Credit: Airell DesLauriers.

### Photometric Calibration

To fully model the fragmentation behaviour of a meteoroid, it is necessary to
have a well-calibrated light curve. The Alberta event was observed by both
space-based GLM instruments and one fixed GoPro HERO5 action camera in Calgary
($\sim 400$ km from the fireball). Note that the GFO cameras used for
astrometry were partially saturated over the height range of interest and
therefore not used in the photometric calibration. However, as the Nikon D810
used by the GFO have CMOS (and not CCD) chips for imaging, the astrometric
position picks are reliable even in saturation [5].

The GoPro camera had a low sensitivity and in conjunction with the large range
to the fireball it was able to capture the whole fireball without saturating
despite only having 8 bits of depth. As the camera did not observe any stars,
the absolute calibration was done indirectly using seven distant streetlights
visible in the video (similar method was previously successfully applied in
refs. [98, 99]). A separate digital single-lens reflex (DSLR) photograph of
stars and the streetlights was taken by placing the DSLR camera next to the
GoPro camera $-$ the apparent magnitudes of the streetlights were measured on
the DSLR photo and used as a basis for the GoPro calibration. The mean
photometric error was $\pm 0.27$ mag and the vignetting coefficient was
estimated to be 0.001 $\mathrm{rad~{}px^{-1}}$ (see ref. [5]).

An attempt was made to measure the photometry from scattered light on the
Cochrane security camera video (method of ref. [98]), but the camera had a
wide dynamic range (WDR) feature. This produces image levels that are not
linear responses to light and was thus not able to be used. Such image
enhancement features may prevent using modern security cameras for scattered
light fireball photometry in the future.

Converting the energy observed by the GLM into magnitudes is challenging due
to its narrow 1.1 nm pass band around 777.4 nm, making it necessary to assume
a spectral energy distribution to compute a bolometric magnitude. For slower
meteoroids such as meteorite-dropping fireballs, it is possible to assume a
blackbody spectrum and derive a conversion [7], but at high speeds elemental
and atmospheric lines are more pronounced making the blackbody assumption
invalid. Furthermore, the intensity of the oxygen triplet line that the GLM is
observing was found to significantly increase with meteoroid speed [100]. For
these reasons, we performed a manual calibration between the GLM group energy
and magnitude using three fast and bright (around $-11$ mag) fireballs
observed by the NASA Meteoroid Environment Office [101] and All-sky Meteor
Orbit System (AMOS) all-sky cameras [2]. Among many fireballs observed by
these systems, only two fireballs observed with NASA systems had GLM light
curves and were observed sufficiently far away not to saturate the cameras.
Some saturated frames in the AMOS recording (2020/10/19 12:42:55 UTC) were
corrected using a calibration curve for saturated pixels, based on calibrated
measurements of bright planets and Moon in different phases. The in-atmosphere
speeds of the fireballs were 58, 66, and $69~{}\mathrm{km~{}s^{-1}}$,
comparable to the Alberta fireball. We used the classical equation to compute
the magnitude:

$M=-2.5\log E_{G}+p_{0}$ (14)

where $E_{G}$ is the GLM group energy in femtojoules and the $p_{0}$ is the
photometric offset in magnitudes. For all three fireballs, the GLM light
curves matched best for $p_{0}=-9.2$, with an error of $\pm 0.1$ mag. The
comparison between the optical and GLM light curves is shown in Figure 9.

Figure 9: Comparison between optical light curves and GLM-derived light curves
of calibration fireballs.

### Trajectory Details

Table 4 details the parameters of the begin and end point of the fireball.
Figure 10 shows the trajectory fit residuals and the observed deceleration.
The trajectory fit is tight and within the expected astrometric accuracy. The
fireball did not show much deceleration before a height of 60 km. The initial
velocity was computed as the average velocity above the height of 70 km.

