Optimal aeroassisted return from high earth orbit with plane change

This paper gives a complete analysis of the problem of aeroassisted return from a high Earth orbit to a low Earth orbit with plane change. A discussion of pure propulsive maneuver leads to the necessary change for improvement of the fuel consumption by inserting in the middle of the trajectory an atmospheric phase to obtain all or part of the required plane change. The variational problem is reduced to a parametric optimization problem by using the known results in optimal impulsive transfer and solving the atmospheric turning problem for storage and use in the optimization process. The coupling effect between space maneuver and atmospheric maneuver is discussed. Depending on the values of the plane change i, the ratios of the radii, $\text{n =}\text{r}{}_1\text{r}{}_2$ between the orbits and $\text{a =}\text{r}{}_2\text{R}$ between the low orbit and the atmosphere, and the maximum lift-to-drag ratio E1 of the vehicle, the optimal maneuver can be pure propulsive or aeroassisted. For aeroassisted maneuver, the optimal mode can be parabolic, which requires only drag capability of the vehicle, or elliptic. In the elliptic mode, it can be by one-impulse for deorbit and one or two-impulse in postatmospheric flight, or by two-impulse for deorbit with only one impulse for final circularization. It is shown that whenever an impulse is applied, a plane change is made. The necessary conditions for the optimal split of the plane changes are derived and mechanized in a program routine for obtaining the solution.     

On the limiting mass of a dense stellar matter

In the present work, we have derived an expression $\text{M}{}_{\mathrm{L}}\text{? 4.738 M}{}_{\mathrm{\odot }}$ (M_⊙ = 1.985 × 10³³ g = mass of the Sun) giving the “limiting” value of the mass of a dense stellar matter, by introducing the concept of nuclear size correction in the theory of relativistic Thomas Fermi model for a compressed atom. We find that $\text{M}{}_{\mathrm{L}}\text{? 5.1571 M}{}_{\mathrm{<mtext>Ch</mtext>}}\text{and}\text{=3.2750(M}{}_{\mathrm{<mtext>O</mtext>}}\text{)}{}_{\mathrm{<mtext>Prev</mtext>}}$ [M_Ch and (M_O)_Prev denote respectively the Chandrasekhar and author's “limiting” masses]. By making a comparative study with those of previous results it has been shown that our present treatment would provide satisfactory results for the density ranges from ? ? 10⁸ up to $\text{? ? 10}{}^{11}\text{g}\text{/}\text{cm}{}^3$. Other results of cognate interest in the non-relativistic regime 10³ < ? ? 10⁵ (without the nuclear size effect) are presented. The astrophysical implications of the results are mentioned.     

Analyse du fonctionnement d'un propulseur a éjection modulée

ONERA developed, for studying the response of a propellant to a pressure or velocity fluctuation, an experimental rocket engine whose nozzle throat area can be modulated by a toothed disk.The paper presents a linearized theory of the functioning of this engine in the low frequency domain, i.e. when there is no wave propagation within the combuster.To describe the functioning of this motor, the Ryazantsev-Novozhilov method, which assumes that the gas response is instantaneous, is used. This analysis takes into account the erosion and radiation effects, the combustion efficiency and the thermal losses through the walls.Two particular cases are described, for two values of the Damköhler parameter $\text{D}{}_1\text{=}\text{t}{}_{\mathrm{c}}\text{t}{}_{\mathrm{th}}$, where t_c is the residence time in the combuster and t_th the characteristic thermal time of the heat penetration into the solid propellant. These two cases correspond, one to a classical propellant D₁ > 1, the other to a particular propellant of low burning rate ($\text{J}{}_{\mathrm{b}}\text{? 0.2}\text{to}\text{0.4}\text{mm s}{}^{\mathrm{?1}}$) D₁ < 1. The stability conditions are analysed as well as the pressure amplitute and phase as a function of the nozzle throat modulation frequency.Still in linearized theory, the complete solutions of the problem are presented, using a method of numerical resolution.     

