**3.2 (144898) 2004 VD17: Approaching asteroids**

As for (99942) Apophis, to compute exactly impact solutions for (144898) 2004 VD17 it is necessary to include gravitational perturbations of approaching asteroids. Using software Solex90 we have computed all close approaches of about 140,000 numbering asteroids known in Sept. 2006 with (144898) 2004 VD17 till 2110 year. We have found 5 asteroids with several close approaches to (144898) 2004 VD17 : (3) Juno, (6) Hebe, (7) Iris, (18) Melpomene and (51) Nemausa. These selected asteroids with the 4 massive ones were included to equations of motion of (144898) 2004 VD17 .

The computations of infuence of gravitational perturbations of these asteroids for the motion of (144898) 2004 VD17 were performed using software OrbFit 3.3.1. The masses of asteroids were taken from Michalak (2001) and from Solex90 as computed by A. Vitagliano (2006). The computations were based on 902 optical observations (of which 3 are rejected as outliers) from 2002/02/16.462 to 2006/04/29.090.


Table 7. (144898) 2004 VD17: Influence of approaching asteroids on impact solutions.

The results are in Tab. 7 where:

68 Space Science

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* 

As for (99942) Apophis, to compute exactly impact solutions for (144898) 2004 VD17 it is necessary to include gravitational perturbations of approaching asteroids. Using software Solex90 we have computed all close approaches of about 140,000 numbering asteroids known in Sept. 2006 with (144898) 2004 VD17 till 2110 year. We have found 5 asteroids with several close approaches to (144898) 2004 VD17 : (3) Juno, (6) Hebe, (7) Iris, (18) Melpomene and (51) Nemausa. These selected asteroids with the 4 massive ones were included to

The computations of infuence of gravitational perturbations of these asteroids for the motion of (144898) 2004 VD17 were performed using software OrbFit 3.3.1. The masses of asteroids were taken from Michalak (2001) and from Solex90 as computed by A. Vitagliano (2006). The computations were based on 902 optical observations (of which 3 are rejected as

Date Dist. [RE] Impact probability Source 2102/05/04.894 0.51 5.58 E-04 CLOMON2 2102/05/04.894 0.52 5.53 E-04 IW-a 2102/05/04.894 0.52 5.61 E-04 IW-d 2102/05/04.894 0.52 5.54 E-04 IW-b 2102/05/04.893 0.53 6.37 E-04 IW-bnrel 2102/05/04.894 0.52 5.59 E-04 IW-c 2102/05/04.894 0.52 5.53 E-04 IW-f 2102/05/04.890 0.44 7.35 E-04 SENTRY 2103/05/05.130 0.96 1.48 E-08 CLOMON2 2103/05/05.132 0.74 1.52 E-08 IW-b 2104/05/04.376 0.91 2.77 E-07 CLOMON2 2104/05/04.374 0.53 2.77 E-07 IW-a 2104/05/04.374 0.53 2.76 E-07 IW-d 2104/05/04.372 1.08 2.68 E-07 IW-b 2104/05/04.373 0.61 3.08 E-07 IW-bnrel 2104/05/04.376 0.87 2.78 E-07 IW-c 2104/05/04.377 1.09 2.74 E-07 IW-f 2109/05/04.515 0.84 7.60 E-09 IW-f Table 7. (144898) 2004 VD17: Influence of approaching asteroids on impact solutions.

denotes impact solutions without first four observations from 2002.

**3.2 (144898) 2004 VD17: Approaching asteroids** 

equations of motion of (144898) 2004 VD17 .

outliers) from 2002/02/16.462 to 2006/04/29.090.

*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

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

*IW-d*: no perturbing asteroids

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

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 of (99942) Apophis.

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 effect comes from Ceres, Pallas and Vesta.

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

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

the Earth.

OrbFit Impact Solutions for Asteroids (99942) Apophis and (144898) 2004 VD17 71

motion of asteroids separately. The result of the Yarkovsky effect is removal of small asteroids from the main belt to chaotic mean motion and secular apsidal or nodal resonance zones. Then they can be gradually transported to Earth-crossing orbits. Therefore the Yarkovsky and YORP effects are now considered in relation to objects crossing the Earth orbit, particularly they are important in the motion of potentially dangerous asteroids for

The NEODyS presents only impact solutions based on 1399 optical observations (of which 5 are rejected as outliers) from 2004/03/15.127 to 2008/01/09.666 and also on seven radar data points on 2005/01/27, 2005/01/29, 2005/01/31, 2005/08/07 and 2006/05/06. The NEODyS lists possible impact in 2036, 2056, 2068 – two solutions, 2076 and in 2103. Their solutions are based on Monte Carlo method, including a probabilistic model of the Yarkovsky effect. In this way impact solutions are model dependent. Without any nongravitational perturbation model they found possible impact in 2068/04/12.632 with the

Using all 1490 observations of Apophis and the OrbFit software I computed value of the semimajor axis drift of Apophis equal to **da/dt**=+180 10-4 AU/Myr connected with the Yarkovsky/YORP effects and got following impact solutions as are presented in Table 9.

Table 9. (99942) Apophis. Impact solutions with the Earth using semimajor axis drif, **da/dt**= =+180 10-4 AU/Myr, computed by the author. Similar value of **da/dt**= (235+/-50) 10-4

To compute impact solutions of Apophis we must know exact uncertainty from the Yarkovsky effects and physical parameter uncertainties of Apophis together with the

Table 10 lists orbital elements of (144898) 2004 VD17 performed using all observations available up to 1st Oct., 2011. There were 981 optical observations of which 4 were rejected as outliers. The orbit was computed by the author using the OrbFit software v. 4.2. The JPL NASA Ephemerides DE405 and additional perturbations from massive asteroids: (1) Ceres,

271.359237 1.5081219 0.58860168 90.762748 224.187119 4.223233 9.96E-05 7.36E-08 4.86E-08 3.52E-05 7.93E-06 7.93E-06

Table 10. (144898) 2004 VD17: orbital elements together with theirs 1- variations. 981 observations from 2513 days (2002/02/16.46212 – 2009/01/03.40647), *rms*=0.402". Nominal

*deg* *deg*

*i2000[deg]*

probability of about 3.81 10-6. Similar impact solutions are from the JPL NASA.

Additional perturbations from (1) Ceres, (2) Pallas and (4) Vesta are included.

AU/Myr has computed Grzegorz Sitarski (private information).

astrometric biases and radiation pressure (Giorgini et al. 2007).

(2) Pallas, (3) Juno, (4) Vesta and (10) Hygiea were used.

*M[deg] a[AU] e*

**4.2 (144898) 2004 VD17**

orbit: epoch 2011 Aug. 27.0.

Date Dist. [RE] Impact probability 2043/04/13.901 2.01 2.08 E-07 2064/04/12.824 1.52 1.44 E-06

solutions as Tab. 7 states. The rapidly changes in differences in mean anomaly in Fig. 4 are connected with the close approaches of (144898) 2004 VD17 with the Earth in the years: 2041 (0.01 AU), 2067 (0.03 AU) and 2102 (0.03 AU) for the nominal orbits. Hence chaoticity of the motion of the asteroid appears similar to this of (99942) Apophis but in the case of (144898) 2004 VD17 motion is less influenced.
