An approximate solution of two-body problem is proposed using weighted combination of linear and inversely cubic gravity models. First, two approximations are introduced for the weight coefficients. To enhance the accuracy of the solution, a modified weight coefficient is suggested by a linear combination of the two primary weight coefficients. The accuracy and computational burden of the combined method are compared to those of power series solution, including the Lagrangian coefficients and the recursive formulation introduced by Turner et al. The comparison is made with the same computational burden by setting an appropriate number of terms of power series solution. The advantage among the methods depends on the computational burden of square, trigonometric, and logarithmic functions. In the case that the computational burden of these functions is less than 10 floating point operations, the proposed method has the potential to give a better accuracy, especially for a specific application.
This paper presents a comprehensive study on the performance analysis of 8 conceptual guidance laws for exoatmospheric interception of ballistic missiles. The problem is to find the effective thrust direction of interceptor for interception of short-to-super range ballistic missiles. The zero-effort miss and the generalized required velocity concept are utilized for interception of moving targets. By comparison of the 8 conceptual guidance laws, the thrust direction is suggested to be in the direction of generalized velocity-to-begained, or constant velocity-to-be-gained direction, rather than to be in the direction along zero-effort miss, or that of linear optimal solution for long-to-super range interception. Even for short coasting ranges, the generalized velocity-to-be-gained may be utilized because of reasonable computational burden for required velocity rather than the numerical computation for zero-effort miss or linear optimal solution with the same miss distance error. In addition, the fuel consumption of the suggested direction has less sensitivity due to estimation error in intercept time. The guidance law based on constant velocity-to-be-gained direction and the optimal solution are suitable for satellites launch vehicles and space missions.
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