An Application of Markov Theory to Spacecraft Launch Planning

Maurice E. Graves Northrop Services, Inc., Huntsville, Ala. 35805

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Morris Perlmutter Northrop Services, Inc., Huntsville, Ala. 35805

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Abstract

To illustrate the effective use of meteorological data in the planning of spacecraft launchings, certain statistical relationships are presented based on Markov theory and empirical counts. The practical results are in terms of conditional probability at Kennedy Space Center, and are based on 15 years of recorded summer weather data which are analyzed under a set of natural environmental launch constraints.

Three specific forecasting problems are treated: 1) the length of record of past weather which is useful to a prediction, 2) the effect of persistence on runs of favorable and unfavorable conditions, 3) the forecasting of future weather in probabilistic terms. The first problem yields the order of the operative Markov chain, the second problem offers an opportunity to compare theoretically derived results on runs with experimental counts, and the third problem permits application of the Chapman-Kolmogorov equations to obtain conditional probabilities for unfavorable launch conditions up to 4 days in the future. A link is provided between such general conditions and the probability that a launch will be delayed at any specific afternoon hour.

Abstract

To illustrate the effective use of meteorological data in the planning of spacecraft launchings, certain statistical relationships are presented based on Markov theory and empirical counts. The practical results are in terms of conditional probability at Kennedy Space Center, and are based on 15 years of recorded summer weather data which are analyzed under a set of natural environmental launch constraints.

Three specific forecasting problems are treated: 1) the length of record of past weather which is useful to a prediction, 2) the effect of persistence on runs of favorable and unfavorable conditions, 3) the forecasting of future weather in probabilistic terms. The first problem yields the order of the operative Markov chain, the second problem offers an opportunity to compare theoretically derived results on runs with experimental counts, and the third problem permits application of the Chapman-Kolmogorov equations to obtain conditional probabilities for unfavorable launch conditions up to 4 days in the future. A link is provided between such general conditions and the probability that a launch will be delayed at any specific afternoon hour.

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