I wonder if there is any estimate, no matter how rough it may be, of the friction between interstellar dust and the projectile?


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At sufficiently high speeds, which you will need for an interstellar spacecraft, particles will just crash into the cross section and transfer all of their momentum.

$$F_{drag} = v^2 \rho A$$

Where $v$ is the velocity relative to the medium, $\rho$ is the density of the interstellar medium, and  $A$ is the cross section area of the spacecraft.


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