Terms Of Orbital Elements Research Articles

Mars orbit injection via aerocapture and low-thrust nonlinear orbit control

This research proposes a new strategy for Mars orbit injection, based on aerocapture and low-thrust nonlinear orbit control. The range of periapse altitudes that allow aerocapture is identified as a function of the hyperbolic excess velocity at Mars arrival, with reference to a large variety of atmospheric density profiles and different ballistic coefficients. This analysis proves that a safe periares altitudinal range leading to aerocapture in all atmospheric conditions does not exist. Three different correction maneuvers, aimed at avoiding both impact and escape, are identified. After the atmospheric arc, the spacecraft orbit exhibits large dispersions in terms of orbit elements. Therefore, the identification of an effective autonomous guidance strategy, capable of driving the spacecraft toward the desired operational orbit, is mandatory. To do this, low-thrust nonlinear orbit control is proposed as an effective option. A feedback law for the low-thrust direction and magnitude, with saturation of the thrust magnitude, is defined, and is proven to enjoy global stability properties. As a result, the spacecraft travels toward the operational orbit of interest, i.e. either (a) an areostationary orbit, (b) a quasi-synchronous inclined orbit, or (c) a low-altitude, sunsynchronous orbit. Monte Carlo simulations, with stochastic density profiles and uncertain initial conditions, point out that the strategy at hand is successful and allows reducing the overall propellant budget in comparison to direct orbit injection based on chemical propulsion. Moreover, the overall time of flight typically ranges from 45 to 140 days, and therefore it is much shorter than that required with the use of aerobraking. As a last advantage, low-thrust nonlinear orbit control allows achievement of a variety of operational orbits, with great accuracy.

Modelling of charged satellite motion in Earth’s gravitational and magnetic fields

In this work Lagrange’s planetary equations for a charged satellite subjected to the Earth’s gravitational and magnetic force fields are solved. The Earth’s gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange’s planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).

Fully analytical solution of the electromagnetic perturbations on the motion of the charged satellites in earth’s magnetic field

In this work, the perturbations in all orbital elements due to the motion of the charged satellites in the Earth’s magnetic field using Lagrange’s planetary equations are solved exactly. The geomagnetic and electric force components in terms of orbital elements in full analytic expressions are derived. Lagrange’s planetary equations after substitution with the considered perturbations in Keplerian orbital elements are obtained. To solve the problem in full analytical way, some integrals by Ahmed (Astron. J. 107, 1900 (1994)) are utilized. The time rate of change of all orbital elements of the spacecraft are integrated and represented in matrix notations.

Effect of resonance on the motion of two symmetrical rigid rods

In the paper, we have discussed the effect of resonance in the motion of two symmetrical rods in the light of Hassan et al. (2016), Bhatnagar (1978) and Sharma et al. (2009). Here we have calculated variation in the Eulerian angels due to resonance in terms of orbital elements a, e, Ω, τ and unperturbed Eulerian angels θA0, ϕA0, ψA0 and θB0, ϕB0, ψB0. We have also determined the amplitude and time period for the resonance 2: 1.

Extended Kalman filtering based parameter estimation and drift compensation for a MEMS rate integrating gyroscope

This paper presents an offline extended Kalman filtering based parameter identification and drift compensation for a MEMS ring vibratory gyroscope. Damping and stiffness imperfections are the major error sources in MEMS vibratory gyroscopes. In the rate integrating operation mode, where angle is output instead of angular velocity as in the case of the rate gyroscope, parameter identification is an essential prerequisite for any feedback control and compensation algorithm to minimize angle drift and other errors. The proposed EKF method provides five estimates for the resonator DC loop gain, and another four parameters related to the non-proportional damping and aniso-elasticities. The method is based on the slowly varying averaged dynamic model expressed in terms of orbital elements. The averaging methodology offers important advantages over similar attempts based directly on the dynamic model expressed in terms of fast time varying displacement and velocity of vibration. Firstly, the observed measurements are subjected to significantly lower levels of noise as a consequence of the narrowband demodulation process employed in the calculation of the orbital elements. Secondly, the EKF requires much lower update rate due to the slowly varying nature of the augmented states. These advantages result in a more accurate estimation, improved stability performance and the possibility for real time implementation of the EKF. Numerical simulation and offline implementation of the EKF using experimental gyroscope operation data are provided to validate the proposed method. Moreover, the identified damping imperfections have been used in the drift compensation control in a DSP based real time rate integrating gyroscope control system. Ultimately, the maximum angular drift has been reduced to 1° per second. Spectrum analysis shows the angle drift error is dominated by 4th harmonics caused by dynamics not included in the conventional gyroscope model.

