Relative motion in the terminal phase of interception of a satellite or a ballistic missile

Richard Hord
naca-tn-4399
SEP 1958


The interception of a satellite or a ballistic missile essentially outside the earth's atmosphere is considered with emphasis on the terminal phase of the attack vehicle's flight. For the discussion of the relative motion, a coordinate system is selected which has its origin at the target and axes always parallel to lines fixed in an inertial frame. The resulting vector equation of motion contains, in addition to the thrust term, an apparent gravitational term. Bounds on the magnitude of this apparent acceleration of the interceptor are obtained which permit gaging its importance in relation to thrust acceleration in the terminal phase of interception. Since the apparent gravitational acceleration approaches zero as the interceptor approaches the target, preliminary analyses of the terminal phase of interception can generally be carried out by neglecting gravity altogether. Two types of interception are discussed mathematically and a numerical example is worked out for each type. The type of interception for which the terminal relative approach speed is small compared with the target's speed is, within the limits of the present study, found to be feasible. The practicability of dead-on interception with mass dispersal prior to impact is more difficult to assess; in the example considered, the mass required to be dispersed is found to be of the order of magnitude of the mass of the target.

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