Solar System Dynamics Group Example 2 Trajectory of impact at the Earth surface

### 2008 ST7

#### The small asteroid 2008 ST7 was discovered on September 24, 2008 by the Mount Lemmon Survey, seventeen days after it had passed within 880 000 km of Earth. It has a diameter of about 50 meters. The impact calculations given below were based on Number of original observations: 108 Arc : 2008 09 24 - 2008 10 20 Nominal rms: 0².32 (205 residuals) From this set of data we derived that collisions with Earth are possible in years: 2074, 2082, 2089, 2094A, 2094B, 2094C We focus here on three different posibilities of impact in 2094, namely:

Table 1A. Solution 2094A. Orbital elements of impact orbit for two dates (equ. J2000)

Epoch [TT] a [AU] e i [deg] W [deg] w [deg] M [deg] rms
20081130
20940903
1.933010369
1.925067610
0.513790277
0.512071012
2.4494712
2.4698775
347.8903891
346.4479114
321.6182109
323.2935874
40.9614407
8.1087116
0².32

Impact date: 2094 09 09.992 (UT)   Vimpact= 15.268 km/sec   Ψimpact = 55°.31

Vimpact
The velocity of the asteroid relative to the Earth at the moment of impact.
Ψimpact
The impact angle is measured from the vertical axis that goes through the impact point. Thus, the impact angle is 0 degrees for a vertical impact.
rms
Root mean square for the derived impact orbit.

Table 1B. Solution 2094B. Orbital elements of impact orbit for two dates (equ. J2000)

 20081130 20940903 1.934333348 1.925112946 0.514139095 0.512154878 2.4506673 2.4700094 347.8892982 346.5453794 321.6173648 323.2349883 40.9187258 8.0890246 0².32

Impact date: 2094 09 10.064 (UT)   Vimpact= 15.306 km/sec   Ψimpact = 30°.80

Table 1C. Solution 2094C. Orbital elements of impact orbit for two dates (equ. J2000)

 20081130 20940903 1.938481690 1.992600885 0.515238017 0.525874286 2.4544010 2.7502770 347.8879445 346.3776885 321.6121274 325.1440416 40.7849021 7.2173048 0².36

Impact date: 2094 09 9.903 (UT)   Vimpact= 15.307 km/sec   Ψimpact = 48°.43

Table 2A.

