Combined perturbation on near-earth satellite orbits

Using a semi-analytical method, we have obtained a first-order solution of the equations of motion of near-Earth satellites under the combined perturbing effect due to Earth's figure and air drag.     

The determination of the satellite orbit of Mariner 9

This paper presents a comprehensive analysis of the Mars orbital phase of the Mariner 9 trajectory as determined from Earth based radio data. Both the method and accuracy of the orbit determination process are reviewed. Analysis is presented to show the effects of Mars gravity model and node in the plane of the sky errors on the accuracy of orbit determination. In addition the long term evolution of the orbit from insertion through the first 500 revolutions is presented, and decomposed into effects from the Mars garvity field,n-body perturbations, and solar radiation pressure. Since the orbit period is nearly commensurable with the Mars rotational period, the orbit experiences significant resonance perturbations. The primary perturbation is in-track with a maximum amplitude of 1000 km and a wavelength of 39 spacecraft revolutions.This paper was presented at the AIAA/AAS Astrodynamics Conference, Palo Alto, California, September 11 and 12, 1972. At this time Mariner 9 operations were still underway. The operational life of Mariner 9 ended October 27, 1972, when the supply of nitrogen gas, used for attitude stabilization, was depleted. This paper represents one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, under NASA Contract No. NAS 7-100.     

GEO卫星定轨可视化软件设计

介绍了基于Windows系统开发的GEO卫星定轨可视化软件,该软件是采用Microsoft Visual Studio 2005软件平台,利用Visual Basic.NET编程技术开发设计的,具有预处理观测数据资料、解算GEO卫星精密轨道、分析和图形化轨道解算结果等功能。该软件界面友好、可操作性强、方便省时,有效地提高了GEO卫星定轨工作效率。     

e-VLBI技术及其在卫星定轨中的应用概况

e-VLBI技术继承了VLBI本身具有的极高角分辨率,且其利用高速通讯网络传送观测数据,能够快速得到观测结果,这些优点对于卫星的快速测定轨和提高卫星现有的定轨精度是十分有利的。通过对e-VLBI技术特点的分析及其发展历程的回顾,并结合卫星的差分VLBI观测原理,重点阐述和讨论了e-VLBI技术在我国的应用现状、发展及要求,展望了我国未来e-VLBI的发展前景。     

Relativistic effects in the critical inclination problem in artificial satellite theory

It is well known that in artifical satellite theory special techniques must be employed to construct a formal solution whenever the orbital inclination is sufficiently close to the critical value cos^–1 (1/5). In this article the authors investigate the consequences of introducing certain relativistic effects into the motion of a satellite about an oblate primary. Particular attention is paid to the critical inclination(s), and for such critical motions an appropriate method of solution is formulated.     

Modified multirevolution integration methods for satellite orbit computation

Multirevolution methods allow for the computation of satellite orbits in steps spanning many revolutions. The methods previously discussed in the literature are based on polynomial approximations, and as a result they will integrate exactly (excluding round-off errors) polynomial functions of a discrete independent variable. Modified methods are derived that will integrate exactly products of linear and periodic functions. Numerical examples are given that show that these new methods provide better accuracy for certain satellite problems. It is also shown that information obtained from an approximate analytical solution of the satellite equations of motion, may be used to increase the accuracy and/or efficiency of the multirevolution integration.     

The optimization of satellite orbit for Space-VLBI observation

By sending one or more telescopes into space,Space-VLBI(SVLBI)is able to achieve even higher angular resolution and is therefore the trend of the VLBI technique.For the SVLBI program,the design of satellite orbits plays an important role for the success of planned observation.In this paper,we present our orbit optimization scheme,so as to facilitate the design of satellite orbits for SVLBI observation.To achieve that,we characterize the uv coverage with a measure index and minimize it by finding out the corresponding orbit configuration.In this way,the design of satellite orbit is converted to an optimization problem.We can prove that,with an appropriate global minimization method,the best orbit configuration can be found within the reasonable time.Besides that,we demonstrate that this scheme can be used for the scheduling of SVLBI observations.     

Analytical solutions to the four post-Newtonian effects in a near-Earth satellite orbit

On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J ₂) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.     

