**2.1 The Influence of** *sigma\_LOV* **and radar observation**

The orbital elements of (99942) Apophis in Tab. 1 were computed by the author using all 1007 observations up to this date (Sep. 14th, 2006) and software OrbFit where *M* - mean anomaly, *a* - semimajor axis, *e* - eccentricity, – argument of perihelion, - longitude of the ascending node, *i2000* - inclination of the orbit. These orbital elements are referred to the *J2000* equator and equinox.


Table 1. (99942) Apophis: orbital elements. 1007 observations from 885 days (2004/03/15.11 - 2006/08/16.63 ), *rms*=0.302". Nominal orbit: epoch 2006 Jun. 14.0.

Fig. 1 presents the orbit of (99942) Apophis 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. It is clearly seen that orbit of this asteroid crosses the orbit of the Earth and approaches that of Venus. The influence of the radar observations in computations of impact solutions for (99942) Apophis were performed using all observations available before date of MACE 2006. There were 987 optical observations (of which 6 were rejected as outliers) from 2004/03/15.108 to 2006/03/26.509, and also seven radar data points on 2005/01/27, 2005/01/29, 2005/01/31 and 2005/08/07.

Tab. 2 lists impact solutions for (99942) Apophis computed by the author for these settings: multiple solutions, use scaling, line of variation (LOV) with the largest eigenvalue (Milani et al. 2002) in comparison with these published at NEODYS CLOMON2

site: http://newton.dm.unipi.it/neodys/index.php?pc=1.1.2&n=99942

and at the NASA SENTRY site: http://neo.jpl.nasa.gov/risk/a99942.html.

The software OrbFit ver. 3.3.1 for UNIX was used. In this impact table everywhere weighing of observations was as CLOMON2. In Tab. 2 *date* is a calendar day for the potential impact; *dist.[RE]* – minimum distance, the lateral distance from LOV (line of variation, which represent the central axis of the asteroid's elongated uncertainty region); *impact probability* - computed with a Gaussian bidimensional probability density; *IW* – 60 Space Science

2005b). The main goal of our work was to compare our results generated by OrbFit with the results presented by CLOMON2 system which uses the same OrbFit software and with the results of JPL NASA SENTRY. The second purpose was to prove how differently small effects in motion of asteroid change impact solutions. It was possible thanks to public available source code of the OrbFit software. The orbital uncertainty of an asteroid is viewed as a cloud of possible orbits centered on the nominal solution, where density is greatest. This is represented by the multivariate Gaussian probability density and the use of this probability density relies on the assumption that the observational errors are Gaussian (Milani et al., 2002). Now, August 2011, we have new version of the OrbFit software, v.4.2, implementing the new error model based upon Chesley, Baer and Monet

The orbital elements of (99942) Apophis in Tab. 1 were computed by the author using all 1007 observations up to this date (Sep. 14th, 2006) and software OrbFit where *M* - mean

of the ascending node, *i2000* - inclination of the orbit. These orbital elements are referred to the

333.507245 0.92226793 0.19105946 126.393030 204.460151 3.331317

Fig. 1 presents the orbit of (99942) Apophis 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. It is clearly seen that orbit of this asteroid crosses the orbit of the Earth and approaches that of Venus. The influence of the radar observations in computations of impact solutions for (99942) Apophis were performed using all observations available before date of MACE 2006. There were 987 optical observations (of which 6 were rejected as outliers) from 2004/03/15.108 to 2006/03/26.509, and also seven radar data points on 2005/01/27,

Tab. 2 lists impact solutions for (99942) Apophis computed by the author for these settings: multiple solutions, use scaling, line of variation (LOV) with the largest eigenvalue (Milani et

The software OrbFit ver. 3.3.1 for UNIX was used. In this impact table everywhere weighing of observations was as CLOMON2. In Tab. 2 *date* is a calendar day for the potential impact; *dist.[RE]* – minimum distance, the lateral distance from LOV (line of variation, which represent the central axis of the asteroid's elongated uncertainty region); *impact probability* - computed with a Gaussian bidimensional probability density; *IW* –

Table 1. (99942) Apophis: orbital elements. 1007 observations from 885 days (2004/03/15.11 - 2006/08/16.63 ), *rms*=0.302". Nominal orbit: epoch 2006 Jun. 14.0.

al. 2002) in comparison with these published at NEODYS CLOMON2 site: http://newton.dm.unipi.it/neodys/index.php?pc=1.1.2&n=99942 and at the NASA SENTRY site: http://neo.jpl.nasa.gov/risk/a99942.html.