Effect of Resonance on the Motion of Two Cylindrical Rigid Bodies

The effect of resonance on the motion of two cylindrical rigid bodies has been studied in the light of Bhatnagar [1] [2] [3] and under some defined axiomatic restrictions. Here we have calculated variation in Eulerian angles due to resonance in terms of orbital elements and unperturbed Eulerian angles.

Meteor Showers: which ones are real and where do they come from?

AbstractThe IAU Meteor Shower Working List contains 369 showers, of which only 64 are considered established (per February 28, 2012). In this invited review, we will give an overview of international efforts to validate the remaining showers. We report on the showers that were validated in this triennium and proposed to receive the predicate “established" at the present General Assembly. The meteoroid orbit surveys characterize the meteoroid streams in terms of orbital elements and their dispersions, which is ground truth for efforts to identify their parent comets, study the fragmentation history of the (mostly dormant) comet population in the inner solar system, and understand the origin of the zodiacal cloud.

Visual Contact between Two Earth’s Satellites

Problem statement: In this study, an analytical expression for predicting mutually visible between Earth’s satellites is developed. Approach: A relative satellite-satellite visibility function is developed in terms of orbital elements for two satellites in the same orbital plane. Also, a simple computational algorithm is expressed to compute the visibility function. Results: This study presents a new and easy method to determine the visibility times between two satellites which are in the same orbital plane. Conclusion: The satellite-satellite visibility function is solved by an easy treatment.

A Comparison of Lorentz, Planetary Gravitational, and Satellite Gravitational Resonances

We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966, Theory of Satellite Geodesy, Blaisdell, Waltham, MA). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. This procedure is analogous to the derivation of gravitational disturbing functions, except, since the Lorentz force has no associated potential, the perturbation of each orbital element must be calculated separately. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet.We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called "d'Alembert rules" for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant "jumps," depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

Generalized perturbation equations of celestial mechanics

Generalized perturbation equations of celestial mechanics in terms of orbital elements are derived. The most general case is considered: Keplerian motion of two bodies caused by gravitational forces between them is disturbed by disturbing acceleration acting on each of the bodies separately and by changes of masses of these bodies. It is also pointed out why derivation presented in Klacka (1992a) is completely physically correct only for constant masses.

Perturbation equations of celestial mechanics

Perturbation equations of celestial mechanics in terms of orbital elements are completely derived in application to the motion of interplanetary dust particle in the gravational field of the Sun and under the action of disturbing forces. Consideration of change of mass of interplanetary dust particle is the most important feature of this derivation. The results obtained are completely general in the case of constant masses.

Tesseral harmonic perturbations for high order and degree harmonics

A new formula has been derived for geopotential expressed in terms of orbital elements. The summation sequence was changed so that the terms of the same frequencies would be grouped and the generalized lumped coefficients were derived. The proposed formula has the same form for both odd and evenl-m. Applying Hori's perturbation method, new formulae were derived for tesseral harmonic perturbations in nonsingular orbital elements:l+g, h, e cosg,e sing, L, andH. We show the possibility of effective application of the derived formulae to the calculation of orbits of very low satellites taking into account the coefficients of tesseral harmonics of the Earth's gravitational field up to high orders and degrees. As an example the perturbations up to the order and degree of 90 for the orbit of GRM satellites were calculated. The calculations were carried out on an IBM AT personal computer.

Perturbation Methods for Satellite Orbits

The literature in astrodynamics abounds with perturbation techniques for satellite orbits. Various formulations have been generated in terms of orbit elements, the satellite position and velocity vectors, or combinations thereof. The computational effectiveness of any perturbation scheme depends largely on the definitions used for the dynamic state variables. Some methods are aimed at long-range predictions and orbit lifetime studies, others at short-range predictions for guidance. This paper may serve as an introduction to this field for the nonspecialist, in that it reviews the classical variation-of-parameters technique and discusses several engineering analyses that were generated in the post-Sputnik era. It also points to some connections between these relatively simple approaches and more elaborate methods of celestial mechanics. Thus it may contribute toward a comparison of several “professional” approaches whose relative merits are often debated among experts.