Modified Newton-Raphson methods for preliminary orbit determination

Preliminary orbit determination is a multipoint boundary value problem which may be solved by the generalized Newton-Raphson iteration. When applied formally the method suffers from extensive computer storage requirements, fairly long execution times and in some cases, insufficient accuracy. In this work we seek to remove these practical difficulties via modification of the computational algorithm in such a way that solution storage is eliminated for the most part and computational speed and tolerance to imprecise integration algorithms is improved. The modified methods are applied to nine typical preliminary orbit determination problems to demonstrate fast convergence and short computation times, even with very poor starting values for the iteration. Excellent precision of the resulting solution is also demonstrated as well as the algorithm's ability to handle circular, elliptic, parabolic and hyperbolic orbits.     

Errors in orbit determination

The gaussian noise which affects tracking measurements causes an error in the computed value of the orbit parameters. This study provides a method for evaluating: (a) the length of the arc over which the satellite must be tracked; (b) the number of measurements to be made along this arc; (c) the position of the arc with respect to the orbit, necessary to reach the desired accurary of the calculated orbit parameters for a given pointing error of the tracking antenna. It has been assumed that the errors of the tracking measurements have a known gaussian probability distribution, which may differ for each measurement. The equations relating the orbit parameters to the measurements performed have been linearized. It has been shown that the orbit parameters are gaussian random variables and their variance has been calculated as a function of (a), (b) and (c).This paper was presented at the AIAA/AAS meeting, Princeton University, August 1969.     

Upper-atmosphere zonal winds from satellite orbit analysis

In this paper we review and interpret the values of upper-atmosphere rotation rate (zonal winds) obtained by analysing satellite orbits determined from observations. The history of the method is briefly reviewed, the basic principles are explained, objections to the method are answered, and three examples are given. Existing analyses of the atmospheric rotation rate A are critically reviewed, and, after rejecting some and revising others, we are left with 85 values. These are divided according to local time and season, to give the variation of A with height in nine situations—namely morning, evening and average local time, for summer, winter and average season. These observational results indicate that the value of Λ (in rev/day), averaged over both local time and season, increases from 1.0 at 125 km to 1.22 at 325 km and then decreases to 1.0 at 430 km and 0.82 at 600 km. The value of Λ is higher in the evening (18–24 h), with a maximum value (near 1.4) corresponding to a West-to-East wind of 150 m s^?1 at heights near 300 km. The value of Λ is lower in the morning (06–12 h), with East-to-West winds of order 50 m s^?1 at heights of 200–400 km. There is also a consistent seasonal variation, the values of Λ being on average 0.15 higher in winter and 0.1 lower in summer than the average seasonal value. No significant variation with solar activity is found, but there is a slight tendency for a greater rotation rate at lower latitudes for heights above 300 km. Unexpectedly, the values for the 1960s are found to be significantly higher than those for the 1970s. Finally, these observational values are compared with the theoretical global model of Fuller-Rowell and Rees: there is complete agreement on the trends, though there are some differences in the mean values.     

Launch window study for the highly eccentric orbit satellite HEOS-1

A satellite with a high eccentricitye0.95 is strongly perturbed by the sun and the moon. This fact and mission constraints restrict considerably the possible launch times for such a satellte. The launch window calculations can be performed in two steps in order to save computing time. An approximate analytical solution provides a general survey of the launch opportunities. An accurate numerical approach is then necessary for the exact definition of the launch window. In the case of the orbit of HEOS-1 (satellite 68 10901), moreover the consideration of the injection errors has been of great importance.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969.     

Resonant attitude instabilities for a symmetric satellite in a circular orbit

The roll-yaw attitude motion of a spinning symmetric satellite in a circular orbit is investigated with particular emphasis on the behavior near resonance. Resonance in circular orbit occurs if there is a low-order commensurability between the coupled roll-yaw attitude frequencies. For the so-called Delp region where the Hamiltonian describing the linearized attitude oscillations is not positive definite, there can exist, near resonance, a simultaneous growth or decay of the energy of the two normal modes. Two sections of the resonance line ₂=3 ₁ permitting the largest effects are determined and the equations of motion are integrated numerically as a check on the resonance theory. In particular, resonance-induced instabilities are confirmed.     

An analytical iterative algorithm for the prediction of special satellite orbit points with the Brouwer orbit theory

Employing a direct recursive algorithm in relation with analytical theories will yield a considerable saving in computer time, as opposed to simulating a point by point integration through repeated evaluations of the orbit theory. As a case in point, we shall compute the set of osculating orbiting elements corresponding to special events within the revolution of an artificial satellite.     