*deg*

– argument of perihelion,

*deg*


*i2000[deg]*

(2010).

**2. Some impact solutions for (99942) apophis** 

anomaly, *a* - semimajor axis, *e* - eccentricity,

*M[deg] a[AU] e*

2005/01/29, 2005/01/31 and 2005/08/07.

*J2000* equator and equinox.

**2.1 The Influence of** *sigma\_LOV* **and radar observation** 

computed solutions by author of this paper; *nr* denotes solution without radar observations and equal to *sigma\_LOV* - approximate location along the LOV in sigma space; values of sigma are usually in the interval [-3,3] which represent 99.7 % probability of occurrence of real asteroid in this confidence region (Milani et al. 2002). The impact probability is not reported if the computed value is less than 1E-11. The presented are only the input data in OrbFit software, not the real - positive or negative, along the LOV. For example = 3 denotes that the real is between -3 and +3. For different setting of value we observe slightly different impact solutions mainly in the date of possible impact. The differences between the results from the NEODyS (CLOMON2) and the JPL NASA (SENTRY) are evident because they are independent systems as state at: http://neo.jpl.nasa.gov/risk/doc/sentry\_faq.html. For example impact probabilities different by a factor of ten or so are not extraordinary.

Fig. 1. The orbit of (99942) Apophis projected to the ecliptic plane, where *x*-axis is directed to vernal equinox.

OrbFit Impact Solutions for Asteroids (99942) Apophis and (144898) 2004 VD17 63

From results in Tab. 2 we can see that we must include radar observations in computations of impact solutions for (99942) Apophis. Without radar observations we have not impact solutions in 2042, 2044, 2053 and beyond 2063 year. Instead we have mistaken dates of possible impacts in 2035, 2046, 2055 and 2056 years. The usefulness of radar observations is

=1 were

presented e.g. in the paper of Yeomans et. al. (1987). No impact solutions for

**2.2 (99942) Apophis: Approaching asteroids** 

perturbations from Ceres, Pallas, Vesta and Hygiea.

Pallas and Vesta.

found. Time of computations of single solution was about 3 hrs with 1.7 MHz processor.

To compute exactly impact solutions for (99942) Apophis it is necessary to include gravitational perturbations of approaching massive asteroids. Usually SENTRY include 3 massive asteroids: (1) Ceres, (2) Pallas and (4) Vesta, CLOMMON2 - as SENTRY or 4 asteroids: (1) Ceres, (2) Pallas, (4) Vesta and (10) Hygiea. Using the software Solex ver. 9.0 we have investigated all close approaches of about 140,000 numbered asteroids known in Sept. 2006 with (99942) Apophis within 0.2 AU till 2100 year. We have found 4 asteroids with several close approaches to (99942) Apophis: (433) Eros, (887) Alinda, (1685) Toro and (1866) Sisyphus. These selected asteroids together with the 4 massive ones (Ceres, Pallas, Vesta and Hygiea) were included to equations of motion of (99942) Apophis. The computations of influence of gravitational perturbations of these asteroids for the motion of (99942) Apophis were performed using software OrbFit ver. 3.3.1. The masses of asteroids were taken from Michalak (2001) and from Solex as computed by A. Vitagliano. First of all we must include Ceres in our gravitational model which has about 30 % of the mass of the main belt asteroids and the asteroids which have the closest approaches with (99942) Apophis. All results in Tab. 3 are computed using the JPL Planetary and Lunar Ephemerides DE405 and relativistic effects.

The suitable results in Tab. 3 were computed based on 996 optical observations of which 5 are rejected as outliers from 2004/03/15.108 to 2006/07/27.614, and also on seven radar

In Tab. 3 and in all others SENTRY denotes the results from the JPL NASA and CLOMON2 from the NEODYS site. The author results are: *IW-a*: no perturbing asteroids; *IW-b*: Ceres and 4 close approaching asteroids to (99942) Apophis: Eros, Alinda, Toro, Sisyphus; *IW-c*: 4 perturbing asteroids: Ceres, Pallas, Vesta, Hygiea; *IW-d*: 5 perturbing asteroids: Ceres, Pallas, Vesta, Hygiea and approaching asteroid Eros; *IW-e*: 3 perturbing asteroids: Ceres,

