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.     

Variations in air density,satellite drag coefficient and atmospheric rotation rate from analysis of the orbit of 1966-92D

Variations in air density, the satellite drag coefficient, and the atmospheric rotation rate at 60°S lat and 120–130 km height during the period September 1968–June 1969 have been determined from analysis of the high-eccentricity orbit of the 4th Molyniya 1 upper-stage rocket body, 1966-92D. The results show good correlation between density increases and strong geomagnetic activity, although solar flares of equal geomagnetic index value do not consistently produce density changes of equal magnitude. A 30 per cent semi-annual variation was observed, but there was no indication of the 50 per cent lower thermosphere seasonal-latitudinal variation that was predicted from the CIRA 1972 atmosphere. The satellite drag coefficient was observed to begin decreasing with height at an altitude where the molecular mean free path, λ, was twice the satellite's length. The coefficient decreased to a value approaching 1.0 as the satellite's perigee height fell below the altitude where λ was one-half the length. A mean atmospheric rotation rate of 1.1 ± 0.1 Earth rot/day was obtained for the last 20 days of decay. However, variations were observed with west-to-east wind speeds of ?100 m/sec measured for a local time of 13 hr.     

Software for calculating orbit and mass of visual binaries

This paper presents an overview on the software that will be used at the Bosscha Observatory of Indonesia for calculating the orbit and mass of visual binary system. The programme is based on the Thiele-van den Bos methods. The algorithm is designed for elliptic motions and applicable to personal computer.     

The orbit and atmospheric trajectory of the Orgueil meteorite from historical records

Abstract— Using visual observations that were reported 140 years ago in the Comptes Rendus de l'Académie des Sciences de Paris, we have determined the atmospheric trajectory and the orbit of the Orgueil meteorite, which fell May 14, 1864, near Montauban, France. Despite the intrinsic uncertainty of visual observations, we were able to calculate a reasonably precise atmospheric trajectory and a moderately precise orbit for the Orgueil meteoroid. The atmosphere entry point was ?70 km high and the meteoroid terminal point was ?20 km high. The calculated luminous path was ?150 km with an entry angle of 20°. These characteristics are broadly similar to that of other meteorites for which the trajectory is known. Five out of six orbital parameters for the Orgueil orbit are well constrained. In particular, the perihelion lies inside the Earth's orbit (q ?0.87 AU), as is expected for an Earth‐crossing meteorite, and the orbital plane is close to the ecliptic (i ?0°). The aphelion distance (Q) depends critically on the pre‐atmospheric velocity. From the calculated atmospheric path and the fireball duration, which was reported by seven witnesses, we have estimated the pre‐atmospheric velocity to be larger than 17.8 km/sec, which corresponds to an aphelion distance Q larger than 5.2 AU, the semi‐major axis of Jupiter orbit. These results suggest that Orgueil has an orbit similar to that of Jupiter‐family comets (JFCs), although an Halley‐type comet cannot be excluded. This is at odds with other meteorites that have an asteroidal origin, but it is compatible with 140 years of data‐gathering that has established the very special nature of Orgueil compared to other meteorites. A cometary origin of the Orgueil meteorite does not contradict cosmochemistry data on CI1 chondrites. If CI1 chondrites originate from comets, it implies that comets are much more processed than previously thought and should contain secondary minerals. The forthcoming return of cometary samples by the Stardust mission will provide a unique opportunity to corroborate (or contradict) our hypothesis.     

Relativistic effects for near-earth satellite orbit determination

The relativistic formulations for the equations which describe the motion of a near-Earth satellite are compared for two commonly used coordinate reference systems (RS). The discussion describes the transformation between the solar system barycentric RS and both the non-inertial and inertial geocentric RSs. A relativistic correction for the Earth's geopotential expressed in the solar system barycentric RS and the effect of geodesic precession on the satellite orbit in the geocentric RS are derived in detail. The effect of the definition of coordinate time on scale is also examined. A long-arc solution using 3 years of laser range measurements of the motion of the Lageos satellite is used to demonstrate that the effects of relativity formulated in the geocentric RS and in the solar system barycentric RS are equivalent to a high degree of accuracy.     

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.     

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.     

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.     

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.     

Retrieval of atmospheric mass densities in lower thermosphere below 200 km from precise orbit of re-entry object CZ-3B R/B by analytical and numerical methods

