A global view of the isochronous trajectory families by Hamilton's hodographic transformation

An overall view of the characteristic features of the isochronous trajectory families is presented. The trajectories are assumed Keplerian, isoenergetic, and satisfying Lambert's conditions, that is the sum of radial distances of the two termini, and their linear separation are both constant. A geometric approach is adopted by using Hamilton's hodographic transformation. The connection between Hamilton's hodographic isochronism and the Lambert's theorem is briefly reviewed, and the interrelations among the Hamiltonian set of parameters and the Lambertian sets are developed. The totality of the isochronous trajectory families is then viewed in the velocity space. Various Lambertian invariants as well as some essential noninvariants are examined, and relevant formulas derived. The salient features of some particular isochronous families are then summarized; and Hamilton's time integral is briefly treated. The analysis is essentially two-dimensional, with its extension to the three-dimensional case finally discussed.     

A new treatment of Lambertian mechanics

Lambert's formulas for the time of orbital flight between two points in space are rederived by first establishing a universal differential equation governing the time function, independent of the conic type of the trajectory, the focal characteristics of the trajectory sector, and the range angle. A unified form of Lambert's formulas is then obtained as the general solution of the differential equation, and the various forms of the classical Lambert's formulas are obtained as its particular solutions under different boundary conditions. Following this basic treatment, various hypergeometric expansions for Lambert's time function and its derivatives are developed, and the behavior of the function and its implications in the solution of Lambert's problem and the isochronous trajectories are briefly reviewed. Finally, a short comparison of the present treatment with those found in current literature on Lambertian Mechanics is made and briefly discussed.     

Tracking and data relay satellite system: NASA's new spacecraft data acquisition system

The growth in NASA's ground network complexity and cost triggered a search for an alternative. Through a lease service contract, Western Union will provide to NASA 10 years of space communications services with a Tracking and Data Relay Satellite System (TDRSS). A constellation of four operating satellites in geostationary orbit and a single ground terminal will provide complete tracking, telemetry and command service for all of NASA's Earth orbital satellites below an altitude of 12,000 km. The system is shared: two satellites will be dedicated to NASA service; a third will provide backup as a shared spare; the fourth satellite will be dedicated to Western Union's Advanced Westar commercial service. Western Union will operate the ground terminal and provide operational satellite control. NASA's Network Control Center will provide the focal point for scheduling user services and controlling the interface between TDRSS and the rest of the NASA communications network, project control centers and data processing facilities. TDRSS single access user spacecraft data systems should be designed for efficient time shared data relay support. Reimbursement policy and rate structure for non-NASA users are currently being developed.     

Orbit prediction and shuttle rendezvous strategy for eureca

The European Retrievable Carrier (EURECA) is a platform to be launched, deployed and retrieved in low Earth orbit by the Space Shuttle.A newly developed analytical orbit prediction method is described which meets the severe requirements for EURECA's orbit propagation. It is based on an averaging procedure including the Earth's zonal harmonics J₂, J₃ and J₄ and a refined treatment of the air drag perturbation where EURECA's large solar panels are taken into account. Some orbit prediction results are included.In order to offer more flexibility for the Shuttle retrieval of EURECA, it is proposed to execute a part of the rendezvous manoeuvres by EURECA. A corresponding strategy is described.     

Orbital design and technological feasibility of Halley mission

Missions to Halley's comet in 1985–1986 are discussed. They include pre-perihelion encounter, post-perihelion encounter, the utilization of Venus swing-by, one round mission in which the spacecraft goes the round of the Sun before the encounter and missions to the point beneath the perihelion of Halley's orbit. Technological feasibility of the small spacecraft is also discussed on the basis of the use of the improved version of M-3S launch vehicle.     

Design of phase-locked loop for communication system via on-board signal processing satellites

The energy inconsistency for a multiple access system via an active satellite with simple repeating of signals is claimed. The on-board ideal signal processing algorithm resolving this inconsistency is considered and the optimal group signal processing algorithm in a manner of digital signals shape transformation followed by their time compression is suggested. The necessity for individual clock synchronization of ground stations is shown and the synchronous multiple access system block diagram with an optimal on-board signal processing is discussed.A phase disturbance dynamics of a two-loops clock synchronization system with variable time delay is investigated. A nonlinear differential-difference equation is obtained and for the first order PLL with time delay the exact solutions are found in cases of relay and linear shapes phase discriminator's characteristics. Phase errors' expressions are derived and the main factors of accuracy limiting caused by PLL's feedback time delay are established.     