From Table 3 we can see that there is significant role of massive asteroids in motion of Apophis, specially after 2042. Some impact solutions does not exist in given year. For example, in April, 2069 there are only impact solutions with additional perturbing effect from together: Ceres, Eros, Alinda, Toro, Sisyphus and the second solution with

Fig. 2 shows the changes of differences in mean anomaly between asteroid (99942) Apophis on nominal orbits for different cases. In Fig. 2(a) there are differences in mean anomaly between (99942) Apophis with and no relativistic effects included. Fig. 2(b) presents differences in mean anomaly of (99942) Apophis between orbits computed without perturbing asteroids and with perturbation from: *1* - Ceres, Pallas and Vesta, *2* - Ceres, Pallas, Vesta, and Hygiea and *3* - Ceres, Pallas, Vesta, Hygiea and Eros. It is clear from Fig.

data points on 2005/01/27, 2005/01/29, 2005/01/31, 2005/08/07 and 2006/05/06.


Table 2. (99942) Apophis: influence of different *sigma\_LOV* and radar observations for computed impact solutions. Note nr means solution without radar observations. SENTRY and CLOMON2 are systems of impact risk computing of the JPL NASA and the NEODYS, respectively. IW are results by the author.

From results in Tab. 2 we can see that we must include radar observations in computations of impact solutions for (99942) Apophis. Without radar observations we have not impact solutions in 2042, 2044, 2053 and beyond 2063 year. Instead we have mistaken dates of possible impacts in 2035, 2046, 2055 and 2056 years. The usefulness of radar observations is presented e.g. in the paper of Yeomans et. al. (1987). No impact solutions for =1 were found. Time of computations of single solution was about 3 hrs with 1.7 MHz processor.

## **2.2 (99942) Apophis: Approaching asteroids**

62 Space Science

date dist[RE] impact probability source 2035/04/14.131 1.36 1.82E-05 IW, 3 , nr 2036/04/13.371 1.15 1.61E-04 CLOMON2 2036/04/13.370 0.53 1.60E-04 SENTRY 2036/04/13.371 1.14 3.46E-05 IW, 3 2036/04/13.371 1.15 1.02E-04 IW, 3 , nr 2036/04/13.371 1.14 3.46E-05 IW, 6 , 2037/04/13.644 1.36 1.96E-07 CLOMON2 2037/04/13.640 0.63 2.00E-07 SENTRY 2037/04/13.644 1.36 2.46E-05 IW, 3 , nr 2037/04/13.644 1.36 1.45E-08 IW, 6 2038/04/13.659 1.73 1.59E-10 CLOMON2 2040/04/13.135 1.65 8.17E-09 IW, 3 2040/04/13.173 1.11 3.40E-08 IW, 3 , nr 2042/04/13.726 1.80 3.62E-07 CLOMON2 2042/04/13.710 0.99 4.60E-07 SENTRY 2042/04/13.719 1.38 9.29E-08 IW, 3 2044/04/13.297 2.10 2.57E-07 CLOMON2 2044/04/13.296 2.08 5.89E-08 IW, 3 2044/04/13.264 1.79 6.23E-11 IW, 6 2046/04/13.797 1.98 3.84E-08 IW, 3 , nr 2053/04/12.913 1.39 1.80E-07 IW, 3 2054/04/13.401 1.46 6.95E-09 CLOMON2 2054/04/13.400 0.60 7.20E-09 SENTRY 2054/04/13.403 1.27 1.14E-06 IW, 3 , nr 2054/04/13.404 1.30 4.79E-10 IW, 6 2055/04/13.730 1.25 4.33E-07 IW, 3 , nr 2056/04/12.867 0.70 3.71E-08 IW, 3 , nr 2059/04/13.954 2.08 4.31E-10 CLOMON2 2059/04/13.954 2.07 4.81E-08 IW, 3 , nr 2059/04/13.953 2.07 3.48E-11 IW, 6 2063/04/13.796 1.30 1.80E-10 CLOMON2 2063/04/13.795 1.26 1.18E-11 IW, 6 2068/04/12.631 0.69 1.77E-06 IW, 3 2068/04/12.631 0.26 1.04E-06 IW, 6 2069/04/13.078 0.97 2.58E-07 CLOMON2 2069/04/13.078 0.99 2.46E-07 IW, 3 2069/10/15.972 0.48 1.20E-07 CLOMON2 2069/10/15.970 0.41 2.55E-07 IW, 3 2069/10/15.970 0.27 2.32E-07 IW, 6 2078/04/13.442 1.93 5.23E-09 CLOMON2

Table 2. (99942) Apophis: influence of different *sigma\_LOV* and radar observations for computed impact solutions. Note nr means solution without radar observations. SENTRY and CLOMON2 are systems of impact risk computing of the JPL NASA and the NEODYS,

respectively. IW are results by the author.

