Elliptic orbit

Summary

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense, it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1. In a gravitational two-body problem with negative energy, both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit. Examples of elliptic orbits include Hohmann transfer orbits, Molniya orbits, and tundra orbits. Velocity Under standard assumptions, no other forces acting except two spherically symmetrical bodies m1 and m2, the orbital speed (v,) o

Official source

https://en.wikipedia.org/wiki/Elliptic_orbit

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Regularity of solutions for a fourth-order elliptic system via Conservation law

Changyu Guo

In this paper, we obtain interior Holder continuity for solutions of the fourth-order elliptic system Delta(2)u = Delta(V center dot del u) + div(w del u) + W center dot del u formulated by Lamm and Riviere [Comm. Partial Differential Equations 33 (2008) 245-262]. Boundary continuity is also obtained under a standard Dirichlet or Navier boundary condition. We also use conservation law to establish a weak compactness result which generalizes a result of Riviere for the second-order problem.

2019

We study how the gas in a sample of galaxies (M-* > 10(9) M-circle dot) in clusters, obtained in a cosmological simulation, is affected by the interaction with the intracluster medium (ICM). The dynamical state of each elemental parcel of gas is studied using the total energy. At z similar to 2, the galaxies in the simulation are evenly distributed within clusters, later moving towards more central locations. In this process, gas from the ICM is accreted and mixed with the gas in the galactic halo. Simultaneously, the interaction with the environment removes part of the gas. A characteristic stellar mass around M-* > 10(10) M-circle dot appears as a threshold marking two differentiated behaviours. Below this mass, galaxies are located at the external part of clusters and have eccentric orbits. The effect of the interaction with the environment is marginal. Above, galaxies are mainly located at the inner part of clusters with mostly radial orbits with low velocities. In these massive systems, part of the gas, strongly correlated with the stellar mass of the galaxy, is removed. The amount of removed gas is subdominant compared with the quantity of retained gas, which is continuously influenced by the hot gas coming from the ICM. The analysis of individual galaxies reveals the existence of a complex pattern of flows, turbulence and a constant fuelling of gas to the hot corona from the ICM, which could mean that the global effect of the interaction of galaxies with their environment is substantially less dramatic than previously expected.

Oxford Univ Press2017

GPS based navigation performance analysis within and beyond the Space Service Volume for different transmitters’ antenna patterns

Paul David Blunt, Cyril Botteron, Vincenzo Capuano, Pierre-André Farine, Endrit Shehaj

In the last years, Global Navigation Satellite System (GNSS) based navigation in high earth orbits (HEOs) has become a research field of interest, since it can increase the spacecraft’s autonomy, reducing the operating costs. However, the GNSS availability and the GNSS-based navigation performance for a spacecraft orbiting above the GNSS constellation, is strongly constrained by the signals’ power levels at the receiver position and by its sensitivity. The simulated level of signal power at the receiver’s position may considerably increase or decrease when assuming different gain/attenuation values of the transmitter antenna for a certain azimuth and elevation. Assuming a slightly different antenna pattern, therefore may significantly change the simulated signal’s availability results and accordingly the simulated navigation accuracy, leading to an inexact identification of the requirements for the GNSS receiver. This problem concerns particularly the case of orbital trajectories above the GNSS constellation, where most of the signals received are radiated from the secondary lobe of the transmitters’ antennas, for which typically very little information is known. At the time of this study, it was possible to model quite accurately the GPS L1 antenna patterns for IIR and IIR-M Blocks because of the precise information available. No accurate information was available for the GPS L1 antenna patterns of IIF Block. Even less accurate information was available on the GPS L5 antenna patterns. In this context, this paper aims at investigating the effect of different antenna pattern assumptions on the simulated signal availability and on the consequent simulated navigation performance of a spaceborne receiver orbiting in a very highly elliptical orbit from the Earth to the Moon. Initially the impact of averaging the transmitter’s antenna gain over the azimuth, typical assumption in many studies, is analyzed. Afterwards, we also consider three different L5 antenna patterns assumed in the literature (the precise pattern are unfortunately not yet fully available). For each of the considered antenna pattern assumptions, we simulate received signal power level, availability, GDOP and navigation accuracy, in order to evaluate their different effect. Finally, once identified the most conservative assumptions for the transmitters’ antenna patterns, for each elevation of the receiver antenna, we also compute the number of available GNSS observations and we analyze their distribution.

2017

GPS based navigation performance analysis within and beyond the Space Service Volume for different transmitters’ antenna patterns

Paul David Blunt, Cyril Botteron, Vincenzo Capuano, Pierre-André Farine, Endrit Shehaj

2017