Mathematical model of sequential information integration in a satellite-inertial system for determining the movement of a geodesic platform

The article is devoted to the matter of on-board integrating positional information delivered by the navigation satellite system (NSS) at a two-position reception and inertial information on the vector of apparent acceleration, measured by a three-component unit of newtonometers. The problem of determining the angular parameters (spatial orientation) of the geodesic platform (GP) movement, which is solved against the background of the trajectory linear kinematic parameters e stimation and the specific force vector causing the trajectory causality. The task of determining the spatial orientation of the SE is formulated; it is shown that to specify two vectors known in different coordinate trihedrons is enough for its solution, and considering the force vector and the relative position vector of two NSS receivers as such is proposed. A numerical study was performed and some of its results including elements of the trajectory of motion, forces and Euler – Krylov angles with derivatives estimates were presented verifying the initial model representations.

Can an infinitely long object fit in an expanding universe?

Does space stretch its contents as the universe expands? Usually, we say the answer is no—the stretching of space is not like the stretching of a rubber sheet that might drag things with it. In this paper, we explore a potential counterexample—namely, we show that it is impossible to make an arbitrarily long object in an expanding universe, because it is impossible to hold the distant end of the object ‘stationary’ with respect to us (as defined in the Friedmann–Lemaître–Robertson–Walker metric). We show that this does not mean that expanding space has a force associated with it, rather, some fictitious forces arise due to our choice of reference frame. By choosing our usual time slice (where all comoving observers agree on the age of the universe), we choose a global frame that does not correspond to the frame of any inertial observer. As a result, simple relativistic velocity transforms generate an apparent acceleration, even where no force exists. This effect is similar to the fictitious forces that arise in describing objects in rotating reference frames, as in the case of the Coriolis effect.

The Almagest Greek and Roman Occultations Re-Visited

The errors in the timings of the Almagest occultations are investigated to ascertain what contribution they made to Fotheringham and Longbottom’s 1915 result for the (tidal) acceleration of the Moon. It is found that their result is quite close to the modern value, once the apparent acceleration of the Moon due to the retardation of the Earth’s spin rate is removed.