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Does the Oort cloud act as a kind of shield for the Solar System? When an interstellar object impacts the cloud, does its momentum get absorbed substantially?

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The Oort cloud is extremely diffuse, and while there are numerous small bodies, they're spread out over a very large region of space. Assuming that the outer Oort Cloud ranges from 20,000 AU to 50,000 AU and contains $\sim10^{12}$ bodies on the scale of a kilometer or greater, I find an average number density $n$ of 0.002 objects per cubic astronomical unit. Put another way, there would be two of these objects contained within a cube with sides 10 AU across.

We can define an optical depth of sorts, $\tau$, as $$\tau=n\sigma l$$ with $\sigma$ the cross-section of the two objects and $l$ the thickness of the cloud. Assuming that $\sigma$ is on the order of maybe a few square kilometers (probably an overestimate) and that $l$ is 30,000 light-years, we find that the optical depth of the outer Oort cloud is $\tau\approx10^{-14}$ (a bit lower, but I've rounded up). The probability of an incoming body colliding with an Oort Cloud object is then $$P=1-e^{-\tau}\approx0$$ The upshot is that no, the Oort Cloud doesn't act as a shield, as it's extremely unlikely that an interstellar interloper would be stopped.

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No. The Oort cloud is a cloud of comets and icy asteroids, not a physical barrier. Just like everywhere in the Solar system, it is mostly made up a empty space, and wouldn't absorb the impact of an interstellar object in any meaningful way.

The Sun does protect the Solar System from things like the interstellar wind with it's magnetic field - this is called the heliosphere - but it's separate from the Oort cloud. The Oort cloud actually extends far beyond the heliosphere.

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