Linear optimal control theory is applied to develop terminal guidance laws for aerodynamically controlled re-entry vehicles. The quadratic performance function minimized includes the terminal state error, the integral of the state deviation from the nominal trajectory, and the integral of control corrections, where the weighting coefficients are trajectory dependent parameters. The vehicle is assumed to be controlled by lift acceleration magnitude and bank angle. By use of linear regulator theory, perturbation feedback control gains are calculated and used with state errors to compute corrections to the commanded nominal lift acceleration and bank angle. A four-state perturbation model is used to approximate the six-state trajectory dynamics for the derivation of the guidance feedback gain matrix. The notable feature of the approach described in this paper stems from the elimination of the velocity magnitude state in the flight dynamics perturbation model. In addition, time is eliminated as the independent variable in favor of distance, resulting in a four-state perturbation model. With these and other assumptions, the control variables are lift acceleration and bank angle, which are the natural ones for an acceleration controlled vehicle using accelerometers for measurement. This unique approach to modeling avoids the need for consideration of angle of attack and aerodynamic drag in the guidance equations. The guidance law implementation is thus independent of vehicle parameters such as mass and surface area, atmospheric density, and the aerodynamic coefficients of lift and drag. The resulting guidance law is evaluated using a three-degree-of-freedom simulation, in which the angle of attack and accelerations are limited and the trajectory dynamics are described by a six-state set of differential equations. Good performance is obtained for a variety of initial state errors, and off-nominal conditions in atmospheric density and vehicle aerodynamic lift and drag coefficients.