Walter Hohmann's contributions towards space flight: an appreciation on the occasion of the centenary of his birthday

In 1923 Hermann Oberth published his book “Die Rakete zu den Planetenräumen” (The Rocket into Planetary Space), in 1924 Max Valier's book “Der Vorstoss in den Weltenraum” (The Advance into Space) appeared while in the U.S.A. already in 1919 Robert H. Goddard reported on his rocket experiments. Altogether different from the publications just mentioned was a book entitled “Die Erreichbarkeit der Himmelskörper” (The Attainability of Celestial Bodies) published in 1925. Its author was Dr.-Ing. Walter Hohmann, born 18 March 1880, civil engineer for the city authorities of Essen, who had already made, during World War I, calculations as to the amount of fuel, initial mass and flight time necessary for flights from the Earth to other planets. The transfer trajectories investigated by Hohmann and today attributed with his name have a great practical significance for space flight onto the present. In the lecture a critical appreciation of Hohmann's work is given.     

Developing the next phase in NASAs satellite communications program

NASAs early efforts in satellite communications development brought confidence in space technology use for improved telecommunications. New, worldwide satellite communications systems have resulted, and are now on a commercial, self-sustaining operational basis. Since 1973, NASA has conducted hundreds of user experiments and demonstrated newer technology using ATS-1, -3, -6 and CTS. Now, projections show that the commercial demand will continue to increase, soon exceeding the current technology's capacity.As a result, U.S. Space Policy affirmed in 1978 that NASA should embark again on a research and development program for satellite communications with specific, characterized goals. The resulting plan's elements include $\text{30}\text{20}\text{GHz}$ Ka-band technology, extending the current work in advanced multi-beam antennas; a narrowband system and technology study that could lead to mobile and transportable communications developments; and studies of future uses of technology in communications. The program plan and its evolution are described, followed by a report of current progress and future expectations.     

A minicomputer finite elements program for microgravity hydroelastic analysis

A general hydroelastic analysis formulation is presented by using Green's function. Emphasis is placed on the case of an incompressible fluid model which is applicable to flexible tank hydroelastic analysis. Variational formulation of the sloshing problem is established in order to obtain a numerical treatment by a mixed finite element method. A minicomputer program is illustrated and the hydroelastic analysis technique is checked as an efficient and accurate approach with some numerical solutions.     

Statistical method for ground and sky coverage calculation

A novel statistical method has been devised for evaluating the ground and the sky coverage of an observation experiment on board a satellite. Owing to its unrivalled rapidity compared with other conventional calculation techniques, the method can be applied to evaluate the coverage percentages for the whole globe or any area on it, to calculate the visibility percentages for one or more ground stations and to determine the percentages of observation time of any given celestial direction including Sun, Moon, Earth and Ground Stations constraints. The orbits considered can be elliptical and account is taken of the drift due to the Earth's oblateness.     

Inertially fixed pitch stabilization of satellites by solar radiation pressure

Utilization of solar radiation pressure to stabilize the pitch attitude of an unsymmetrical satellite along an inertially-fixed orientation is investigated. A controller employing two rotatable highly reflective control surfaces is proposed and a control strategy involving both nominal and feedback controls is synthesized. Accounting for the apparent annual motion of the Sun, the validity of the concept throughout the year is established through a stability analysis of the system. The influence of the Earth's shadow on the controller performance is also analyzed. The speed of response as well as the pointing accuracy capabilities of the system appear to be quite acceptable for long-life scientific missions.     

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.     

The french educational satellite arsene

ARSENE (Ariane, Radio-amateur, Satellite pour l'ENseignement de l'Espace) is a telecommunications satellite for Amateur Space Service. Its main feature is that more than 100 students from French engineering schools and universities have been working since 1979 for definition phase and satellite development. The highest IAF awards has been obtained by “ARSENE students” in Tokyo (1980) and Rome (1981). The French space agency, CNES and French aerospace industries are supporting the program. The European Space Agency offered to place ARSENE in orbit on the first Ariane mark IV launch late 1985.     

Moscow declaration

This declaration was made at the International Conference on Aerospace Complex Conversion, organized by the United Nations in Moscow, 12–16 October 1992. It provides a follow-on to the UN conference on ‘Conversion - opporunities for development and environment’ held in Dortmund, Germany, 24–27 February 1992, and reported in the August 1992 issue of Space Policy by Professor K.H. Böckstiegel, who chaired the Plenary Session in Moscow.     