Table 4: Fireball trajectory parameters. | Latitude (+N) | Longitude (+E) | Height (km, WGS84) | Time (UTC)
---|---|---|---|---
Begin point | $53.7732^{\circ}\pm 0.092~{}\mathrm{km}$ | $-112.0861^{\circ}\pm 0.036~{}\mathrm{km}$ | $130.819\pm 0.082$ | 2021-02-22 13:23:17.683
End point | $54.6182^{\circ}\pm 0.213~{}\mathrm{km}$ | $-113.2543^{\circ}\pm 0.040~{}\mathrm{km}$ | $46.498\pm 0.066$ | 2021-02-22 13:23:20.101

Figure 10: Left: Spatial trajectory fit residuals versus height. Right: The
observed lag (“the distance that the meteoroid falls behind an object with a
constant velocity that is equal to the initial meteoroid velocity”[65].)

The reference time for the trajectory is 2021-02-22 13:23:17.683 UTC (Julian
date 2459268.057843548711). The state vector in the Earth-centered inertial
(ECI) coordinates in the epoch of date is given in Table 5, the state vector
covariance matrix is given in Table 6, and the orbital covariance matrix is
given in Table 7.

Table 5: ECI trajectory state vector. $X=$ | -1844963 | $\pm$ | 44 | $\mathrm{m}$
---|---|---|---|---
$Y=$ | -3384728 | $\pm$ | 193 | $\mathrm{m}$
$Z=$ | 5227379 | $\pm$ | 153 | $\mathrm{m}$
$V_{X}=$ | 2161 | $\pm$ | 41 | $\mathrm{m/s}$
$V_{Y}=$ | -61705 | $\pm$ | 15 | $\mathrm{m/s}$
$V_{Z}=$ | 5244 | $\pm$ | 155 | $\mathrm{m/s}$
Table 6: ECI state vector covariance matrix.  |  $X$ (m) |  $Y$ (m) |  $Z$ (m) |  $V_{X}$ (m/s) |  $V_{Y}$ (m/s) |  $V_{Z}$ (m/s)
---|---|---|---|---|---|---
$X$ | $+1.778\mathrm{e}{+03}$ | $+4.430\mathrm{e}{+02}$ | $+4.577\mathrm{e}{+03}$ | $+1.499\mathrm{e}{+03}$ | $+8.165\mathrm{e}{+02}$ | $+4.720\mathrm{e}{+03}$
$Y$ | $+4.430\mathrm{e}{+02}$ | $+3.851\mathrm{e}{+04}$ | $-7.591\mathrm{e}{+02}$ | $+1.377\mathrm{e}{+03}$ | $+4.232\mathrm{e}{+03}$ | $+2.417\mathrm{e}{+03}$
$Z$ | $+4.577\mathrm{e}{+03}$ | $-7.591\mathrm{e}{+02}$ | $+2.168\mathrm{e}{+04}$ | $+4.334\mathrm{e}{+03}$ | $+2.671\mathrm{e}{+03}$ | $+2.039\mathrm{e}{+04}$
$V_{X}$ | $+1.499\mathrm{e}{+03}$ | $+1.377\mathrm{e}{+03}$ | $+4.334\mathrm{e}{+03}$ | $+1.491\mathrm{e}{+03}$ | $+9.583\mathrm{e}{+02}$ | $+4.765\mathrm{e}{+03}$
$V_{Y}$ | $+8.165\mathrm{e}{+02}$ | $+4.232\mathrm{e}{+03}$ | $+2.671\mathrm{e}{+03}$ | $+9.583\mathrm{e}{+02}$ | $+1.448\mathrm{e}{+03}$ | $+3.880\mathrm{e}{+03}$
$V_{Z}$ | $+4.720\mathrm{e}{+03}$ | $+2.417\mathrm{e}{+03}$ | $+2.039\mathrm{e}{+04}$ | $+4.765\mathrm{e}{+03}$ | $+3.880\mathrm{e}{+03}$ | $+2.163\mathrm{e}{+04}$
Table 7: Orbital covariance matrix. $T_{p}$ is the Julian date of last perihelion (nominal $T_{p}$ = 2459230.729594). | $e$ |  $q$ (au) |  $T_{p}$ (day) |  $\Omega$ (deg) |  $\omega$ (deg) |  $i$ (deg)
---|---|---|---|---|---|---
$e$ | $+8.321\mathrm{e}{-06}$ | $+4.075\mathrm{e}{-06}$ | $+2.410\mathrm{e}{-04}$ | $+1.762\mathrm{e}{-08}$ | $+6.764\mathrm{e}{-04}$ | $-5.763\mathrm{e}{-04}$
$q$ | $+4.075\mathrm{e}{-06}$ | $+2.367\mathrm{e}{-06}$ | $+1.240\mathrm{e}{-04}$ | $+1.009\mathrm{e}{-08}$ | $+3.757\mathrm{e}{-04}$ | $-3.302\mathrm{e}{-04}$
$T_{p}$ | $+2.410\mathrm{e}{-04}$ | $+1.240\mathrm{e}{-04}$ | $+7.079\mathrm{e}{-03}$ | $+5.341\mathrm{e}{-07}$ | $+2.031\mathrm{e}{-02}$ | $-1.746\mathrm{e}{-02}$
$\Omega$ | $+1.762\mathrm{e}{-08}$ | $+1.009\mathrm{e}{-08}$ | $+5.341\mathrm{e}{-07}$ | $+5.399\mathrm{e}{-11}$ | $+1.607\mathrm{e}{-06}$ | $-1.767\mathrm{e}{-06}$
$\omega$ | $+6.764\mathrm{e}{-04}$ | $+3.757\mathrm{e}{-04}$ | $+2.031\mathrm{e}{-02}$ | $+1.607\mathrm{e}{-06}$ | $+6.030\mathrm{e}{-02}$ | $-5.258\mathrm{e}{-02}$
$i$ | $-5.763\mathrm{e}{-04}$ | $-3.302\mathrm{e}{-04}$ | $-1.746\mathrm{e}{-02}$ | $-1.767\mathrm{e}{-06}$ | $-5.258\mathrm{e}{-02}$ | $+5.786\mathrm{e}{-02}$

