Previously, we have considered the equations of motion of the three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each other). Analysing such a system of equations, we considered the case of small-body motion of negligible mass m3 around the second of two giant-bodies $m_1$, $m_2$ (which are rotating around their common centre of masses on Kepler’s trajectories), the mass of which is assumed to be less than the mass of central body. In the current development, we have derived a key parameter $\eta$ that determines the character of quasi-circular motion of the small third body $m_3$ relative to the second body $m_2$ (planet). Namely, by making several approximations in the equations of motion of the three-body problem, such the system could be reduced to the key governing Riccati-type ordinary differential equations. Under assumptions of R3BP (restricted three-body problem), we additionally note that Riccati-type ODEs above should have the invariant form if the key governing (dimensionless) parameter $\eta$ remains in the range $10^{−2}$ ∻ $10^{−3}$. Such an amazing fact let us evaluate the forbidden zones for Moon’s orbits in the inner solar system or the zones of distances (between Moon and Planet) for which the motion of small body could be predicted to be unstable according to basic features of the solutions of Riccati-type.

One of the scientific objectives of the Ooty Wide Field Array (OWFA) is to observe the redshifted Hi emission from $z \sim 3.35$. Although predictions spell out optimistic outcomes in reasonable integration times, these studies were based purely on analytical assumptions, without accounting for limiting systematics. A software model for OWFA has been developed with a view to understanding the instrument-induced systematics, by describing a complete software model for the instrument. This model has been implemented through a suite of programs, together called Prowess, which has been conceived with the dual role of an emulator as well as observatory data analysis software. The programming philosophy followed in building Prowess enables a general user to define an own set of functions and add new functionality. This paper describes a co-ordinate system suitable for OWFA in which the baselines are defined. The foregrounds are simulated from their angular power spectra. The visibilities are then computed from the foregrounds. These visibilities are then used for further processing, such as calibration and power spectrum estimation. The package allows for rich visualization features in multiple output formats in an interactive fashion, giving the user an intuitive feel for the data. Prowess has been extensively used for numerical predictions of the foregrounds for the OWFA \HI~ experiment.