Optimal transfer from the lagrangian points

The transfer from the equilateral Lagrangian points of the Earth-Moon system is analysed. The final states of the velocity of the space vehicles and of the rotation velocity of the propulsion vector are assumed given. The trajectory which ensures the transfer in optimal time consists of three arcs. On this trajectory the rotation velocity of the direction of the propulsion has the extremal value or corresponds to the Lawden's tangent law. The use of the matching of the arcs together with transversality conditions and final conditions determines the constants of integration and the evolution time. The resulting parametric equations of the optimal trajectory are of integral form.     

The darboux point and the conjugate point on optimal deorbit for reentry trajectories

The concept of the Darboux point at which an extremal loses its global optimality is extended to the case of discontinuous control. Using Contensou's domain of maneuverability, the condition for optimal switching at a corner is derived and the optimality of the trajectory in the neighborhood of a Darboux point is analyzed. The theory is applied to the problems of minimum-fuel planar and noncoplanar deorbit from elliptical orbits for atmospheric entry at a prescribed angle. In each case, the global optimal trajectory is assessed and it is found that in these nonlinear problems the Darboux point and the conjugate point are distinct. The global optimality is always lost before local optimality.     

Synthesis of flight results of the Cactus accelerometer for accelerations below 10−9g

The Cactus accelerometer, developed at ONERA and making up the payload of the Castor satellite, has been operating continuously and normally for 40 months. Thanks to the great quantity of data acquired and to a well adapted processing technique, acceleration measurements were in fact obtained with a better sensitivity than that expected before launch.This paper presents a synthesis of the work carried out in the past year and concerning the measurement of very low accelerations. These are due, for the most part, to the Earth IR radiation pressure when the satellite is in the Earth's shadow, and to the thrust it is subjected to under the influence of the anisotropy of its own radiation.     

Recovery of long-wavelength mean gravity anomalies for the dedicated gravitational satellite (gravsat) mission

This paper describes a computer simulation study that was undertaken to determine how well long-wavelength variations in the Earth's gravitational field can be recovered using data from the Dedicated$\text{Grav}$itational $\text{Sat}$ellite (GRAVSAT) mission. This mission is to consist of two low altitude (160 km) spacecraft in essentially the same orbit but separated in phase by 100–300 km. Geodetic data are measurements of the relative range rate to an accuracy of about 1 μm/s at 4 sec intervals. Specifically, a Bayesian covariance simulation was used to investigate simultaneous recovery of the spacecraft ephemerides and a global distribution of 20° × 20° mean gravity anomaly blocks. Sources of errors considered were tracking station positions, gravitational constant, Earth body tides, tropospheric modeling and measurement noise. It should be noted that this simulation does not include as an error source variations in the gravity field that have a character different from what was modeled. Consequently, this study demonstrates the potential of the low-low system as configured to recover the long-wavelength variations in the gravity field.Using only one days worth of data, the mean of the standard deviations of the 162 20° × 20° gravity anomaly blocks is about 1 μgal. For a 6 month mission (assuming a reduction proportional to the square root of the data intervals) this projects to < 0.1 μgal. Because of the potential of increased measurement precision at shorter separation distances, and the relative insensitivity of the recovery process to separation distance, it should be possible to recover both long and short wavelength variations with a modest distribution of separation distances tailored primarily to the short wavelength recovery. Effects of the uncertainty in the gravitational constant and Love's numbers are negligible. In a simulation not reported on, increasing the altitude of the orbit to 200 km from 150 km, degraded, as expected, the accuracy of the recovered parameters by only 7%.     

On autonomous tracking of a minor celestial body

There is suggested an algorithm of the autonomous tracking of a minor celestial body (comet, asteroid or satellite) by the photo-TV-camera of the spacecraft during its flyby in the vicinity of the celestial body, investigated by the data of images obtained by this camera. This algorithm allows prediction of the celestial body angular position in order to point the onboard camera to the body. The field of applicability for the suggested algorithm taking into account various errors is being investigated. The problems of the optimization of the program of the autonomous tracking in order to decrease the prediction errors or to increase the prediction time interval are considered. The results obtained are illustrated by the example of the autonomous tracking of Halley's comet nucleus.