### Orbital Integration

To investigate the influence of planetary interactions with the meteoroid’s
orbit, we backtracked 100 clones within the measured uncertainty. The RADAU
[102] 15th-order integrator was used with an error tolerance of $10^{-12}$ and
an external time step of 1 day. Because of its high inclination, the only
appreciable approaches to the planets are at its other (ascending) node, which
is near Mars’ orbit. However, no clone passed closer than 1.1 AU from this
planet. Figure 11 shows the variation in the heliocentric elements as a
function of distance from Mars. The simulations start 60 days prior to impact
and run for 365 days further back. A slight jump in each of the elements can
be seen at the minimum distance from Mars, but it is small: it will not affect
a potential parent body search and does not affect the proposed origin of the
object.

Note that the orbital elements do not become completely constant even well
after the Mars encounter. This is because they are heliocentric elements, and
for such a large semi-major axis orbit, Jupiter’s tug both on the Sun and the
object create ongoing small changes. Even if the orbital elements were
considered in the barycentric frame, the effect of ongoing planetary
perturbations on such loosely bound orbits means that the orbital elements
will have trends over time regardless of the reference frame.

An extended integration backwards over 2000 years, corresponding to several
orbits of the clones, reveals that planetary perturbations have had only a
small effect on the orbital elements of the meteoroid over this time span
(Figure 12).

Figure 11: Change in orbital elements over time, between -60 and -365 days
before impact. Each clone is color-coded individually and represents one
sample within the orbital covarience matrix. Time is not shown on any axis,
but the clones that start at t - 60 days are clustered at zero and spread out
as we go further back in time, as the distance from Mars decreases and then
increases again. Figure 12: Change in orbital elements over time during a 2000
year backwards integration with all planets included. Each clone is color-
coded individually. Planetary perturbations produce small nearly-stochastic
changes in the orbital elements.

