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Table 7:

List of asteroids identified as potential major perturbers of Mars.
Asteroid H.D $\sum \theta_{1}$ Linear Reg. $\sum$ X Williams ``Major'' m $\sigma(m)/m$ Comm. Secular
${\rm N^{\rm o}}$ name 10 100 1 2 3 a e i   (1984) JPL $\left[M_{\odot}\right]$ $\left[\%\right]$ $P_{\rm M}{:}P_{\rm a}$ effects
1 Ceres X X X - - X X X 6 X X $4.75\times 10^{-10}$ 0.07 - X
2 Pallas X X X - - X X X 6 X X $1.03\times 10^{-10}$ 1.3 - X
4 Vesta X X X - - X X X 6 X X $1.34\times 10^{-10}$ 0.09 - X
7 Iris X X - X - X X X 6 X X $6.30\times 10^{-12}$ 3.0 - X
3 Juno - X - X - X X X 5 X X $1.51\times 10^{-11}$ 2.4 - X
6 Hebe - X - X - X X X 5 X X $6.46\times 10^{-12}$ 6.9 2:1 X
8 Flora - X - X - X X X 5 X X $1.65\times 10^{-12}$ 12.1 - X
10 Hygiea - X X - - X X X 5 X X $4.45\times 10^{-11}$ 0.8 - X
14 Irene - X - X - X X X 5 X X $2.31\times 10^{-12}$ 7.1 - X
51 Nemausa - X - - X X X X 5 X X $2.13\times 10^{-12}$ 11.5 - X
324 Bamberga - X - X - X X X 5 X X $5.50\times 10^{-12}$ 12.1 7:3 X
511 Davida - X - X - X X X 5 X X $2.20\times 10^{-11}$ 3.4 3:1 X
532 Herculina - X - X - X X X 5 X X $7.22\times 10^{-12}$ 8.2 - X
11 Parthenope - - - X - X X X 4 - X $3.09\times 10^{-12 }$ 5.5 - X
15 Eunomia - X - X - - X X 4 X X $1.57\times 10^{-11}$ 1.8 - X
18 Melpomene - X - - X X - X 4 X X $1.83\times 10^{-12}$ 21.2 - X
29 Amphitrite - X - X - - X X 4 X X $5.92\times 10^{-12}$ 2.9 13:6 X
41 Daphne $^{\star\star}$ - X - - X - X X 4 X X $3.47\times 10^{-12}$ 9.6 - X
52 Europa - - - X - X X X 4 X X $8.29\times 10^{-12 }$ 4.6 - X
654 Zelinda - X - - - X X X 4 - X $1.36\times 10^{-12}$ - - -
704 Interamnia - X - X - - X X 4 X X $1.86\times 10^{-11}$ 4.3 - X
747 Winchester - X - - X X - X 4 X X $3.33\times 10^{-12}$ 30.4 - -
9 Metis - X - - - X X - 3 X X $2.44\times 10^{-12}$ 10.8 - X
16 Psyche - X - X - - - X 3 X X $1.10\times 10^{-11}$ 3.7 - X
19 Fortuna - X - X - - X - 3 X X $6.38\times 10^{-12}$ 3.1 - X
24 Themis - - - X - X X - 3 X X $5.11\times 10^{-12 }$ 10.5 - X
31 Euphrosyne - - - X - - X X 3 X X $1.10\times 10^{-11}$ 7.1 3:1 X
94 Aurora - - - X - X X - 3 - X $5.66\times 10^{-12 }$ 5.1 3:1 X
105 Artemis - X - - - X X - 3 - X $1.11\times 10^{-12}$ - - -
130 Elektra $^{\star\star}$ - - - - - X X X 3 - - $3.32\times 10^{-12}$ - - -
145 Adeona - - - X - X - X 3 - X $2.27\times 10^{-12 }$ 24.9 - X
154 Bertha - - - - X X X - 3 - - $4.16\times 10^{-12 } $ - - -
192 Nausikaa - X - - - X X - 3 - X $7.25\times 10^{-13}$ 40.9 2:1 -
194 Prokne - - - - X X - X 3 - X $3.14\times 10^{-12 }$ 18.0 9:4 X
313 Chaldaea - X - - - X X - 3 - - $5.88\times 10^{-13}$ - - -
375 Ursula - - - X - - X X 3 - - $6.63\times 10^{-12}$ 11.4 - X
