## Program Opik

original version march 2007, this version january 2017.
Tabaré Gallardo (Dpto. Astronomía, Instituto de Física , Facultad de Ciencias)

### Collision and ejection probability

The collision probability of an asteroid or comet with a planet depends on its orbital elements (a,e,i,w). While in general (a,e,i) have small changes with time, the argument of the perihelion, w, varies continuously from 0 to 360 degrees. For some values of w the distance between both orbits (MOID) is small and the probability of collision is high and for other values of w the MOID is large and the collision probability is zero. The Opik method gives a mean probability of collision considering that w is continuously changing. It is a statistical value valid for an orbit with given (a,e,i) and undefined w. For a specific object with defined (a,e,i,w) it is better to use numerical simulations in order to estimate the collision probability for an epoch near the present. The Opik method gives a mean probability over several millon years. The Opik method gives the collision probability per orbital revolution of the asteroid, from this value it is calculated the mean collision time, that means, the mean time after which the object collides with the planet. Basics of the method can be found here.
In some cases the planet can eject the asteroid from the solar system. The method of Valsecchi et al. 2000 allows to estimate the mean time for the ejection. If the collision time is greater than the ejection time it is more probable that the asteroid will be ejected before a collision occurs. The Opik method does not take into account other perturbers than the planet considered, so it only provides an idea of the timescales involved.

Example. Calculate the mean collision time with Earth of the Tesla Roadster using the orbital elements
a=1.333
e=0.261
i=1.096