Encounter of an asteroid with a planet

This paper describes the trajectory of an asteroid (or a comet or spacecraft) as it approaches a planet of much greater mass. The solution of this two-body problem is an instructive first approximation to more refined treatments that include the gravitational forces of the Sun and of planets other than the target planet. Detailed properties of encounter trajectories are derived. As an illustration, it is shown that the collision cross section of the planet is greater by a factor F = 1 + ( v escape ∕ v 0 ) 2 compared to its cross section in the absence of gravitational forces, where v escape is the minimal escape speed from the surface of the planet and v 0 is the approach speed of the asteroid at an effectively infinite distance. Sample values of F are given for Earth, Mars, Jupiter, and Saturn.