To compute exactly impact solutions for (99942) Apophis it is necessary to include gravitational perturbations of approaching massive asteroids. Usually SENTRY include 3 massive asteroids: (1) Ceres, (2) Pallas and (4) Vesta, CLOMMON2 - as SENTRY or 4 asteroids: (1) Ceres, (2) Pallas, (4) Vesta and (10) Hygiea. Using the software Solex ver. 9.0 we have investigated all close approaches of about 140,000 numbered asteroids known in Sept. 2006 with (99942) Apophis within 0.2 AU till 2100 year. We have found 4 asteroids with several close approaches to (99942) Apophis: (433) Eros, (887) Alinda, (1685) Toro and (1866) Sisyphus. These selected asteroids together with the 4 massive ones (Ceres, Pallas, Vesta and Hygiea) were included to equations of motion of (99942) Apophis. The computations of influence of gravitational perturbations of these asteroids for the motion of (99942) Apophis were performed using software OrbFit ver. 3.3.1. The masses of asteroids were taken from Michalak (2001) and from Solex as computed by A. Vitagliano. First of all we must include Ceres in our gravitational model which has about 30 % of the mass of the main belt asteroids and the asteroids which have the closest approaches with (99942) Apophis. All results in Tab. 3 are computed using the JPL Planetary and Lunar Ephemerides DE405 and relativistic effects.

The suitable results in Tab. 3 were computed based on 996 optical observations of which 5 are rejected as outliers from 2004/03/15.108 to 2006/07/27.614, and also on seven radar data points on 2005/01/27, 2005/01/29, 2005/01/31, 2005/08/07 and 2006/05/06.

In Tab. 3 and in all others SENTRY denotes the results from the JPL NASA and CLOMON2 from the NEODYS site. The author results are: *IW-a*: no perturbing asteroids; *IW-b*: Ceres and 4 close approaching asteroids to (99942) Apophis: Eros, Alinda, Toro, Sisyphus; *IW-c*: 4 perturbing asteroids: Ceres, Pallas, Vesta, Hygiea; *IW-d*: 5 perturbing asteroids: Ceres, Pallas, Vesta, Hygiea and approaching asteroid Eros; *IW-e*: 3 perturbing asteroids: Ceres, Pallas and Vesta.

From Table 3 we can see that there is significant role of massive asteroids in motion of Apophis, specially after 2042. Some impact solutions does not exist in given year. For example, in April, 2069 there are only impact solutions with additional perturbing effect from together: Ceres, Eros, Alinda, Toro, Sisyphus and the second solution with perturbations from Ceres, Pallas, Vesta and Hygiea.

Fig. 2 shows the changes of differences in mean anomaly between asteroid (99942) Apophis on nominal orbits for different cases. In Fig. 2(a) there are differences in mean anomaly between (99942) Apophis with and no relativistic effects included. Fig. 2(b) presents differences in mean anomaly of (99942) Apophis between orbits computed without perturbing asteroids and with perturbation from: *1* - Ceres, Pallas and Vesta, *2* - Ceres, Pallas, Vesta, and Hygiea and *3* - Ceres, Pallas, Vesta, Hygiea and Eros. It is clear from Fig.

OrbFit Impact Solutions for Asteroids (99942) Apophis and (144898) 2004 VD17 65

Fig. 2. (99942) Apophis. Differences in mean anomaly between nominal orbits from different solutions: *(a)* - 4 perturbing asteroids: relativistic/non relativistic effects included; *(b)* -

The question was appeared how the model of the Solar System used influences for the impact solutions of (99942) Apophis. Generally the JPL Planetary and Lunar Ephemerides DE203, DE405 or DE406 (SENTRY), DE405 (CLOMON2), DE406 (some in this paper) or DE405/WAW (Sitarski, 2002) were used. DE405 ephemerides (includes both nutations and librations) are computed for time span JED 2305424.50 (1599 DEC 09) to JED 2525008.50 (2201 FEB 20). DE406 is the new "JPL Long Ephemeris" (includes neither nutations nor librations). They works for time span JED 0624976.50 (-3001 FEB 04) to 2816912.50 (+3000 MAY 06). This is the same ephemeris as DE405, though the accuracy of the interpolating polynomials has been lessened. Using OrbFit software v.3.3.2 for Linux and 994 optical observations of (99942) Apophis from 2004/03/15.108 to 2006/06/02.602, and also on seven radar data points on 2005/01/27, 2005/01/29, 2005/01/31, 2005/08/07 and 2006/05/06 we

different number of perturbing asteroids (see text).

have found some impact results for different planetary ephemerides.

