Linearization of the nonlinear equations and iterative solution is the most well-known scheme in many engineering problems. For geodetic applications of the LEO satellites, e.g. the Earth’s gravity field recovery, one needs to provide an initial guess of the satellite location or the so-called reference orbit. Numerical integration can be utilized for generating the reference orbit if a satelli...

satellite orbit determination is a method of determining the state vector, i.e., position and velocity, of a low earth orbiting (leo) satellite or interplanetary spacecraft. during the past two decades, many satellites with various applications including geodetic applications have been launched at low altitudes. for instance, topex / poseidon, champ, grace and goce are the examples of the geode...

This paper presents a set of linearized equations was derived for the motion, relative to an elliptical reference orbit, of an object influenced by J2 perturbation terms. Approximate solution for simulations was used to compare these equations and the linearized keplerian equations to the exact equations. The inclusion of the linearized perturbations in the derived equations increased the high ...

Formation  ying is a key technology for both deep-space and orbital applications that involve multiple spacecraft. Many future space applications will beneŽ t from using formation  ying technologies to perform distributed observations (e.g., synthetic apertures for Earth mapping interferometry) and to provide improved coverage for communication and surveillance. Previous research has focused ...

Improvements on current one-component extraction procedures of spin-orbit pseudopotentials are investigated for high accuracy computation of spin-orbit coupling energies. By means of the perturbation-theory formalism we first show that spin-orbit pseudopotentials, extracted at the one-component self-consistent-field level from a reference all-electron Dirac-Coulomb or Dirac-Coulomb-Breit calcul...

The Local Orbital Reference Frame (LORF) is a Cartesian frame tangential to the trajectory of an orbiting satellite. The orbital motion of the satellite entrains the movement of the LORF around an Inertial Reference Frame (IRF). In this paper, the classical orbit equations (written in terms of inertial position and velocity vectors) are transformed into the LORF orbit equations, by means of ful...

During LEP Operation for Luminosity production, the closed orbit is systematically corrected towards a reference orbit which has been empirically found to produce high luminosities. Machine studies have been undertaken to try and understand the mechanism by which the vertical closed orbit affects the luminosity. The dominant parameter has been found to be the residual vertical dispersion, in pa...