## Thursday, September 22, 2011

### Drag Force For Non-interacting Particles

For an extremely rarefied atmosphere we can assume that its particles do not interact with each other and that the collisions with the moving spacecraft are independent. To simplify the problem we represent the spacecraft by a flat plate of mass M perpendicular to the direction of motion and moving with a speed V. Let an individual particle of mass m be initially at rest. From the point of view of the plate the particle initially moves toward it with speed V and after the collision it will move away from it with speed V if no energy is lost in the collision and the mass of the particle is much less than the mass of the plate. To get the view from the perspective of the surrounding atmosphere we have to add the speed of the plate to these values for the speeds of the particle and we get v = 0 before the collision and v = 2V after. If n is the number density of the atmosphere the work, ΔW, done by the plate on N particles as it moves through a distance Δx and the drag force, D, are determined as follows.

The pressure, D/A, is known as ram pressure. If the particles are sent off sideways by the collision the drag force and the pressure are reduced. The corrective factor depends on the geometry an object. If a spacecraft with a flat forward surface is not perpendicular to the direction of motion but at an angle the resulting lateral force can produce lift and cause the spacecraft to skip off the atmosphere.