1. The problem statement, all variables and given/known data An object from space (like an asteroid) approaches Earth. A collision will occur if the scattering cross-section is less than π*Re2. If the distance of closest approach is much greater than Re, no collision would occur. Find an implicit expression for the cross-section in terms of g, vo, and Re. Show explicitly that the cross-section approaches the minimum value for large vo, and find the appropriate dimensionless parameter. g: acceleration due to Earth's gravity vo: velocity of incoming object Re: radius of Earth 2. Relevant equations Rutherford scattering formula: dσ/dΩ = k2/16E2*1/sin4(θ/2) Total energy: E = ½μr'2 - k/r + L2/2μr2 3. The attempt at a solution I knew to use the Rutherford scattering formula because the scattering cross-section arises from an inverse square law (the gravitational force.) By doing some manipulation of the force constant: GMem ≈ g*m Me + m ≈ Me ⇒ μ ≈ m and approximating E by the kinetic energy T at very large r: E ≈ ½mvo2 I arrive at dσ/dΩ = g^2/4vo2*1/sin4(θ/2) This is an expression including g, and vo... but where can we relate Earth's radius, Re? It seems like the differential cross section will approach Re for large vo, but I can't seem to express that mathematically. I'll need help understanding that first part. I could then use hints for finding the impact parameter per the last part of the question. I'm quite confused at this point.