This paper opens a series of articles expounding the fundamentals of the route theory for satellite constellation design for Earth discontinuous coverage. In Part 1 of the series the analytical model for Earth coverage by satellites’ swath conforming to the essential of discontinuous coverage, in contrast to continuous coverage, is presented. The analytic relations are consecutively derived for calculation of single- and multi-satellite Earth surface latitude coverage as well as for generating full set of typical satellite visibility zone time streams realized in the repeating latitude coverage pattern for given arbitrary satellite constellation. The analytic relations mentioned are used for developing the method for analysis of discontinuous coverage of fixed arbitrary Earth region for given satellite constellation using both deterministic and stochastic approaches. The method provides analysis of the revisit time for given satellite constellation, as a result of high speed (fractions of a second or seconds) computer calculations in a wide range of possible revisit time variations for different practical purposes with high accuracy which is at least on par with that provided by known numerical simulating methods based on direct modeling of the satellite observation mission, or in a number of cases is even superior to it.

Project LONGSTOP, the LONg-term Gravitational STudy of the Outer Planets, began as an attempt to investigate the problem of the stability of the outer planets — from Jupiter to Pluto — by means of modern numerical and analytical methods over 108 years, a timespan approaching the known age of the system. Modifications to the pure Newtonian 6-body system model were introduced and special care was devoted in choosing the initial conditions for the computed system to resemble the real one as much as possible. The expertise gained with the outer planets was later applied to another 6-body problem of our Solar System, the satellites of Uranus. The paper describes the various considerations leading to the model adopted, the method of integration, the error accumulation, the results achieved; a description is also given of the post-processing methods used. Among the main results are the discovery of so far unknown long periodic variations in the major semiaxes of the outer planets with periods of about 1 million years. The secular frequency of these energy variations involves the pericentres of Jupiter and Uranus and turns out to play a major role in shaping the dynamical structure of the Solar System. It appears also in a secular small divisor of much longer period (about 31 million years) which seems to be responsible for the accumulation of spectral lines in some regions of the long-periodic spectrum of the outer Solar System; it suggests that 100 million years might be long enough a timespan already to reveal the presence of non-regular — although small — regions of motion in the phase space.