Cooke, Bill

Moorhead, Althea

NASA Technical Reports Server

Enhancement of the natural Earth satellite
population through meteoroid aerocapture
Althea Moorhead, Bill Cooke
NASA Meteoroid Environment Office
April 28, 2014
https://ntrs.nasa.gov/search.jsp?R=20140010988 2019-08-31T19:27:52+00:00Z
1972 Great Daylight Fireball
Image credit: ANSMET, James M. Baker
Source Population
In-atmosphere
Post-atmosphere
Earth-grazing meteoroids
Questions:
How many re-exit?
How many are
aerocaptured?
Ratcliff et al. (1993)
Hills & Goda (1997)
Hunten (1997)
Can they become natural
Earth satellites?
Granvik et al. (2012)
Moorhead Meteoroid aerocapture 3/ 21
Source Population
In-atmosphere
Post-atmosphere
source population in-atmosphere post-atmosphere
Outline
Moorhead Meteoroid aerocapture 4/ 21
Source Population
In-atmosphere
Post-atmosphere
Number and Size
10−7 10−4 10−1 102 105 108 1011 1014 1017 1020
10−10
10−6
10−2
102
106
N = 3.7 KE−0.9
KE (kt TNT equivalent)
N
/y
ea
r
Small fireball (Halliday, 1996)
Lunar impacts (Suggs et al., 2014)
Lunar impacts (Madiedo et al., 2014)
Infrasound/acoustic (ReVelle, 1998)
Satellite (Brown, 2002)
Spacewatch (Rabinowitz et al., 2000)
LINEAR (Harris, 2002)
LINEAR (Stewart)
NEAT (Rabinowitz et al., 2000)
Lunar cratering (Werner et al., 2002)
Moorhead Meteoroid aerocapture 5/ 21
Source Population
In-atmosphere
Post-atmosphere
Velocity
10 20 30 40 50 60 70 80
10−5
10−4
10−3
10−2
10−1
v (km/s)
fra
ct
io
n
(k
m
/s
)−
1
Radar (CMOR)
All-sky (NASA & SOMN)
Moorhead Meteoroid aerocapture 6/ 21
Source Population
In-atmosphere
Post-atmosphere
Directionality
N
 ×
S
Data from NASA All-Sky Fireball Network
and Southern Ontario Meteor Network
Moorhead Meteoroid aerocapture 7/ 21
Source Population
In-atmosphere
Post-atmosphere
Directionality
0 2 4 6 8 10 12 14
0
0.1
0.2
0.3
0.4
0.5 Anisotropy is (mostly) preserved
deflection angle (◦)
fra
ct
io
n
pe
rh
alf
de
gr
ee
Moorhead Meteoroid aerocapture 8/ 21
Source Population
In-atmosphere
Post-atmosphere
The trajectory in the atmosphere
x
y
R⊕
Hbl
θ
FgFD
Compute trajectory under
Earth’s gravity and
atmospheric drag
~Fg = −GM⊕mr2 rˆ
~FD = −12ρav
2CdAvˆ
Moorhead Meteoroid aerocapture 9/ 21
Source Population
In-atmosphere
Post-atmosphere
Model Earth
Earth as ellipsoid MSIS-E 90 model
0 500 1,000
10−18
10−10
10−2
h (km)
ρ
(g
/c
c)
“in-atmosphere” = within 100 km of the surface
Moorhead Meteoroid aerocapture 10/ 21
Source Population
In-atmosphere
Post-atmosphere
Ablation
Meteoroid ablation is a function of mass and velocity
(Ceplecha, 2000):
m˙ = −σCdAρ−2/3d ρm2/3v3
Meteoroids modeled as spheres (Cd = 0.47, A = 1.21)
Effective ablation coefficient (σ) includes some fragmentation
Moorhead Meteoroid aerocapture 11/ 21
Source Population
In-atmosphere
Post-atmosphere
Catastrophic fragmentation
Occurs when ram pressure
exceeds material strength:
S < ρv2
Model fragmentation:
20% chance of
fragmentation every 0.1 s
0-50% reduction in
primary mass
48 Z. Ceplecha and D. ReVelle
at approximately the same heights, where also a large number
of tiny particles was released and overwhelmingly
contributed to Beneov bolide radiation. This is very different
from the Lost City bolide, where radiation of individual large
fragments was relatively more important compared to the
radiation of small fragment clusters.
The terminal mass of the main body of Beneov was found
to be 2.7 kg. However, large fragments are certainly hidden in
the overwhelming radiation originating from clusters of small
fragments. Information on these larger fragments are available
only from the study of Borovika et al. (1998), who analyzed
very large fragments from their individually discernible trails
Table 4. FM solution for the Innisfree bolide.
hf m dtf dtu  8
(km) (%) (sec) (sec) (c.g.s.) (s2 km2)
71.8 2.0 2.1 1.3 0.96 0.008
58.1 3.8 1.0 0.5 0.86 0.008
55.6 30 2.2 0.8 0.46 0.008
46.2 42 2.0 0.85 0.27 0.008
41 – – – 0.25 0.008
38 – – – 0.65 0.008
36 20 1.5 0.8 0.60 0.008
34.7 11 1.5 1.1 0.48 0.008
26 6 0.8 0.4 0.35 0.006
23.72 61 0.32 0.26 0.38 0.004
23.2 1.5 0.8 0.25 0.38 0.004
Table 5. FM solution for the Beneov bolide.
hf m dtf dtu  mF 8
(km) (%) (sec) (sec) (c.g.s.) (%) (s2 km2)
90.4 0.016 1.2 0.50 0.023 0 0.008
80.2 0.001 1.0 0.35 0.07 0 0.008
77.4 0.0007 0.28 0.17 0.16 0 0.008
70.1 0.05 1.0 0.20 0.23 0 0.008
66.1 0.6 1.0 0.28 0.52 65 0.007