451 Patientia - X - X - - - X 3 - X $7.50\times 10^{-12}$ 6.8 - X
5 Astraea - - - - - X X - 2 - X $1.11\times 10^{-12}$ 20.9 11:5 -
13 Egeria - X - X - - - - 2 X X $5.89\times 10^{-12}$ 10.3 11:5 X
20 Massalia - - - - - X X - 2 X X $2.03\times 10^{-12 }$ 8.0 2:1 X
27 Euterpe - X - - X - - - 2 - X $5.82\times 10^{-13}$ 11.2 - -
45 Eugenia $^{\star\star}$ - - - - X - - X 2 X X $2.82\times 10^{-12}$ 3.1 - X
48 Doris - - - X - - - X 2 - - $7.18\times 10^{-12 }$ 6.3 - X
54 Alexandra - - - - X - - X 2 - - $3.00\times 10^{-12 }$ 7.8 - X
59 Elpis - - - - X - - X 2 - - $2.95\times 10^{-12}$ 9.1 - X
63 Ausonia - - - - - X X - 2 - X $ 7.21\times 10^{-13}$ - 2:1 -
78 Diana - - - - - X - X 2 X X $1.15\times 10^{-12 }$ 24.0 9:4 -
88 Thisbe - - - X - - - X 2 - - $5.31\times 10^{-12 }$ 3.4 - X
96 Aegle - - - - X - - X 2 - - $3.23\times 10^{-12}$ 29.5 - -
98 Ianthe - - - - - X X - 2 - X $7.51\times 10^{-13}$ - - -
106 Dione - - - - - X X - 2 - - $2.07\times 10^{-12}$ 48.4 3:1 -
120 Lachesis - - - - X - X - 2 - - $3.47\times 10^{-12}$ 12.5 - -
139 Juewa - - - - - X - X 2 - X $2.53\times 10^{-12 }$ 15.6 - X
216 Kleopatra $^{\star\star}$ - - - - - X X - 2 - X $1.62\times 10^{-12}$ 32.9 5:2 -
230 Athamantis - - - - - X X - 2 - X $8.52\times 10^{-13}$ 38.6 - -
344 Desiderata - X - - - - X - 2 - X $1.52\times 10^{-12}$ - - -
356 Liguria - X - X - - - - 2 - - $1.49\times 10^{-12}$ 18.6 - -
372 Palma - - - - - X - X 2 X X $4.41\times 10^{-12 }$ 32.3 3:1 -
405 Thia - X - - - X - - 2 X X $1.28\times 10^{-12}$ 47.6 - -
409 Aspasia - X - - X - - - 2 X X $2.78\times 10^{-12}$ 23.0 11:5 X
488 Kreusa - - - - - X X - 2 - X $2.23\times 10^{-12}$ - 3:1 -
554 Peraga - - - - - X X - 2 - X $5.80\times 10^{-13}$ 10.8 - -

H.D. relates to the theoretical determination by harmonic decomposition of perturbations on the semi-major axis and the longitude of Mars - period P < 50 years, see Sect. 4.1. The three columns of $\sum \theta_{1}$ are from Table 6 which were obtained by computing the sum of the deflections of Mars over 50 years. Linear Reg. corresponds to the selection from the drift of the semi-major axis, eccentricity and inclination of Mars due to the perturbation of each asteroid - see Sect. 6. Then, we indicate if the asteroid belongs to the list of Williams (1984) and to the major perturbers of Mars in DE ephemeris. The mass m is then given as well as the Gaia precision expected. The last two columns give the commensurability between the periods of Mars $P_{\rm M}$ and of asteroids $P_{\rm a}$ and the selection from secular effects on Mars - Table 5. The binary asteroids are marked by $^{\star\star}$.

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