Related papers: Global Positioning on Earth
A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
We consider the problem of recovering the position and orientation of a camera equipped with an accelerometer from sensor images of two labeled landmarks whose positions in a coordinate system aligned in a known way with gravity are known.…
Increasing numbers of mobile computing devices, user-portable, or embedded in vehicles, cargo containers, or the physical space, need to be aware of their location in order to provide a wide range of commercial services. Most often, mobile…
In this article, we describe a very simple technique to locate naked-eye planets in the sky, to an accuracy of $\sim 1^{\circ}$. The procedure, comprising just three steps, involves very simple manual calculations for planetary orbits…
The discovery of a biosphere on another planet would transform how we view ourselves, and our planet Earth, in relation to the rest of the cosmos. We now know Earth is one planet among eight circling our sun; our sun is part of a swirling…
The classical no-three-in-line problem is to find the maximum number of points that can be placed in the $n \times n$ grid so that no three points lie on a line. Given a set $S$ of points in an Euclidean plane, the General Position Subset…
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
Understanding our place in the universe is an eternal quest. Through the analysis of the 3D structures of 66 nearby open clusters using Gaia DR3 data, we discovered an intriguing pattern: most clusters show their elongation directions…
We consider the geometry of four spatial displacements, arranged in cyclic order, such that the relative motion between neighbouring displacements is a pure rotation. We compute the locus of points whose homologous images lie on a circle,…
We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly…
Fully relativistic coordinates have been proposed for (relativistically) running a "GPS" system. These coordinates are the arrival times of the light signals emitted by four "satellites" (clocks). Replacing the signals emitted by four…
Today, the Global Navigation Satellite Systems, used as global positioning systems, are the GPS and the GLONASS. They are based on a Newtonian model and hence they are only operative when several relativistic effects are taken into account.…
The rapid advancement of connected and autonomous vehicles has driven a growing demand for precise and reliable positioning systems capable of operating in complex environments. Meeting these demands requires an integrated approach that…
An inert sphere of a few meters diameter, placed in a special stable geosynchronous orbit in perpetuo, can be used for a variety of scientific experiments. Ground-based observations of such a sphere, "GeoSphere", can resolve very difficult…
We consider the $N$-body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of locked inertia tensor, we compute the moment of inertia for systems moving on spheres and hyperbolic spheres and show that…
We use group theoretic ideas and coset space methods to deal with problems in polarization optics of a global nature. These include the possibility of a globally smooth phase convention for electric fields for all points on the Poincar\'{e}…
With vast mmWave spectrum and narrow beam antenna technology, precise position location is now possible in 5G and future mobile communication systems. In this article, we describe how centimeterlevel localization accuracy can be achieved,…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…