#### Impact parameters for hypothetical collision in 2094 for solution 2094A

Date
[UT]
λ
[deg]
φ
[deg]
Ψimpact
[deg]
Vimpact
[km/s]
rms
[arcsec]
2094 09 09.99237 237.36562 46.91744 55.31 15.268 0.32
2094 09 09.99237 237.33946 46.92560 55.31 15.268 0.32
2094 09 09.99234 237.12676 46.99246 55.32 15.267 0.32
2094 09 09.99224 236.45940 47.20407 55.32 15.264 0.32
2094 09 09.99245 237.92261 46.74385 55.32 15.271 0.32
2094 09 09.99245 237.91060 46.74760 55.32 15.271 0.32
2094 09 09.99249 238.16063 46.67028 55.32 15.272 0.32
2094 09 09.99216 235.91484 47.37884 55.34 15.261 0.32
2094 09 09.99252 238.42907 46.58780 55.32 15.273 0.32
2094 09 09.99260 238.95349 46.42808 55.33 15.276 0.32
2094 09 09.99205 235.08454 47.64884 55.37 15.257 0.32
2094 09 09.99262 239.07747 46.39058 55.34 15.277 0.32
2094 09 09.99270 239.62292 46.22687 55.36 15.279 0.32
2094 09 09.99194 234.31543 47.90272 55.41 15.253 0.32
2094 09 09.99189 233.94709 48.02556 55.43 15.251 0.32
2094 09 09.99281 240.34959 46.01198 55.39 15.282 0.32
2094 09 09.99183 233.47554 48.18397 55.47 15.248 0.32
2094 09 09.99182 233.39157 48.21232 55.47 15.248 0.32
2094 09 09.99288 240.79590 45.88187 55.42 15.284 0.32
2094 09 09.99176 232.95414 48.36057 55.51 15.246 0.32
2094 09 09.99299 241.52602 45.67202 55.47 15.288 0.32
2094 09 09.99165 232.15611 48.63378 55.58 15.241 0.32
2094 09 09.99316 242.58109 45.37558 55.56 15.292 0.32
2094 09 09.99152 231.10994 48.99713 55.69 15.236 0.32
2094 09 09.99322 243.02263 45.25390 55.61 15.294 0.32
2094 09 09.99144 230.52357 49.20327 55.76 15.232 0.32
2094 09 09.99140 230.15421 49.33395 55.81 15.230 0.32
2094 09 09.99343 244.31474 44.90624 55.76 15.299 0.32
2094 09 09.99348 244.65804 44.81596 55.80 15.300 0.32
2094 09 09.99350 244.73499 44.79586 55.82 15.301 0.32
2094 09 09.99359 245.31050 44.64685 55.90 15.303 0.32
2094 09 09.99359 245.31985 44.64446 55.90 15.303 0.32
2094 09 09.99116 228.18894 50.04029 56.10 15.219 0.32
2094 09 09.99373 246.15646 44.43244 56.03 15.306 0.32
2094 09 09.99107 227.45200 50.30961 56.23 15.215 0.32
2094 09 09.99102 226.99677 50.47705 56.31 15.212 0.32
2094 09 09.99096 226.43926 50.68324 56.41 15.209 0.32
2094 09 09.99095 226.42430 50.68881 56.42 15.209 0.32
2094 09 09.99093 226.20481 50.77033 56.46 15.208 0.32
2094 09 09.99092 226.11539 50.80357 56.48 15.207 0.32
2094 09 09.99405 248.15725 43.94729 56.40 15.313 0.32
2094 09 09.99085 225.45973 51.04837 56.61 15.204 0.32
2094 09 09.99080 225.07256 51.19368 56.69 15.201 0.32
2094 09 09.99415 248.75072 43.80936 56.52 15.315 0.32
2094 09 09.99074 224.52060 51.40164 56.81 15.198 0.32
2094 09 09.99432 249.72693 43.58860 56.74 15.318 0.32
2094 09 09.99064 223.49780 51.78952 57.04 15.192 0.32
2094 09 09.99442 250.36262 43.44887 56.89 15.320 0.32
2094 09 09.99058 222.94770 51.99939 57.17 15.189 0.32
2094 09 09.99053 222.40307 52.20798 57.30 15.186 0.32
2094 09 09.99050 222.16634 52.29895 57.36 15.184 0.32
2094 09 09.99467 251.83035 43.13853 57.27 15.324 0.32
2094 09 09.99045 221.66431 52.49218 57.49 15.181 0.32
2094 09 09.99491 253.23024 42.85852 57.66 15.328 0.32
2094 09 09.99505 254.02363 42.70680 57.90 15.329 0.32
2094 09 09.99025 219.52205 53.32266 58.06 15.169 0.32
2094 09 09.99022 219.22038 53.44032 58.15 15.167 0.32
2094 09 09.99020 218.98391 53.53253 58.21 15.165 0.32
2094 09 09.99515 254.63281 42.59375 58.08 15.331 0.32
2094 09 09.99013 218.17776 53.84766 58.45 15.161 0.32
2094 09 09.99012 218.04759 53.89864 58.49 15.160 0.32
2094 09 09.99010 217.81965 53.98795 58.55 15.158 0.32
2094 09 09.99530 255.49569 42.43863 58.36 15.332 0.32
2094 09 09.99007 217.39765 54.15328 58.68 15.156 0.32