Taking the re-entry object CZ-3B R/B (COSPAR identifier 2012-018D, NORAD catalog number 38253) as an example, retrieval of atmospheric mass densities in lower thermosphere below 200 km from its rebuilt precise orbit is studied in this paper. Two methodologies, i.e. analytical and numerical methods, are adopted in the retrieval. Basic principles of these two methodologies are briefly introduced. Based on the short-arc sparse observational data accumulated in the high accuracy re-entry prediction, orbit determinations of re-entry object CZ-3B R/B are performed sectionally, and then its precise orbit is rebuilt. According to the orbit theory, the variation of orbital semi-major axis of re-entry object CZ-3B R/B induced by atmospheric drag perturbation only is derived from the rebuilt precise orbit. In the derivation of secular change of the orbital semi-major axis of re-entry object CZ-3B R/B induced by atmospheric drag perturbation only, the time-span is set as one minute tentatively. And then retrieval results of atmospheric mass densities in lower thermosphere below 200 km by analytical and numerical methods are presented, as well as their bias deviations from the calculated results of the NRLMSISE-00 empirical model of the atmosphere. Setting bias deviation bands, the corresponding ‘confidence coefficients’ of the retrieved atmospheric mass densities with respect to the model values are given. Average bias deviations of the retrieved atmospheric mass densities by analytical and numerical methods from the model values are also calculated respectively. On the whole, the retrieved atmospheric mass densities by numerical method approach to the model values more closely; the differences between the retrieved results and the model values are relatively smaller at the peaks of atmospheric mass densities than the other places.     

The low-eccentricity earth satellite orbit at the critical inclination

A solution to the orbital motion of an Earth satellite at the critical inclination and with near-zero eccentricity is developed by the von Zeipel method to the first order in the eccentricity, and to the first order in the higher gravitational harmonics, using elements which do not degenerate at zero eccentricity.     

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.     

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.     

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。     

Regular precessions of a gyrostatic satellite in a circular orbit

In the present paper, the regular precessions about the mass center are studied, for a Volterra-type gyrostatic satellite in a circular orbit under a Newtonian force field. All the possible regular precessions are determined.     

Application of the integral variation method to satellite orbit prediction

The Integral Variation (IV) method is a technique to generate an approximate solution to initial value problems involving systems of first-order ordinary differential equations. The technique makes use of generalized Fourier expansions in terms of shifted orthogonal polynomials. The IV method is briefly described and then applied to the problem of near Earth satellite orbit prediction. In particular, we will solve the Lagrange planetary equations including the first three zonal harmonics and drag. This is a highly nonlinear system of six coupled first-order differential equations. Comparison with direct numerical integration shows that the IV method indeed provides accurate analytical approximations to the orbit prediction problem.Advanced Systems Studies; Bldg. 254EElectro-Optical Systems Laboratory; Bldg. 201.     

Determination of the atmospheric neutrino flux from experimental data

The precise knowledge of the atmospheric neutrino fluxes is a key ingredient in the interpretation of the results from any atmospheric neutrino experiment. In the standard atmospheric neutrino data analysis, these fluxes are theoretical inputs obtained from sophisticated numerical calculations. In this work we present an alternative approach to the determination of the atmospheric neutrino fluxes based on the direct extraction from the experimental data on neutrino event rates.      

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.     

Orbit improvement from satellite imaging data obtainable from outer planet missions

Equations of motion are established for a dynamical system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in a simultaneous orbit correction ofn interacting bodies, a notably compact set of variational equations is derived. The above system of differential equations is integrated numerically on a computer.Spacecraft-satellite direction measurements accurate to ±10 were simulated along three representative trajectories (Mariner/Jupiter/Saturn 1977 missions) approaching Io, Titan, and Iapetus to within 41 000, 13 000, and 7 000 km, respectively. For example, from measurements distributed evenly at half-day intervals over a 60-day arc centered on encounter, but none so close that the satellite would fill more than 0.5° in the sky, the orbit of the satelliteand that of the spacraft can be estimated to about 100 km. In addition, the mass of the satellite is obtainable to 2.6% for Io, 1.4% for Titan, and 9% for Iapetus. If only measurements up to 3 days before satellite encounter are included, the orbit of the satelliteor that of the spacecraft can be estimated to about 300 km, all information on mass being lost.The paper concludes with a brief discussion of the need for future work on the orbits of the satellites of the outer planets.     

Determination of the orbit of a natural satellite with hyperbolic flybys

We show that, when a natural satellite like Titan is invisible (e.g., due to an opaque atmosphere) its planetary orbit and its mass can be determined by tracking a spacecraft in close flybys. This is an important problem in the Cassini mission to the Saturnian system, which will be greatly improved by a good astrometric model for all its main components; in particular, an accuracy of a few hundred meters for the orbit of Titan is necessary to allow a measurement of its moment of inertia. The orbit of the spacecraft is the union of elliptical arcs, joined by short hyperbolic transitions: a problem of singular perturbation theory, whose solution leads to a matching condition between the inner hyperbolic orbit and the elliptical orbital elements. Since the inner elements are given in terms of the relative position and velocity of the spacecraft, accurate Doppler measurements in both regions can provide a satisfactory determination of Titan's position and velocity, hence of its Keplerian elements. The errors in this determination are discussed on the basis of the expected Allan deviation of the Doppler method; it is found that the driving errors are those in the elliptical arcs; the fractional errors in Titan's orbital elements are expected to be 10^–7. It is also possible to measure the mass of the satellite; however, when the eccentricity e of the flybys is large, the mass and a scaling transformation are highly correlated and the fractional error in the mass is expected to be e times worse.