Perihelion-aphelion variation
of the flux of Mars impactors
A. Minneci1,2
2
A. Rossi2
G. B. Valsecchi3,2
1 Univ. Paris VII, France
IFAC-CNR, Sesto Fiorentino, Italy
3 IAPS-INAF, Roma, Italy
The work of Daubar et al. (2012)
A number of newly formed Martian craters have been detected in
images taken from spacecraft; in the case of such a detection, the
date of formation has to fall between the date of image in which
the crater is absent and that of the image in which the crater is
present.
Daubar et al. (2012) use these data to test whether a seasonal
variation of the current cratering rate is detectable.
Such a seasonal variation should be the consequence of a greater
flux of impactors experienced by Mars when at aphelion, compared
to a smaller flux at perihelion.
The work of Daubar et al. (2012)
Daubar et al. find that, if the total area covered by images is taken
into account, an aphelion enhancement of the impact rate is not
very convincingly shown by the data.
Results for larger data set
We have repeated the computation with a larger data set (45 vs 38
craters), taken by different mission instruments; we cannot take
into account the total area covered by the images.
The perihelion distribution of asteroids
The previous results seem somewhat unsatisfactory, possibly due to
poor statistics; a perihelion-aphelion asymmetry should be present
since, as Daubar et al. show, many more asteroids have their
perihelion at the distance corresponding to Mars aphelion than to
Mars perihelion.
Our approach
We reexamine the orbital side of the question, using:
• only good orbits (either numbered or multi-opposition
main-belt asteroids, and single-opposition NEAs with well
determined orbital elements), taken from AstDyS
(http://hamilton.dm.unipi.it/astdys2/) and NEODyS
(http://newton.dm.unipi.it/neodys2/);
• a reasonably unbiased sample, having eliminated all objects
fainter than H = 16 (this sample is practically complete);
• the actual
p spatial density of asteroids in the plane R, z, with
R=
x 2 + y 2;
• the actual probability of presence of Mars in the plane R, z.
Kresák’s work
Kresák was the first to study quantitatively the spatial density of
asteroids; the above figure is taken from his 1979 paper; the data
refer to the 100 largest asteroids.
Kresák’s figure with our data sample
4
x 10
2.5
1
2
0.5
1.5
0
1
−0.5
0.5
−1
1.5
2
2.5
3
3.5
4
0
We have repeated Kresák’s computation with our data set; the
density is color-coded, and the two vertical lines mark the
perihelion and aphelion of the orbit of Mars.
Zooming in near Mars
0.5
40
0.4
35
0.3
0.2
30
Z
0.1
25
0
20
−0.1
15
−0.2
10
−0.3
5
−0.4
−0.5
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
0
R
This is an enlargement in the region of Mars; the orbit of the latter
is marked by dots, equispaced in mean anomaly.
Putting it all together
The histogram shows the product of the probability of presence of
both Mars and an asteroid for each value of R; the striking
perihelion-aphelion variation is due to the strongly increasing
density of asteroids going farther from the Sun.
Secular evolution of Mars’ eccentricity
The figure, from Laskar et al. (2004), shows the secular evolution
of the Martian orbital eccentricity; the current value is not far from
the maximum.
Conclusions and open questions
• There should be a noticeable increase in the cratering rate at
epochs in which Mars is close to aphelion, compared to
epochs in which it is close to perihelion.
• This difference is not convincingly shown by current data,
possibly due to poor statistics.
• One wonders how the situation varies with time: Mars’ orbital
eccentricity can be much lower than the current one, and the
perihelion-aphelion asymmetry may be much less noticeable
during those phases of its secular evolution.
References
Daubar, I. J., McEwen, A. S., Byrne, S., and Kennedy, M. R., in
LPSC Abstracts 43, 2740 (2012)
Kresák, L., in Proc. IAU Symp. 81, 239-244 (1979)
Laskar, J., Correia, A. C. M., Gastineau, M., Joutel, F., Levrard,
B., and Robutel, P., Icarus 170, 343-364 (2004)