Small cryogenic propulsion unit for upper stage application

The feasibility study was conducted to use the cryogenic propulsion system for the third stage of the future H-1 vehicle. While the $\text{LO}{}_2\text{LH}{}_2$ third-stage mass fraction is less than the current solid propellant third stage, the 50% higher Isp results in a significantly higher payload. Two basic configurations of the new propulsion system were proposed: one pressure-fed system and two pump-fed systems. The first is a pressure-fed system providing a 700 kg thrust at an Isp of 441 sec with restart capability. The second is a pump-fed system, operating on an expander cycle principle. A midget turbopump with a 90 000 rpm shaft speed feeds the thrust chamber which delivers 1 ton of thrust at an Isp of 471 sec. The third proposed system is also a pump-fed design using a unique expander bleed cycle, and delivers a 1 ton thrust at an Isp of 470 sec with a turbopump speed of 80 000 rpm. The results of engine testing predict the performance feasibility of respective propulsion system designs.     

Analysis and implementation of in-plane stationkeeping of continuously perturbed Walker constellations

The stationkeeping of symmetric Walker constellations is analyzed by considering the perturbations arising from a high order and degree Earth gravity field and the solar radiation pressure. These perturbations act differently on each group of spacecraft flying in a given orbital plane, causing a differential drift effect that would disrupt the initial symmetry of the constellation. The analysis is based on the consideration of a fictitious set of rotating reference frames that move with the spacecraft in the mean sense, but drift at a rate equal to the average drift rate experienced by all the vehicles over an extended period. The frames are also allowed to experience the $J_2$-precession such that each vehicle is allowed to drift in 3D relative to its frame. A two-impulse rendezvous maneuver is then constructed to bring each vehicle to the center of its frame as soon as a given tolerance deadband is about to be violated. This paper illustrates the computations associated with the stationkeeping of a generic Walker constellation by maneuvering each leading spacecraft within an orbit plane and calculating the associated velocity changes required for controlling the in-plane motions in an exacting sense, at least for the first series of maneuvers. The analysis can be easily extended to lower flying constellations, which experience additional perturbations due to drag.     

On orbit control using gravity gradient effects

Possibility of orbit control using gravity gradient (GG) effects without any mass expulsion is discussed. For simplicity, a dumb-bell type satellite and circular orbits are mainly considered. It is shown that the GG effects can be applied to convert attitude torques into orbital torques and vice versa. In central gravitational force fields, maximum orbital torques or thrusts are available from the GG force when roll or pitch angle is $\text{±}\text{π}\text{4}$ provided that the attitude angle is null when the dumb-bell axis coincides with the local vertical. Such external torques as geomagnetic or solar wind pressure can be utilized to maintain the $\text{±}\text{π}\text{4}$ attitude, then the orbital torques are available forever. In non-central gravitational fields, without any external torque, the orbital radii of circular orbits can be increased by controlling the satellite attitude using electric energy. The use of the Earth's oblateness effects and the exterior Lunar potential is discussed.     

Order of magnitude analysis of convective effects in dendritic solidification

The different types of convective phenomena which may occur during the dendritic solidification of metallic alloys are discussed from an order of magnitude analysis. Bulk thermal convection and/or interdendritic solutal convection have to be considered according to the values of the experimental data. Scaling laws for the solute boundary layer resulting from bulk thermal convection have already been derived. It is shown here that the interdendritic flow depends on a solutal Grashof number Gr based on the horizontal density gradient and a characteristic length L_s which is of the order of the liquid channels width. For Gr < 1, which is generally verified in practical cases, the interdendritic flow velocity U_r is proportional to the Grashof number. This a priori law compares favorably with the results of horizontal solidification experiments where the mean interdendritic flow velocity has been estimated from the resulting measured macrosegregation. In these experiments, as well as for most horizontal dendritic solidifications of metallic alloys at 1 g, the ratio $\text{U}{}_{\mathrm{r}}\text{R}$ (R is the growth rate) is of order one. In order to cancel the interdendritic flow effects, this ratio has to be lowered by one order of magnitude. According to our analysis, this can be obtained by performing the experiments either at a slightly reduced g level (～10^?1 g), or at 1 g in a vertical stable configuration with a sufficiently low residual horizontal thermal gradient.     