### Ablation Modelling Results

We model the fragmentation behaviour of the fireball in two ways. (1) by
direct erosion of the main body (EM), and (2) by ejecting larger fragments
which erode independently (EF). Figure 13 shows the details of the
fragmentation on the simulated light curve which are also listed in Table 8,
and Figure 14 shows the mass loss with increasing dynamic pressure. The
modelled physical properties of the fireball are given in Table 9. We only
provide a single solution with no error estimate. The model is fit manually
and a still unresolved question in the field is how to provide meaningful
model uncertainties. The model is highly non-linear and defining a robust cost
function has also not yet been addressed. Previous attempts to automate the
model fits ignored either the dynamics or the photometric measurements and
failed to model the fragmentation directly [103, 104, 105]. In our approach,
we use the dynamics as a hard constraint to accurately classify the material
type and include additional fragmentation details to explain the light curve.
This established method is often used to accurately model meteorite-dropping
fireballs and accurately predict the masses of meteorites on the ground [54,
74].

Figure 13: Details of the modelled individual fragmentations of the meteoroid marked on the simulated light curve. The solid black line is the total light production, the dashed black line is the magnitude of the main body from which fragments are released, green dashed lines are the magnitudes of the eroding fragments, and purple lines are the magnitudes of the grains ejected either from the main body or the eroding fragments. Arrows indicate where the fragmentations occurred with which parameters, and stars indicate the beginning of individual fragment/grain light curves. Table 8: Modelled fragmentation behaviour. The total mass of all ejected fragments is 1.04 kg. The fragment mass percentage in the table is reference to the mass of the main fragment at the moment of ejection. The mass distribution index for all grains was $s=2.0$. The values of the dynamic pressure are computed using the drag coefficient $\Gamma$ used in the modelling for the appropriate height, as described in Supplementary Table 7.  Timea | Height | Velocity | Dyn pres |  Main $m$ | Fragment | $m$ | $m$ | Erosion coeff |  Grain $m$
---|---|---|---|---|---|---|---|---|---
(s) | (km) |  ($\mathrm{km~{}s^{-1}}$) | (MPa) | (kg) |  | (%) | (kg) |  ($\mathrm{kg~{}MJ^{-1}}$) | range (kg)
1.49 | 76.0 | 62.03 | 0.09 | 1.73 | EF | 8 | 0.139 | 0.030 |  $10^{-7}$ \- $10^{-6}$
1.52 | 75.0 | 62.02 | 0.10 | 1.59 | EF | 20 | 0.317 | 0.035 |  $10^{-6}$ \- $10^{-4}$
1.57 | 73.0 | 62.00 | 0.10 | 1.25 | EM | - | - | 0.030 |  $10^{-6}$ \- $10^{-5}$
1.72 | 67.5 | 61.88 | 0.21 | 0.93 | EM | - | - | OFF | -
1.79 | 65.0 | 61.78 | 0.30 | 0.87 | EF | 35 | 0.310 | 0.020 |  $10^{-5}$ \- $10^{-3}$
1.84 | 63.0 | 61.66 | 0.38 | 0.54 | EF | 15 | 0.081 | 0.020 |  $10^{-7}$ \- $10^{-6}$
1.90 | 61.0 | 61.49 | 0.48 | 0.42 | EF | 18 | 0.075 | 0.080 |  $10^{-7}$ \- $10^{-6}$
2.12 | 52.7 | 59.84 | 1.28 | 0.17 | EF | 50 | 0.084 | 0.005 |  $10^{-4}$ \- $10^{-3}$
2.17 | 51.2 | 59.07 | 1.52 | 0.06 | EF | 50 | 0.030 | 0.050 |  $10^{-6}$ \- $10^{-5}$
a Seconds after 13:23:17.683 UTC. |
EM = Main fragment erosion; EF = New eroding fragment. |
Figure 14: Modelled mass loss as a function of increasing dynamic pressure. Model fragmentation points and masses of major fragments are marked with red circles. $\eta$ marks the change in the erosion coefficient, and $\sigma$ the change in the ablation coefficient of the main body. Table 9: Modelled physical properties of the fireball. Description |  | Value
---|---|---
Initial mass (kg) | $m_{0}$ | 1.8
Initial speed at 180 km ($\mathrm{km~{}s^{-1}}$) | $v_{0}$ | 62.10
Zenith angle | $Z_{c}$ | $54.885^{\circ}$
Bulk density ($\mathrm{kg~{}m^{-3}}$) | $\rho$ | 3300
Grain density ($\mathrm{kg~{}m^{-3}}$) | $\rho$ | 3500
Ablation coefficient ($\mathrm{kg~{}MJ^{-1}}$) | $\sigma$ | 0.009
(below 60 km) | $\sigma$ | 0.007
Shape factor (sphere) | $A$ | 1.21
Drag coefficient | $\Gamma$ | 0.8
(below 75 km) | $\Gamma$ | 0.6