Variational and symplectic integrators for satellite relative orbit propagation including drag

Orbit propagation algorithms for satellite relative motion relying on Runge–Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge–Kutta-based integrators, even in the presence of atmospheric drag.     

A multi-arc approach for chaotic orbit determination problems

Chaotic dynamical systems are characterized by the existence of a predictability horizon, connected to the notion of Lyapunov time, beyond which predictions of the state of the system are meaningless. In order to study the main features of orbit determination in the presence of chaos, Spoto and Milani (Celest Mech Dyn Astron 124:295–309, 2016) applied the classical least-squares fit and differential correction algorithm to determine a chaotic orbit and a dynamical parameter of a simple discrete system—Chirikov standard map (cf. Chirikov in Phys Rep 52:263, 1979)—with observations distributed beyond the predictability horizon. They found a time limit beyond which numerical calculations are affected by numerical instability: the computability horizon. In this article, we aim at pushing forward such inherent obstacle to numerical calculations in chaotic orbit determination by applying the classical and the constrained multi-arc method (cf. Alessi et al. in Mon Not R Astron Soc 423:2270–2278, 2012) to the same dynamical system. These strategies entail the determination of an orbit when observations are grouped in separate observed arcs. For each arc, a set of initial conditions is determined and, in the case of the constrained multi-arc method, all subsequent arcs are constrained to belong to the same trajectory. We show that the use of these techniques in place of the standard least-squares method has significant advantages: Not only can we perform accurate numerical calculations well beyond the computability horizon, in particular, the constrained multi-arc strategy improves considerably the determination of the dynamical parameter.     

On the true circular orbit of a satellite

The osculating orbit of a planetary satellite moving in the equatorial plane of the central body under the influence of a rotational symmetric perturbation force is elliptical in first order approximation even if the true orbit is always circular. The satellite motion is influenced by a resonance effect due to this perturbing force. An inclined true satellite orbit cannot be circular.     

Regional positioning using a low Earth orbit satellite constellation

Global and regional satellite navigation systems are constellations orbiting the Earth and transmitting radio signals for determining position and velocity of users around the globe. The state-of-the-art navigation satellite systems are located in medium Earth orbits and geosynchronous Earth orbits and are characterized by high launching, building and maintenance costs. For applications that require only regional coverage, the continuous and global coverage that existing systems provide may be unnecessary. Thus, a nano-satellites-based regional navigation satellite system in Low Earth Orbit (LEO), with significantly reduced launching, building and maintenance costs, can be considered. Thus, this paper is aimed at developing a LEO constellation optimization and design method, using genetic algorithms and gradient-based optimization. The preliminary results of this study include 268 LEO constellations, aimed at regional navigation in an approximately 1000 km \(\times \) 1000 km area centered at the geographic coordinates [30, 30] degrees. The constellations performance is examined using simulations, and the figures of merit include total coverage time, revisit time, and geometric dilution of precision (GDOP) percentiles. The GDOP is a quantity that determines the positioning solution accuracy and solely depends on the spatial geometry of the satellites. Whereas the optimization method takes into account only the Earth’s second zonal harmonic coefficient, the simulations include the Earth’s gravitational field with zonal and tesseral harmonics up to degree 10 and order 10, Solar radiation pressure, drag, and the lunisolar gravitational perturbation.     

Methods of calculating atmospheric densities from satellite orbit data

Formulae relating atmospheric density to the rate of change of period of a satellite have been obtained by various workers for two asymptotic cases: (i) eccentricity e small (< 0.3) and (ii) e large (> 0.012). These results arc reviewed, and in the overlapping region, 0.012 < e < 0.3, the formulae are shown to be in agreement to the various orders of magnitude considered.     

On error bounds and initialization in satellite orbit theories

The order of magnitude of the error is investigated for a first-order von Zeipel theory of satellite orbits in an axisymmetric force field, i.e., first-order long period and short-period effects are included along with second order secular rates. The treatment is valid for zero eccentricity and/or inclination. In the case where initial position and velocity vectors are known, the in-track position error over time intervals of order 1/J ₂ is kept at 0(J ₂ ²), like the other position errors and velocity errors, by calibration of the mean motion with the aid of the energy integral. The results are specifically applicable to accuracy comparisons of the Brouwer orbit prediction method with numerical integration. A modified calibration is presented for the general asymmetric force field which includes tesseral harmonics.