# Probability of an oblique impact

The solar system as it exists today has been shaped by large impacts that happened during the formation of the planets. Some of those impacts have been argued to have been oblique impacts. An example is the impact that formed the Imbrium basin on the Moon:

https://news.brown.edu/articles/2016/07/imbrium

which has been estimated to be due to an impactor of a diameter of about 250 km. Invoking obliqueness may suggest that the probability of such an impact is very small, undermine the explanation offered.

The problem is then as follows. Using the appropriate definition of obliqueness, which is that if the trajectory of the asteroid were continued after the impact, some parts of the asteroid would miss the Moon, what is the probability that a particular impact on the Moon by an impactor of diameter D will be an oblique impact? What is this probability for the case of the Imbrium impact?

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#### Solution Preview

In the following we take the lunar radius to be R = 3474.2 km. Suppose the impactor of diameter D is on a trajectory such that the first point of contact will happen at some point P on the Moon. We then ignore the deviation of this trajectory from a straight line. The point on the impactor Q that hits the surface at P then moves on a line that's parallel to the point on the opposite side of ...

#### Solution Summary

The Solution explains how to compute the probability of a particular impact on the moon.