Date Dist. [RE] Author JPL 2036/04/13.371 1.15 CLOMON2 (DE405) 2036/04/13.371 1.15 IW DE405 2036/04/13.371 1.15 IW DE406 2042/04/13.720 1.41 CLOMON2 (DE405) 2042/04/13.718 1.37 IW DE405 2042/04/13.718 1.37 IW DE406 2044/04/13.295 2.09 CLOMON2 (DE405) 2044/04/13.295 2.08 IW DE405 2044/04/13.295 2.05 IW DE406

Table 4. (99942) Apophis: Influence of the JPL Ephemerides on impact solutions.

**2.3 (99942) Apophis: The JPL Ephemerides** 

2(a) that a relativistic effects play a great role in motion of asteroid - over 30 degs difference in mean anomaly between asteroids with and no these effects in the next 100 years. However in Fig. 2(b) the infuence of close approaching asteroids is evident but these effects are several times smaller than the relativistic effects. The rapidly changes in differences in mean anomaly in Fig. 2 are connected with the close approaches of (99942) Apophis with the Earth in the years: 2029 (0.00025 *AU*) and 2057 (0.022 *AU*) for the nominal orbits. Hence chaoticity of the motion of the asteroid appears (Wlodarczyk, 2001). The infuence of number of perturbing asteroids on impact solutions for (99942) Apophis lists Tab. 3.


Table 3. (99942) Apophis: influence of approaching asteroids for computed impact solutions.

Fig. 2. (99942) Apophis. Differences in mean anomaly between nominal orbits from different solutions: *(a)* - 4 perturbing asteroids: relativistic/non relativistic effects included; *(b)*  different number of perturbing asteroids (see text).

#### **2.3 (99942) Apophis: The JPL Ephemerides**

64 Space Science

2(a) that a relativistic effects play a great role in motion of asteroid - over 30 degs difference in mean anomaly between asteroids with and no these effects in the next 100 years. However in Fig. 2(b) the infuence of close approaching asteroids is evident but these effects are several times smaller than the relativistic effects. The rapidly changes in differences in mean anomaly in Fig. 2 are connected with the close approaches of (99942) Apophis with the Earth in the years: 2029 (0.00025 *AU*) and 2057 (0.022 *AU*) for the nominal orbits. Hence chaoticity of the motion of the asteroid appears (Wlodarczyk, 2001). The infuence of number

of perturbing asteroids on impact solutions for (99942) Apophis lists Tab. 3.

date dist[RE] impact probability source 2036/04/13.370 0.53 2.20E-05 SENTRY 2036/04/13.371 1.15 2.40E-04 CLOMON2 2036/04/13.371 1.15 2.40E-04 IW-a 2036/04/13.371 1.15 2.12E-05 IW-b 2036/04/13.371 1.15 2.39E-04 IW-c 2036/04/13.371 1.15 2.12E-05 IW-d 2036/04/13.371 1.15 2.39E-05 IW-e 2037/04/13.640 0.63 8.5E-08 SENTRY 2042/04/13.715 2.06 6.59E-08 CLOMON2 2042/04/13.718 1.37 6.61E-08 IW-a 2042/04/13.717 1.40 6.09E-08 IW-b 2042/04/13.717 1.38 6.73E-08 IW-c 2042/04/13.717 1.40 6.11E-08 IW-d 2042/04/13.717 1.38 6.73E-08 IW-b 2044/04/13.296 2.09 4.07E-08 CLOMON2 2044/04/13.298 2.13 3.89E-08 IW-a 2044/04/13.294 2.11 3.70E-08 IW-b 2044/04/13.298 2.13 3.45E-08 IW-d 2053/04/12.913 1.39 1.27E-07 CLOMON2 2054/04/13.400 0.59 2.70E-09 SENTRY 2068/04/12.630 0.62 1.79E-06 IW-a 2068/04/12.630 0.52 1.63E-06 IW-c 2068/04/12.633 0.48 8.19E-07 IW-d 2068/04/12.631 0.37 1.03E-06 IW-e 2069/04/13.079 2.00 4.43E-07 CLOMON2 2069/04/13.078 0.97 5.51E-07 IW-b 2069/04/13.079 0.96 4.72E-07 IW-c 2069/10/15.596 0.62 1.02E-07 CLOMON2 2069/10/15.972 0.49 2.63E-07 CLOMON2 2069/10/15.970 0.38 4.70E-07 IW-b 2069/10/15.972 0.59 2.90E-07 IW-c 2069/10/15.971 0.56 4.21E-07 IW-d 2077/04/13.166 1.79 4.33E-08 CLOMON2 Table 3. (99942) Apophis: influence of approaching asteroids for computed impact solutions.

