## Comparison of accuracy and efficiency of methods for estimating the probability of collision of celestial bodies with the Earth

Transactions of IAA RAS, issue 46, 117–125 (2018)

**DOI**: 10.32876/ApplAstron.46.117-125

**Keywords**:
collisions of potentially dangerous bodies with the Earth, probability of collsion, methods for estimating the probability of a collision, orbits, asteroids.

### Abstract

The paper considers existing linear and nonlinear methods for estimating the probability of a collision, compares their accuracy and efficiency by the example of the problem of asteroid collisions with the Earth, when the point of a potential collision is far enough from the nominal body position. Correct estimation of the probability of collisions is necessary when developing optical, radar and VLBI observation programs of potentially dangerous bodies. Particular attention is paid to comparing linear probability estimation methods — the target plane method and the curvilinear coordinate system method, since they are best suited to search for potential collisions of a newly open body when it is necessary to quickly estimate the probability of a collision and, if necessary, take appropriate measures. A modification of the target plane method is proposed, which makes it possible to obtain probability values comparable to the probabilities obtained by the non–linear Monte Carlo method and the linear method using a curvilinear coordinate system.

### Citation

`V. A. Shor, D. E. Vavilov, T. A. Vinogradova, N. B. Zheleznov, O. M. Kochetova, V. B. Kuznetsov, Yu. A. Chernetenko. Comparison of accuracy and efficiency of methods for estimating the probability of collision of celestial bodies with the Earth // Transactions of IAA RAS. — 2018. — Issue 46. — P. 117–125.`

```
@article{shor2018,
abstract = {The paper considers existing linear and nonlinear methods for estimating the probability of a collision, compares their accuracy and efficiency by the example of the problem of asteroid collisions with the Earth, when the point of a potential collision is far enough from the nominal body position. Correct estimation of the probability of collisions is necessary when developing optical, radar and VLBI observation programs of potentially dangerous bodies. Particular attention is paid to comparing linear probability estimation methods — the target plane method and the curvilinear coordinate system method, since they are best suited to search for potential collisions of a newly open body when it is necessary to quickly estimate the probability of a collision and, if necessary, take appropriate measures. A modification of the target plane method is proposed, which makes it possible to obtain probability values comparable to the probabilities obtained by the non–linear Monte Carlo method and the linear method using a curvilinear coordinate system.},
author = {V.~A. Shor and D.~E. Vavilov and T.~A. Vinogradova and N.~B. Zheleznov and O.~M. Kochetova and V.~B. Kuznetsov and Yu.~A. Chernetenko},
doi = {10.32876/ApplAstron.46.117-125},
issue = {46},
journal = {Transactions of IAA RAS},
keyword = {collisions of potentially dangerous bodies with the Earth, probability of collsion, methods for estimating the probability of a collision, orbits, asteroids},
pages = {117--125},
title = {Comparison of accuracy and efficiency of methods for estimating the probability of collision of celestial bodies with the Earth},
url = {http://iaaras.ru/en/library/paper/1883/},
year = {2018}
}
```

```
TY - JOUR
TI - Comparison of accuracy and efficiency of methods for estimating the probability of collision of celestial bodies with the Earth
AU - Shor, V. A.
AU - Vavilov, D. E.
AU - Vinogradova, T. A.
AU - Zheleznov, N. B.
AU - Kochetova, O. M.
AU - Kuznetsov, V. B.
AU - Chernetenko, Yu. A.
PY - 2018
T2 - Transactions of IAA RAS
IS - 46
SP - 117
AB - The paper considers existing linear and nonlinear methods for
estimating the probability of a collision, compares their accuracy
and efficiency by the example of the problem of asteroid collisions
with the Earth, when the point of a potential collision is far enough
from the nominal body position. Correct estimation of the probability
of collisions is necessary when developing optical, radar and VLBI
observation programs of potentially dangerous bodies. Particular
attention is paid to comparing linear probability estimation methods
— the target plane method and the curvilinear coordinate system
method, since they are best suited to search for potential collisions
of a newly open body when it is necessary to quickly estimate the
probability of a collision and, if necessary, take appropriate
measures. A modification of the target plane method is proposed,
which makes it possible to obtain probability values comparable to
the probabilities obtained by the non–linear Monte Carlo method and
the linear method using a curvilinear coordinate system.
DO - 10.32876/ApplAstron.46.117-125
UR - http://iaaras.ru/en/library/paper/1883/
ER -
```