Probabilistic model for analyzing the revisit time of multi-satellite orbital constellation

Аuthors

Zanin K. A.^*, Dmitriev V. I.^**

Lavochkin Research and Production Association, NPO Lavochkin, 24, Leningradskay str., Khimki, Moscow region, 141400, Russia

*e-mail: ZaninKA@laspace.ru
**e-mail: DmitrievVI@laspace.ru

Abstract

This article presents a probabilistic numerical-analytical method for estimating the average revisit time of multi-satellite orbital constellation. It is noted that the design of modern orbital constellations spaceborne electro-optical observation system differs from traditional methods. To improve the observation frequency of given areas, spacecraft are positioned in inclined orbits rather than sun-synchronous orbits, as was previously the case. A known analytical method for estimating orbital constellation parameters are based on analytical estimates of path repeatability under iso-route conditions. For constellations in different orbits, numerical statistical modeling is typically used. The one approach to obtaining analytical estimates is the development of probabilistic methods. Modern orbital constellations comprise tens and hundreds of spacecraft, allowing the use of probability theory methods for their modeling. Analytical estimates, compared to numerical ones, allow for the establishment of a qualitative relationship between orbital design parameters, the number of satellites, and the observation frequency. The developed method is based on analytical relationships between the frequency of capture within the swath and the probability density of spacecraft distribution as functions of latitude, longitude, and orbital inclination. An estimate of the probability density of observation is obtained depending on inclination, orbital altitude, swath, and the number of spacecrafts. It is shown that using orbits with different inclinations improves the observation frequency in a given latitude zone. The method enables the optimal distribution of orbital planes by inclination and number of spacecrafts to organize high-frequency observation in a given region. An example of estimating the observation frequency for a World View Legion constellation is provided. A convergence of the estimates with the results of numerical statistical modeling is demonstrated. 

Keywords:

probabilistic model; spaceborne electro-optical observation system; multi-satellite orbital constellation; probability density; number of spacecrafts; orbital architecture; orbital inclination; metrics of efficiency; revisit time; latitudinal band

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