Resistance to the Motion of a Small Sphere Moving Through a Gas

Abstract

The problem considered is that of the resistance to a sphere moving through a gas when the radius of the sphere is small compared with the mean free path of the gas. This problem is of astrophysical significance in relation to the behaviour of interstellar grains in interstellar gas. Expressions for the resistance at any speed are found in the two cases of specular and diffLise reflection of the gas molecules at the surface of the sphere. These expressions reduce to the well known linear and quadratic laws at low and high speeds respectively, but comparison of these laws with the exact expressions shows that they are inaccurate at intermediate speeds. New approximate expressions are suggested which give a high degree of accuracy over the whole range of translation speeds while retaining a simple algebraic form suitable for application to astronomical problems.