Peter Vereš, Juraj Tóth, Leonard Kornoš

Search for very close approaching Search for very close approaching NEAsNEAs

Comenius University, Bratislava, Slovakia

Faculty of mathematics, physics and informatics

Department of astronomy, physics of the Earth and meteorology

Objectives

• Create NEA model population

• Simulation of geometrical conditions during close Earth encounters

• Detection probability of synthetic population

Known NEA population

NEA NEC PHO IEO

05/01/2006 3769 77 774 5

Size depending on

avg. A

Known population

Bottke model

2001

Rabinowitz model

1994

Stuart model

2004

D>1000m 95% 73% 71%

D>100m 8,7% 3,2% 3,2%

D>10m

253137302614383747

55.10 % 510 % 43.10 %

5020750

• Known NEO counts versus models

Known NEA population• Orbital elements & size distribution of NEA

• Smaller NEAs – lesser count

• Closest approaches to the Earth within Moon orbit distance & their size distribution

Survey programs

1 25log( ) 2.5log 1V r H G G

0.63

1 exp 3.33tan2

1.22

2 exp 1.87 tan2

120

0,15;0,40G

10 105log 2,5logH C D A

Apparent magnitude

Absolute magnitude – Albedo - Size

Our work: 18m – 1kmalbedo vs. diameter 23m – 100m

28m – 10m

Limiting conditions:

WFS• Idea to search in the close Earth vicinity, wide field vs. low limit. mag.

WFS: f=0,15m 0,18m 15°2 14m 450°/h 30sLINEAR: f=2,2m 1,00m 2°2 20m 210°/h 5s

WFS limitations

Creating model populationModels versus known population

Creating model populationRandom number generation according to distributions a, e, i, H

N bodies – each contains 6 orbital elements, size (H)

NEO space correction

Angular elements – random seed

Generation accuracy

10 964 780 synthetic bodies

Numerical integration

Numerical integrator (Montebruck-Pfleger)

JPL database DE406 (accuracy +3000years = ~25m in planets orbits)

Multistep backward integration of Adams-Bashforth-Moulton type

Perturbing elements vs. Keplerian motion, 12-grade of accuracy

Reduction: only Sun & Earth perturbing

Input (name, MJD, a, e, i,, , v, H)

Output (name, MJD, , R, h, Ph, RA, DC )

Integration time 1 year

Output conditions: V<14m a (mean Earth-Moon distance)

Results

Inside Moon orbit

ResultsAnnual size distribution inside Moon orbit

Results reduction for WFS

30

• Possible discoveries for H>19 bodies + visual mag. condition = 18 discoveries

• For H>19, >0,46AU, , angular velocity limiting magnitude correction

for WFS, site of observation – declination restriction, obs. time restriction = 3,6

– 5,4 discoveries

• Analyzing each encounter as real (real time and date, RA & DA, time spent

inside search area ) = 3,35 discoveries

• Synthetic asteroid No. 2 961 437 collides with the Earth 25,6 ~ 26H D m

Results reduction for WFS

Apparent movement of 18 simulated bodies, their orbit type & sizes

• 80 NEA inside Moon orbit annually

• 18 NEA are capable to find under ideal conditions annually with WFS

• 3 NEA are easily to find with WFS Modra annually

• Optimistic models expect up to 120 discoveries with WFS

• Limiting magnitude +18m & preserving wide field expect rapid number of

discoveries in the close Earth vicinity

• High angular motion is expected

Final results

1 60 '/ min

Future

• Actual & accurate models

• Higher number of integrated orbits – bodies down to bolid size (1 meter)

• Longer integration time – fluctuations and orbits perturbation due to close

encounters

• Build of WFS, discoveries & confirmation of our model and other models

• Upgraded survey system with +18m limit magnitude