Analytical solutions for the relative motion of spacecraft subject to Lorentz-force perturbations

A spacecraft capable of producing higher-than-natural electrostatic charges may achieve propellantless orbital maneuvering via the Lorentz-force interaction with a planetary magnetic field. Development of maneuver strategies for these propellantless vehicles is complicated by the fact that the perturbative Lorentz force acts along only a single line of action at any instant. Relative-motion dynamical models are developed that lead to approximate analytical solutions for the motion of charged spacecraft subject to the Lorentz force. These solutions indicate that the principal effects of the Lorentz force on a spacecraft in a circular orbit are to change the intrack position and to change the orbit plane. A rendezvous example is presented in which a spacecraft with a specific charge of ?3.81 $\times$ 10^?4 C/kg reaches a target vehicle initially 10 km away (on the same equatorial low-Earth orbit) in 1 day. Fly-around maneuvers may be achieved in low-Earth orbit with specific charges on the order of 0.001 C/kg.     

Orbit prediction for IRAS using vector and analytic techniques

This paper describes the techniques of a vector approach to the solution of the differential equations of motion of a near-Earth satellite. The method provides a good stable foundation for developing the orbital elements, thus allowing an analytic approach to be used in subsidiary algorithms. The mathematical concepts used in these algorithms are explained, and equations are developed for calculating Earth and Moon eclipses, radiation zone crossings, atmospheric density effects, solar cell decay, look angles and a geographical ephemeris. Results are presented for the IRAS satellite, and show that prediction errors of less than $\text{1}\text{1}\text{2}$ sec over one week or errors of less than 15 sec over $\text{3}\text{1}\text{2}$ months are possible.     

A specific case of stability of cylindrical precession of a satellite

In a central Newtonian gravitational field, the motion of a dynamically symmetrical satellite along an elliptical orbit of arbitrary eccentricity is considered. The particular motion of the satellite is known when its axis of symmetry is perpendicular to the orbit plane, and the satellite rotates about this axis with a constant angular velocity (cylindrical precession). A nonlinear analysis of stability of this motion has been performed under the assumption that the geometry of the satellite mass corresponds to a thin plate. At small values of orbit eccentricity e the analysis is analytical, while numerical analysis is used for arbitrary values of e.     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

Implementation of a semianalytic satellite theory with recovery of short period terms

First order averaging is applied to the artificial satellite problem to obtain the averaged orbit which includes the secular, long and medium period effects of the oblateness of the Earth and the third body perturbations of the moon and sun. Perturbation theory is then used to recover the short period effects due to J₂, the moon, and sun. The perturbation analysis is carried out by means of Lie series and is developed through the first order. Optimization of the resulting short period series was then accomplished in several steps: first all separate algebraic coefficients were precalculated and stored; then all redundant SIN/COS calls were eliminated; next all repetition of numeric and algebraic coefficients were precalculated in pairs; application of the distributive principle allowed a significant reduction in additions and multiplications; finally trigonometric identities were used to further reduce the SIN/COS computations. The result of this optimization along with an interpolator for the averaged equations of motion results in a computer program which requires only $\text{1}\text{6}$ the CPU time (with no loss in accuracy) of the original non-optimized test program.     

Theoretical study about the Marangoni convection in a liquid column in zero-gravity

The thermal Marangoni effect on the surface of a liquid bridge induces a convection inside the liquid. For an imposed arbitrary periodic axial circumferential temperature distribution on the liquid surface the velocity distributions in radial-, angular- and axial direction are determined theoretically by solving the linearized Navier-Stokes equations. Of particular interest is the effect of the viscosity parameter $\text{v}\text{a}{}^2$ and axial wave length to diameter ratio $\text{l}\text{a}$. It was found that the increase of viscosity decreases the magnitude of the velocity distributions and that for small axial wave length to diameter ratios the radial- and axial velocities exhibit peak values close to the free surface of the liquid. This is in a less pronounced way also true for the angular velocity, which shows for increasing moderate values $\text{l}\text{a}\text{(0 ≤}\text{l}\text{a}\text{≤ 2}$) a strong increase in magnitude and for larger axial wavelength a decrease again. For increasing axial wavelength the peak value of the radial- and axial velocity shifts towards the center of the liquid bridge, of which for a further increase a decrease of the magnitude appears.     