The question was appeared how the model of the Solar System used influences for the impact solutions of (99942) Apophis. Generally the JPL Planetary and Lunar Ephemerides DE203, DE405 or DE406 (SENTRY), DE405 (CLOMON2), DE406 (some in this paper) or DE405/WAW (Sitarski, 2002) were used. DE405 ephemerides (includes both nutations and librations) are computed for time span JED 2305424.50 (1599 DEC 09) to JED 2525008.50 (2201 FEB 20). DE406 is the new "JPL Long Ephemeris" (includes neither nutations nor librations). They works for time span JED 0624976.50 (-3001 FEB 04) to 2816912.50 (+3000 MAY 06). This is the same ephemeris as DE405, though the accuracy of the interpolating polynomials has been lessened. Using OrbFit software v.3.3.2 for Linux and 994 optical observations of (99942) Apophis from 2004/03/15.108 to 2006/06/02.602, and also on seven radar data points on 2005/01/27, 2005/01/29, 2005/01/31, 2005/08/07 and 2006/05/06 we have found some impact results for different planetary ephemerides.


Table 4. (99942) Apophis: Influence of the JPL Ephemerides on impact solutions.

OrbFit Impact Solutions for Asteroids (99942) Apophis and (144898) 2004 VD17 67

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.

Date Dist. [RE] Impact probability Source 2102/05/04.894 0.51 6.66E-4 CLOMON2 2102/05/04.894 0.44 6.7 E-4 SENTRY - - IW, 1 2102/05/04.894 0.52 6.71E-4 IW, 1.5 2102/05/04.894 0.52 6.22E-4 IW, 1.5 ,w=1 2102/05/04.894 0.52 6.71E-4 IW, 2 2102/05/04.894 0.52 6.71E-4 IW, 2, w=1 2102/05/04.894 0.52 6.66E-4 IW, 3 2102/05/04.894 0.52 6.22E-4 IW, 3, w=1 2102/05/04.894 0.52 6.30E-4 IW, 3 no scal. 2102/05/04.894 0.52 9.37E-4 IW, 3, fn 2102/05/04.894 0.52 6.71E-4 IW, 4 2102/05/04.894 0.52 6.71E-4 IW, 5 2102/05/04.894 0.52 6.71E-4 IW, 6 2104/05/04.373 0.58 3.26E-7 CLOMON2 - - SENTRY - - IW, 1 2104/05/04.372 1.05 3.29E-7 IW, 1.5 2104/05/04.377 1.15 3.14E-7 IW, 1.5 ,w=1 2104/05/04.374 0.54 3.29E-7 IW, 2 2104/05/04.374 0.54 3.29E-7 IW, 2, w=1 2104/05/04.373 0.74 3.29E-7 IW, 3 2104/05/04.374 0.52 3.10E-7 IW, 3, w=1 2104/05/04.374 0.55 3.15E-7 IW, 3, no scal. 2104/05/04.375 0.58 4.80E-7 IW, 3, fn 2104/05/04.374 0.52 3.31E-7 IW, 4 2104/05/04.376 0.88 3.38E-7 IW, 5 2104/05/04.374 0.54 3.36E-7 IW, 6 2105/05/04.655 0.41 3.84E-8 IW, 3, no scal. 2109/05/04.637 0.62 9.72E-9 IW, 1.5, w=1

and weighting of observations has a small influence for

and weighting for impact

These observations were available up to date of MACE 2006.

Table 6. (144898) 2004 VD17: Inluence of different *sigma\_LOV (*

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

solutions.

Tab. 6 shows that the infuence of

impact solutions for (144898) 2004 VD17.

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."
