**3. Some impact solutions for (144898) 2004 VD17**

#### **3.1 The influence of** *sigma\_LOV* **and weighting**

The orbital elements of (144898) 2004 VD17 presented in Tab. 5 were computed using all known observations up to 14th Sept., 2006 by the author with the software OrbFit 3.3.2 for Linux where *M* - mean anomaly, *a* - semimajor axis, *e* - eccentricity, - argument of perihelion, - longitude of the ascending node, i*2000* - inclination of the orbit. These orbital elements are referred to the *J2000* equator and equinox. Fig. 3 presents the orbit of (144898) 2004 VD17 projected to the ecliptic plane, where *x*-axis is directed to vernal equinox. The dotted lines indicate the part of the orbit below the ecliptic plane. The orbit of this asteroid crosses the orbit of the Earth and that of Venus.


Table 5. (144898) 2004 VD17: orbital elements. 933 observations from 1553 days (2002/02/16.46 - 2006/05/24.10), *rms*=0.351". Nominal orbit: epoch 2006 Jun. 14.0.

Fig. 3. The orbit of (144898) 2004 VD17 projected to the ecliptic plane, where *x*-axis is directed to vernal equinox.

66 Space Science

As we can see in Tab. 4 the results for the JPL ephemerides DE405 and DE406 are almost the same. However Andrea Milani in his e-mail on Juni, 6-th, 2006 wrote: "A particularly good result (using DE405 or DE406), given the strong instability of these solutions, as a result of the very close approach in 2029. My congratulations for your very accurate computations."

The orbital elements of (144898) 2004 VD17 presented in Tab. 5 were computed using all known observations up to 14th Sept., 2006 by the author with the software OrbFit 3.3.2 for

perihelion, - longitude of the ascending node, i*2000* - inclination of the orbit. These orbital elements are referred to the *J2000* equator and equinox. Fig. 3 presents the orbit of (144898) 2004 VD17 projected to the ecliptic plane, where *x*-axis is directed to vernal equinox. The dotted lines indicate the part of the orbit below the ecliptic plane. The orbit of

340.212924 1.5082009 0.58866739 90.686443 224.242137 4.223018

Table 5. (144898) 2004 VD17: orbital elements. 933 observations from 1553 days (2002/02/16.46 - 2006/05/24.10), *rms*=0.351". Nominal orbit: epoch 2006 Jun. 14.0.

Fig. 3. The orbit of (144898) 2004 VD17 projected to the ecliptic plane, where *x*-axis is

*deg* *deg* - argument of

*i2000[deg]*

**3. Some impact solutions for (144898) 2004 VD17** 

this asteroid crosses the orbit of the Earth and that of Venus.

Linux where *M* - mean anomaly, *a* - semimajor axis, *e* - eccentricity,

**3.1 The influence of** *sigma\_LOV* **and weighting** 

*M[deg] a[AU] e*

directed to vernal equinox.

The impact solutions of (144898) 2004 VD17 in Tab. 6 were computed using 891 optical observations (of which 1 was rejected as outlier) from 2002/02/16.462 to 2006/04/22.871. These observations were available up to date of MACE 2006.

Tab. 6 shows that the infuence of and weighting of observations has a small influence for impact solutions for (144898) 2004 VD17.


Table 6. (144898) 2004 VD17: Inluence of different *sigma\_LOV (* and weighting for impact solutions.

Mainly it have an effect on value of impact probability. Similar the problem of scaling of LOV (Milani et al., 2002) is neglecting in this case. Otherwise everywhere weighing is as CLOMON2, further settings are: multiple solution, use scaling (fn denotes impact solution

OrbFit Impact Solutions for Asteroids (99942) Apophis and (144898) 2004 VD17 69

*IW-c*: 5 close approaching asteroids to (144898) 2004 VD17 : Juno, Hebe, Iris, Melpomene and

*IW-f*: all 9 perturbing asteroids: Ceres, Pallas, Juno, Vesta, Hebe, Iris, Hygiea, Melpomene

All results in Tab. 7 are computed with DE405 ephemeris and using relativistic effects (without case *IW-bnrel*). We can see that the impact solutions for asteroid (144898) 2004 VD17 does not differ so much using different number of perturbing asteroids as in the case

Fig. 4 shows the changes of differences in mean anomaly between asteroid (144898) 2004 VD17 on nominal orbits for different cases. In Fig. 4 (a) there are differences in mean anomaly between (144898) 2004 VD17 with and no relativistic effects included. Fig. 4 (b) presents differences in mean anomaly of (144898) 2004 VD17 between orbits without perturbing asteroids (solution *IW-d*) and with ones: 1 - solution *IW-a* (Ceres, Pallas and Vesta included), 2 - *IW-b* (Ceres, Pallas, Vesta, Hygiea), 3 - *IW-c* (Juno, Hebe, Iris, Melpomene, Nemausa), 4 - *IW-f* (Ceres, Pallas, Juno, Vesta, Hebe, Iris, Hygiea, Melpomene, Nemausa). The curves 1, 2 and 4 on the Fig. 4 are very similar, then the most perturbing

Fig. 4. (144898) 2004 VD17. Differences in mean anomaly between nominal orbit from different solutions: (a) – 4 perturbing asteroids: relativistic/non relativistic effects included; (b) – different number of perturbing asteroids: 1 - Ceres, Pallas and Vesta; 2 – Ceres, Pallas, Vesta and Hygiea; 3 – Juno, Hebe, Iris, Melpomene and Nemausa; 4 – Ceres, Pallas, Juno,

As in the case of (99942) Apophis the greatest infuence for motion (144898) 2004 VD17 have relativistic effects, about 10 times greater than the perturbing effects of additional massive asteroids. Even so we must use perturbing massive asteroids for computed precise impact

Vesta, Hebe, Iris, Hygiea, Melpomene and Nemausa (see text) .

*IW-a*: solutions with 3. perturbing asteroids: Ceres, Pallas and Vesta

*IW-b*: 4 perturbing asteroids: Ceres, Pallas, Vesta, Hygiea *IW-bnrel*: as *IW-b* without relativistic effects included

The results are in Tab. 7 where:

*IW-d*: no perturbing asteroids

effect comes from Ceres, Pallas and Vesta.

Nemausa

and Nemausa

of (99942) Apophis.

without scaling), LOV with the largest eigenvalue; *w*=1 denotes without weighing of observations. On the MPML (Minor Planet Mailing List) forum the problem was connected with 4 first observations of (144898) 2004 VD17 recovered from 2002 year. It was appear that adding these observations does not affect on impact solutions considerably. In Tab. 6 *fn*  denotes impact solutions without first four observations from 2002.