Navigation Solution to Maneuver a Spacecraft Relative to a Sphere Centered on a Cooperative Satellite

A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within a sphere, with a user defined radius, centered around a non-maneuvering satellite within a constrained time. The differential correction algorithm develops and utilizes the State Transition Matrix along with the Equations of Motion and multiple satellite?s state information to determine the optimum trajectory to achieve the desired results. The results from the differential correction algorithm are very accurate for prograde orbits, as presented. The results allow for orbit design trade-offs, including satellites? initial inclinations, semi-major axes, as well as the ballistic coefficients. The results also provide an empirical method to determine the optimum ΔV$\mathrm{\Delta }V$ solution for the provided problem. Understanding that the minimum fuel solution lies with a semi-major axis ratio of 1, a very accurate empirical approximation is presented for semi-major axis ratio values less than and greater than 1. This work ultimately provides the generalized framework for applying the algorithm to a unique user defined maneuvering spacecraft scenario.     

Results of the early orbit manoeuvres of the ampte-uks

The Active Magnetospheric Particle Tracer Explorers (AMPTE) program consists of three satellites which were launched on 16th August 1984. The scientific aim of the mission is to inject lithium and barium tracer ions inside and outside the Earth's magnetosphere and to detect and monitor these ions as they diffuse through the inner magnetosphere. The first of these three satellites, the U.S. Charge Composition Explorer (CCE) was launched into an elliptical orbit of apogee 8 R_e. The other two satellites are the West German Ion Release Module (IRM) and the U.K. Subsatellite (UKS), both of which were launched on the same vehicle into a highly elliptical orbit of apogee 18 R_e. At discreet intervals during the mission the IRM will release ions into the solar wind, and the movement of these ions will be monitored by the UKS. Depending on the particular scientific requirement, the UKS has to be positioned accurately at a given distance behind the IRM. Initially the UKS has to be located 100 km behind the IRM, and held there for ～9 months. It will then be moved a distance of ～1 R_e behind the IRM. In order to manoeuvre the UKS around its orbit, a cold gas jet system is incorporated on the satellite, allowing impulses to be applied both along and perpendicular to the orbit velocity vector. The orbit control system also has to cater for relative orbit changes due to air drag at perigee, as the IRM and the UKS have different $\text{area}\text{mass}$ ratios. This paper presents an account of the orbit control system implemented on the UKS, together with the mathematical approach adopted, and results from manoeuvres made in the first weeks of the mission.     

Broad-search algorithms for the spacecraft trajectory design of Callisto–Ganymede–Io triple flyby sequences from 2024 to 2040, Part II: Lambert pathfinding and trajectory solutions

Triple-satellite-aided capture employs gravity-assist flybys of three of the Galilean moons of Jupiter in order to decrease the amount of ΔV$\mathrm{\Delta }V$ required to capture a spacecraft into Jupiter orbit. Similarly, triple flybys can be used within a Jupiter satellite tour to rapidly modify the orbital parameters of a Jovicentric orbit, or to increase the number of science flybys. In order to provide a nearly comprehensive search of the solution space of Callisto–Ganymede–Io triple flybys from 2024 to 2040, a third-order, Chebyshev's method variant of the p-iteration solution to Lambert's problem is paired with a second-order, Newton–Raphson method, time of flight iteration solution to the _V∞$V_{\infty }$-matching problem. The iterative solutions of these problems provide the orbital parameters of the Callisto–Ganymede transfer, the Ganymede flyby, and the Ganymede–Io transfer, but the characteristics of the Callisto and Io flybys are unconstrained, so they are permitted to vary in order to produce an even larger number of trajectory solutions. The vast amount of solution data is searched to find the best triple-satellite-aided capture window between 2024 and 2040.     

Communications transponder performance for Japanese Communications Satellite-2 and prospects for future systems

Communications transponder for the Japanese Communications Satellite-2 (CS-2a and 2b) to be launched into a geostationary orbit by N-II launch vehicle in February and August, 1983, has been developed. The transponder is provided with six-channel K-band ($\text{30}\text{20}\text{GHz}$) transponder including beacon transmitter, which operates in the highest frequency ranges ever utilized on an operational communications satellite, and two-channel C-band ($\text{6}\text{4}\text{GHz}$) transponder. Receiver front end of the K-band transponder consists of a direct mixer followed by a 1.8 GHz IF amplifier and provides 8 dB noise figure. 20 GHz output power is 4 W by final amplification at 5-W TWTA. C-band transponder provides 4 dB noise figure and 4.3-W output power. Key factors for future high capacity transponder are also presented.