Linear Stability of Equilibrium Points in the Generalized Photogravitational Chermnykh's Problem

The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The effect of radiation pressure has been discussed numerically. The collinear points are linearly unstable and triangular points are stable in the sense of Lyapunov stability provided $\mu< \mu_{Routh}=0.0385201$. The effect of gravitational potential from the belt is also examined. The mathematical properties of this system are different from the classical restricted three body problem

Optical effects produced by running onboard engines of low-earth-orbit spacecraft

This paper presents results of optical observations made during Radar-Progress Experiment performed on April 17, 2013 and July 30, 2014 after approach-correction engines (ACE) of Progress M-17M and Progress M-23M cargo spacecraft in the thermosphere had been started. A region of enhanced emission intensity was recorded during engine operation. This may have been related to the scatter of twilight solar emission along the cargo spacecraft exhaust and to the emergence of additional atomic oxygen [OI] emission at 630 nm. The maximum dimension of the observed emission region was ~330–350 km and ~250–270 km along and across the orbit respectively. For the first time after ACE had been started, an expansion rate of emission region was ~ 7 and ~ 3.5 km/s along and across the orbit respectively. The maximum intensity of the disturbance area for Progress M-17M is estimated as ~40–60 R at 2 nm. Progress M-23M Space Experiment recorded a minor disturbance of atmospheric [OI] 630.0 nm emissions, both in near and in far cargo spacecraft flight paths, which might have been associated with the ACE exhaust gas injection

The method of plotting a spatial distribution pattern of the total electron content in the region of artificial airglow of the ionosphere

The method of plotting a spatial distribution pattern of the total electron content (TEC) in the region of artificial airglow of the ionosphere in the red line of the optical spectrum (λ = 630 nm) was developed during the experiments on disturbances of the ionosphere by powerful radio emission of the SURA facility. To test the method, a measurement session on August 29, 2016 from 18:40 to 20:10 UTC, i.e., when the ionospheric and weather conditions varied slightly and allowed simultaneous optical measurements of the artificial airglow of the ionosphere from two spatially separated sites (Vasilsursk near the SURA facility and Magnitka lying ∼ 170 km East of the SURA facility), was selected. As a result of the simultaneous optical measurements, the area of artificial airglow was plotted in a three-dimensional projection and the spatial position of the disturbed region of the ionosphere stimulated by the powerful radio emission of the SURA facility was determined. The method of plotting a spatial pattern of the electron density distribution in the disturbed region of the ionosphere is based on a joint analysis of variations in the TEC on the radio paths “navigation satellite – ground receiving site” for a number of receiving stations of the global navigation satellite systems located within a radius of ∼ 160 km from the SURA facility. By using this method, the values of electron density variations for different spatial cross-sections of the disturbed region of the ionosphere can be obtained. The joint analysis of the experimental data carried out with the help of the method under consideration showed that in the field of the powerful radio wave a disturbed region with the complex structure formed along the magnetic field lines. Plasma inhomogeneities with an increased electron density occurred at the boundaries of the region with a reduced electron concentration. The difference ∆Ne/Ne at the boundaries of the disturbed region, i.e., between the regions with increased and decreased electron density, might reach 10%. The size of the disturbed region is l⊥ ≈ 45 ÷ 60 km across and l|| ≥ 70 km along the Earth's magnetic field lines

The method of plotting a spatial distribution pattern of the total electron content in the region of artificial airglow of the ionosphere

The method of plotting a spatial distribution pattern of the total electron content (TEC) in the region of artificial airglow of the ionosphere in the red line of the optical spectrum (λ = = 630 nm) was developed during the experiments on disturbances of the ionosphere by powerful radio emission of the SURA facility. To test the method, a measurement session on August 29, 2016 from 18:40 to 20:10 UTC, i.e., when the ionospheric and weather conditions varied slightly and allowed simultaneous optical measurements of the artificial airglow of the ionosphere from two spatially separated sites (Vasilsursk near the SURA facility and Magnitka lying ∼ 170 km East of the SURA facility), was selected. As a result of the simultaneous optical measurements, the area of artificial airglow was plotted in a three-dimensional projection and the spatial position of the disturbed region of the ionosphere stimulated by the powerful radio emission of the SURA facility was determined. The method of plotting a spatial pattern of the electron density distribution in the disturbed region of the ionosphere is based on a joint analysis of variations in the TEC on the radio paths “navigation satellite – ground receiving site” for a number of receiving stations of the global navigation satellite systems located within a radius of ∼ 160 km from the SURA facility. By using this method, the values of electron density variations for different spatial cross-sections of the disturbed region of the ionosphere can be obtained. The joint analysis of the experimental data carried out with the help of the method under consideration showed that in the field of the powerful radio wave a disturbed region with the complex structure formed along the magnetic field lines. Plasma inhomogeneities with an increased electron density occurred at the boundaries of the region with a reduced electron concentration. The difference ∆Ne /Ne at the boundaries of the disturbed region, i.e., between the regions with increased and decreased electron density, might reach 10%. The size of the disturbed region is l⊥ ≈ 45 ÷ 60 km across and l‖ > 70 km along the Earth’s magnetic field lines

Numerical modelling of elastic space tethers

In this paper the importance of the ill-posedness of the classical, non-dissipative massive tether model on an orbiting tether system is studied numerically. The computations document that via the regularisation of bending resistance a more reliable numerical integrator can be produced. Furthermore, the numerical experiments of an orbiting tether system show that bending may introduce significant forces in some regions of phase space. Finally, numerical evidence for the existence of an almost invariant slow manifold of the singularly perturbed, regularised, non-dissipative massive tether model is provided. It is also shown that on the slow manifold the dynamics of the satellites are well-approximated by the finite dimensional slack-spring model