66.0 3.6 1.1 0.62 0.52 80 0.007
55.7 0.1 0.8 0.4 1.2 0 0.007
51.5 0.001 1.0 0.2 1.6 0 0.006
45.3 3.0 0.7 0.26 2.2 0 0.006
39.8 14 0.46 0.28 2.0 0 0.005
36.1 38 0.70 0.3 1.8 0 0.005
29.5 19 0.40 0.20 1.1 0 0.005
25.9 83 0.21 0.16 0.84 0 0.005
24.3 97 0.55 0.10 0.43 0 0.005
Table 6. The Beneov bolide: comparison of fragmentation 
heights derived from FM and from intersection of trails. 
For the notation of fragments see Borovika et al. (1998).
FM fragmentation
height
(km)
Separation
height
(km) Fragment #
45.3 42 8
39.8, 36.1 37.5 1, 2
29.5 27 5
25.9, 24.3 24.2, 23.5 7, 6
Fig. 15. The FM computed velocity of the main body of the Innisfree
bolide is compared to the single body solution.
Fig. 16. The FM computed deceleration of the main body of the
Innisfree bolide is compared to the single body solution.
Fig. 17. The FM computed mass of the main body of the Innisfree
bolide is compared to the single body solution with two different K.
Fragmentation model 51
Fig. 28. The FM computed mass of the main body of the Benešov
bolide. The dynamically derived mass (the single body solution) is
not contained in this figure because it is extremely and unrealistically
low (starts with 75 kg).
Fig. 29. The intrinsic ablation coefficient of the Benešov meteoroid
derived from the FM fit to observation.
Fig. 30. The shape density coefficient K of the Innisfree meteoroid
derived from the FM fit to observation.
Fig. 31. The intrinsic luminous efficiency of the Innisfree meteoroid
corresponding to the FM fit to observation.
Fig. 32. Comparison of the intrinsic (the FM derived) and the
apparent ablation coefficient of the PN 39048 bolide.
Fig. 33. Comparison of the intrinsic (corresponding to the FM fit)
and the apparent luminous efficiency of the PN 39048 bolide.
Ceplecha & ReVelle, 2005
Moorhead Meteoroid aerocapture 12/ 21
Source Population
In-atmosphere
Post-atmosphere
Meteoroid composition
Fireball meteoroid properties by type:
Type % ρd σ S
Iron 3 7.8 0.07 200
Stony 29 3.7 0.014 30
Carbonaceous 33 2.0 0.042 10
Cometary 30 0.75 0.1 1
g/cc s2/km2 MPa
Ceplecha (2001)
Hills & Goda (1993)
Moorhead Meteoroid aerocapture 13/ 21
Source Population
In-atmosphere
Post-atmosphere
Surviving population
Out of 107 incident meteoroids:
Grazers Aerocaptures
27,250 10,589
Ablation 18,307 5,040
Frag. 16,754 5,146
Numbers are per year for meteoroids
greater than 1 cm in diameter
Moorhead Meteoroid aerocapture 14/ 21
Source Population
In-atmosphere
Post-atmosphere
Simulations
Image credit: NASA
Simulations include Sun,
Earth, and Moon
Used Mercury,
Bulirsch-Stoer method
Random start between J2K
and J2K + 19 years
(Metonic cycle; Granvik et
al., 2012)
Moorhead Meteoroid aerocapture 15/ 21
Source Population
In-atmosphere
Post-atmosphere
End states
Leaving Earth’s Hill sphere Atmospheric re-entry
Moorhead Meteoroid aerocapture 16/ 21
Source Population
In-atmosphere
Post-atmosphere
End states
Re-entry or escape
after several orbits
Re-entry or escape
after many orbits
Moorhead Meteoroid aerocapture 17/ 21
Source Population
In-atmosphere
Post-atmosphere
Steady-state population
1 10 100
0
0.2
0.4
0.6
0.8
Norbits
CD
F
Using time spent in near-
Earth space and in orbit:
Number
Outbound 3,000
Orbiting 1,600
Moorhead Meteoroid aerocapture 18/ 21
Source Population
In-atmosphere
Post-atmosphere
Period distribution
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
500
1,000
1,500
2,000
P/P%
N
aerocaptured
steady state
Moorhead Meteoroid aerocapture 19/ 21
Source Population
In-atmosphere
Post-atmosphere
Size dependence
100 101 102 103 104 105
10−25
10−18
10−11
10−4
103
× gravitational capture
(Granvik et al., 2012)
diameter, d (cm)
N >
d
N in Earth orbit
N in Hill sphere
Moorhead Meteoroid aerocapture 20/ 21
Source Population
In-atmosphere
Post-atmosphere
Conclusions and future work
0.2% of large meteoroids re-exit the atmosphere
Meteoroid aerocapture can maintain a population of small
(cm-sized) NES’s
∼ 3,000 in near-Earth space
∼ 1,500 orbiting in near-Earth space
Gravitational capture (Granvik et al., 2012) dominates for
meter-sized bodies
Future work:
Convolve results with meteoroid directionality
Moorhead Meteoroid aerocapture 21/ 21


Enhancement of the Natural Earth Satellite Population through Meteoroid Aerocapture

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