Related papers: An Arc-Length Approximation For Elliptical Orbits
Already slightly eccentric orbits, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here, alternative approximations for flat orbits in axisymmetric stellar systems are…
This paper presents a unique approach to the problem of calculating revisit time metrics for different satellite orbits, sensor geometries, and constellation configurations with application to early lifecycle design and optimisation…
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon…
This paper explores orbits in extended mass distributions and develops an analytic approximation scheme based on epicycloids (spirograph patterns). We focus on the Hernquist potential which provides a good model for many astrophysical…
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…
Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited…
Reference systems and frames are crucial for high precision absolute astrometric work, and their foundations must be well-defined. The current frame, the International Celestial Reference Frame, will be discussed: its history, the use of…
On the perimeter length determination of the eight-centered oval. Several studies have shown that an eight-centered oval coincides almost perfectly with the ellipse constructed on the same axes and can be considered as a representation of…
This paper introduces a new analytical method for the determination of the coverage area modeling the Earth as an oblate ellipsoid of rotation. Starting from the knowledge of the satellite's position vector and the direction of the…
The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known $1/r$ (Keplerian) and logarithmic…
We present a novel orbit parameterization in spherical coordinates. This parameterization enables the mixing of varying and invariant orbital parameters, and clarifies the physics of the orbit. It also simplifies the process of placing…
The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
This work presents a new parametrisation suitable for parameter-space studies of heliocentric Earth-impacting orbits. Originally motivated by the issue of potentially hazardous asteroids (PHAs) and the mitigation of such a risk, we show…
Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the…
For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
We use the classical definitions (i) $\pi$ is the ratio of area to the square of the radius of a circle; (ii) $\pi$ is the ratio of circumference to the diameter of a circle, to prove $\pi$'s existence within the purview of Euclidean…