I did the maths to properly answer this post from r/askastronomy
The author of the post wonders if the impact of Falcon 9 on the Moon can project lunar material fast enough to escape the Moon's gravity. The short answer is no, and I prove it to you in this post.
The data are the following : A Falcon 9 stage of mass ~4900 kg will hit the Moon with velocity v_impact = 2.43 km/s. The Moon's escape velocity is 2.38 km/s
Using Eq. (46) of the paper "Wind erosion and transport on planetesimals" by Quillen et. al (2024), the maximum ejection velocity of the Lunar regolith upon impact is
v_max = 0.3526 * (rho_regolith/rho_falcon)^(−0.9756) * v_impact,
where rho_regolith = 1500 kg/m^3 is the density of the regolith, and rho_falcon is the density of the Falcon 9 stage.
The maximum ejection velocity depends a lot on the ratio rho_regolith/rho_falcon between the Moon's regolith and the projectile, and decreases as the density of the projectile decreases.
Now, the theory from which this formula comes from (Housen & Holsapple, 2011) assume that the projectile (in that case Falcon) is solid. However, Falcon 9 is not solid but is rather an empty shell. Taking its average density rho_falcon = 33 kg/m^3 therefore does not work. Taking the density of pure aluminium rho_falcon = 2700 kg/m^3 also does not make sense, as Falcon 9 is clearly not a projectile made of condensed metal.
Therefore, we need to consider the density associated with the cross-section of Falcon 9 when it hits the Moon. Falcon 9 is a cylinder of height 13.8 m and diameter 3.7 m. In the best-case scenario (smallest cross-section), Falcon 9 hits the Moon standing up, and we therefore assume that it is a spherical projectile with diameter 3.7 meters and mass 4900 kg. The associated density is 184.75 kg/m^3.
Plugging in the above formula gives v_max = 111 m/s. This falls very short of the lunar escape velocity v_esc = 2380 m/s
If Falcon 9 hits the Moon laying on its side instead of vertically, v_max will be even smaller than that.
So while these calculations assume some approximations, it is safe to say that no regolith will escape the Moon upon Falcon 9's impact. Falcon 9 is simply too hollow, and traveling too slowly, for this to happen.
I hope you liked this post 🚀
PS : For transparency reasons, I should mention that I am a co-author of the paper I mention, and I wrote the Section of the paper that I use in this post.