Analytic Time Derivatives of Instantaneous Impact Point

Abstract

This paper presents analytic expressions for the time derivatives of a Keplerian instantaneous impact point of a rocket. The derivatives can be obtained by differentiating the series of equations associated with the Keplerian instantaneous impact point of a rocket and are expressed as linear combinations of disturbing acceleration components whose coefficients are functions of the current position and velocity of the rocket. The formulae introduced in this paper have been carefully verified using different cases. The verification results for the proposed derivatives prove that they successfully represent the motion of the instantaneous impact point under various conditions for the disturbing acceleration. The results of this paper could be applied to problems arising in rockets/launch vehicles operations, such as the steering of a rocket or the augmentation of a range safety system.