2094 09 09.99537 255.89779 42.36833 58.50 15.333 0.32
2094 09 09.99539 256.03636 42.34446 58.54 15.334 0.32
2094 09 09.99003 216.91957 54.34091 58.83 15.153 0.32
2094 09 09.98995 215.92020 54.73335 59.14 15.147 0.32
2094 09 09.98982 214.26821 55.38278 59.67 15.138 0.32
2094 09 09.98980 213.90843 55.52415 59.79 15.136 0.32
2094 09 09.99597 259.38511 41.81276 59.76 15.339 0.32
2094 09 09.99603 259.72033 41.76441 59.89 15.339 0.32
2094 09 09.99605 259.81180 41.75134 59.92 15.339 0.32
2094 09 09.98969 212.43536 56.10233 60.28 15.127 0.32
2094 09 09.98968 212.24612 56.17655 60.35 15.126 0.32
2094 09 09.99625 260.95643 41.59363 60.38 15.340 0.32
2094 09 09.99627 261.07806 41.57744 60.43 15.340 0.32
2094 09 09.99642 261.98015 41.46110 60.80 15.341 0.32
2094 09 09.98945 208.43451 57.66038 61.69 15.104 0.32
2094 09 09.99671 263.64240 41.26292 61.52 15.342 0.32
2094 09 09.98941 207.81721 57.89819 61.91 15.101 0.32
2094 09 09.98939 207.29176 58.09996 62.10 15.098 0.32
2094 09 09.98938 207.18279 58.14170 62.14 15.098 0.32
2094 09 09.98931 205.67360 58.71677 62.69 15.089 0.32
2094 09 09.98923 204.07154 59.31988 63.29 15.081 0.32
2094 09 09.98923 204.06268 59.32320 63.29 15.081 0.32
2094 09 09.99734 267.30571 40.89861 63.21 15.342 0.32
2094 09 09.99739 267.61118 40.87262 63.36 15.342 0.32
2094 09 09.98916 202.20000 60.01339 63.99 15.071 0.32
2094 09 09.98915 202.00839 60.08365 64.06 15.070 0.32
2094 09 09.98914 201.75115 60.17778 64.16 15.069 0.32
2094 09 09.98911 201.01545 60.44550 64.43 15.065 0.32
2094 09 09.98910 200.44422 60.65184 64.65 15.063 0.32
2094 09 09.99801 271.24985 40.61254 65.19 15.339 0.32
2094 09 09.98903 198.52331 61.33532 65.36 15.053 0.32
2094 09 09.98901 197.67277 61.63257 65.68 15.049 0.32
2094 09 09.99817 272.22828 40.55776 65.70 15.338 0.32
2094 09 09.99826 272.79416 40.52883 66.00 15.337 0.32
2094 09 09.98891 193.49794 63.03984 67.23 15.031 0.32
2094 09 09.98891 193.31625 63.09901 67.30 15.030 0.32
2094 09 09.98890 193.05043 63.18529 67.39 15.029 0.32
2094 09 09.99868 275.34377 40.42343 67.37 15.332 0.32
2094 09 09.98889 192.40704 63.39253 67.63 15.026 0.32
2094 09 09.99877 275.88392 40.40615 67.67 15.331 0.32
2094 09 09.99879 276.03898 40.40149 67.75 15.331 0.32
2094 09 09.98887 191.28374 63.74877 68.04 15.021 0.32
2094 09 09.98887 190.82386 63.89263 68.20 15.019 0.32
2094 09 09.99889 276.66950 40.38404 68.10 15.330 0.32
2094 09 09.99900 277.37388 40.36716 68.49 15.328 0.32
2094 09 09.98884 188.97919 64.45750 68.86 15.012 0.32
2094 09 09.99914 278.23006 40.35039 68.97 15.326 0.32
2094 09 09.99923 278.82541 40.34110 69.31 15.325 0.32
2094 09 09.99962 281.35139 40.32199 70.75 15.318 0.32
2094 09 09.98879 180.30553 66.84593 71.82 14.982 0.32
2094 09 10.00006 282.37243 40.33893 72.49 15.308 0.32
2094 09 10.00019 283.27671 40.35177 73.02 15.305 0.32
2094 09 09.98880 175.09711 68.06633 76.87 14.937 0.32
2094 09 10.00124 291.14810 40.58687 77.71 15.272 0.32
2094 09 09.98903 151.95211 71.72779 79.68 14.916 0.32
2094 09 10.00177 295.54104 40.78954 80.34 15.250 0.32
2094 09 10.00179 295.78506 40.80180 80.48 15.249 0.32
2094 09 10.00199 297.53155 40.89184 81.52 15.239 0.32
2094 09 10.00220 299.58395 41.00172 82.74 15.228 0.32
2094 09 10.00247 302.27933 41.14980 84.33 15.212 0.32
2094 09 09.98948 125.90438 73.08412 85.36 14.882 0.32

 Fig.1 Three paths of the hypothetical impacts at the Earth surface for small asteroid 2008 ST7. From the top to bottom green trajectories correspond to the sample of clonned impact orbits 2094A, 2094C, 2094B, respectively. Red points represent virtual impact orbits with the smallest angle Ψ ;— these impact orbits are given in the tables 1A, 1B, 1C.