About the influence of second zonal harmonic on the motion of satellite in almost circular orbits

1Pirozhenko, AV, 1Maslova, AI, 2Vasilyev, VV
1Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine
2Earth Observing System Data Analytics, Menlo Park, USA
Space Sci. & Technol. 2019, 25 ;(2):03-11
Publication Language: Russian
          Impacts on satellite motion, caused by the second zonal harmonic of the expansion of the Earth’s gravitation potential in a series, in many cases exceed by far the impacts caused by other perturbing forces. For low near-earth orbits, the effects of the second zonal harmonic are crucial, in distinctions between perturbed trajectory and Kepler orbit. The article deals with the problem of determining the short-period changes in the satellite's trajectory in almost circular orbits under the influence of the second zonal harmonic. This is not a new task. Its solution is given in many fundamental studies of celestial mechanics and space flight mechanics. At the same time, the design of satellites and their systems, in particular, Earth remote sensing satellites, reveals an additional need for simple engineering estimates of distinctions between perturbed trajectory and Kepler orbit. It is necessary to get answers to the following questions: What are the regularities of the perturbed trajectory? How to choose a Keplerian orbit of comparison? What are the changes in radius, velocity, angular position in a perturbed trajectory? What is the deviation of the perturbed orbit from the plane of the comparison orbit?
            We use new variables that describe the deviation of the perturbed trajectory from the circular Kepler orbit of comparison. The introduction of new parameters for almost circular orbits made it possible to obtain linearized equations of motion more simply, and to construct analytical estimates of the deviation of the trajectory from the comparison orbit. The estimates of changes in the radius, velocity, angular position in a perturbed trajectory, and its deviation from the comparison orbit have been constructed and analysed. The conditions for the existence of orbits with a minimum change of radius under the influence of the second zonal harmonic have been determined for one rotation of satellite in orbit. The existence of orbits, which experience only forced oscillations of the radius from the second zonal harmonic, the amplitude of which is a few kilometres, is shown. For example, with an orbit altitude of 675 km, the amplitude of these oscillations does not exceed 3.5 km.
Keywords: new variables, satellite trajectory changes, second zonal harmonic
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