Because this fireball is the first of its type to be ever modelled (large,
high speed rocky meteoroid reaching low altitudes), there were several
differences and uncertainties in chosen parameters as compared to low-velocity
Type I objects:

  1. 1.

The luminous efficiency for Type I objects at high speeds is unknown, as this
is the first object of this kind to be observed. We used the model of ref.
[49] which suggest a value of $~{}\sim 14\%$ for 1 kg objects and $~{}\sim
10\%$ for grains. If the luminous efficiency is akin to low-speed meteorite
dropping fireballs ($\sim 5\%$), the initial mass is $\sim 3\times$ larger (6
kg), but the identification of the meteoroid as a Type I fireball is
unchanged.

  2. 2.

A higher intrinsic ablation coefficient of 0.009 $\mathrm{kg~{}MJ^{-1}}$ (and
0.007 $\mathrm{kg~{}MJ^{-1}}$ below 60 km) was used, as compared to 0.005
$\mathrm{kg~{}MJ^{-1}}$ for low-velocity deeply penetrating fireballs [61].

  3. 3.

The model matches the light curve well even at the beginning of luminous
flight at fainter magnitudes. This is not usually the case for slower
meteorite-dropping fireballs as they undergo a period of preheating [106], and
the classical equations do not capture that complexity in those cases.

### Code availability

The optical data were calibrated using the open source SkyFit2 software
available in the RMS library at URL:
https://github.com/CroatianMeteorNetwork/RMS.

The WesternMeteorPyLib (wmpl) library was used to compute the trajectory and
fit the meteoroid ablation model to the observations. It is available at URL:
https://github.com/wmpg/WesternMeteorPyLib/.

### Data availability

The trajectory data are included in this article as Supplementary Data files.
The raw images and supplementary are available on Zenodo:
https://doi.org/10.5281/zenodo.7225827.

## End Notes

### Acknowledgements

We thank the two anonymous reviewers for their expert comments and valuable
suggestions which greatly improved the quality of the this work. Also, we
thank Mr. Robert Howell for first bringing this fireball to our attention and
Mr. Airell DesLauriers for providing raw footage from his security camera in
Cochrane, AB.

Funding for this work was provided in part through NASA co-operative agreement
80NSSC21M0073 (DV, PGB), by the Natural Sciences and Engineering Research
Council of Canada Discovery Grants program (Grants no. RGPIN-2016-04433 &
RGPIN-2018-05659, DV, PGB), the Canada Research Chairs program (PGB), the
Slovak Research and Development Agency grant APVV-16-0148, and the Slovak
Grant Agency for Science grant VEGA 1/0218/22 (PM, JT).

### Author Contributions

DV coordinated the effort, performed the analysis, implemented the software,
and wrote the manuscript. PGB initially coordinated the effort and provided
scientific insight. HARD computed an initial trajectory and provided the raw
GFO data. PW made valuable scientific interpretations of the results and added
a connection to recent comet discoveries, and performed the orbital
integrations. DEM helped digitize the MORP data, systematically collected and
organized all casual recordings of the fireball, provided the GLM
observations, and identified fireballs for GLM calibration. PM and JT provided
observations of a fireball jointly observed with the AMOS system and GLM. CDKH
and PJAH provided the GFO data from the Miquelon Lake and Vermilion cameras
and helped contact the local people who observed the fireball. EKS and MCT
analyzed the global GFO data set to locate other fireballs of interest and
provided data access. WJC provided initial coordination. DWH provided the
GoPro video and took DSLR images for its photometric calibration.

### Declaration of Competing Interests

The authors declare no competing interests.

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