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1.
An analytic solution, in terms of expansion of a small parameter, for the classical two-body tethered satellite with a specific drag model is obtained. The time of flight as well as the solution regarding the state variable of the system are expressed in terms of quadratures of the anomaly.  相似文献   

2.
Unified analytical solutions to two-body problems with drag   总被引：3，自引：0，他引：3  
The two-body problem with a generalized Stokes drag is discussed. The drag force is proportional to the product of the velocity vector and the inverse square of the distance. The generalization consists of allowing two different proportionality constants for the radial and the transverse components of the force. Under the 'generalized Robertson transformation', the equation of the orbit takes the form of the Lommel equation and admits solutions in terms of Bessel and Lommel functions. The exact, analytical solutions for this type of drag reveal a paradoxical effect of increasing eccentricity for all trajectories. The Poynting–Robertson drag and Poynting–Plummer–Danby problems are discussed as particular cases of the general solution.  相似文献   

3.
The solution of a feedback optimal control problem arising in orbital mechanics is addressed in this paper. The dynamics is that of a massless body moving in a central gravitational force field subject also to a drag and a radial modulated force. The drag is linearly proportional to the velocity and inversely proportional to the square of the distance from the center of attraction. The problem is tackled by exploiting the properties of a suitably devised linearizing map that transforms the nonlinear dynamics into an inhomogeneous linear system of differential equations supplemented by a quadratic objective function. The generating function method is then applied to this new system, and the solution is back transformed in the old variables. The proposed technique, in contrast to the classical optimal control problem, allows us to derive analytic closed-loop solutions without solving any two-point boundary value problem. Applications are discussed.  相似文献   

4.
An analytical solution is given for the motion of an artifical Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational effects of the zonal harmonicsJ 2,J 3, andJ 4 are included, and the drag effects of any arbitrary dynamic atmosphere are included. By a dynamic atmosphere, we mean any of the modern empirical models which use various observed solar and geophysical parameters as inputs to produce a dynamically varying atmosphere model. The subtleties of using such an atmosphere model with an analytic theory are explored, and real world data is used to determine the optimum implementation. Performance is measured by predictions against real world satellites. As a point of reference, predictions against a special perturbations model are also given.  相似文献   

5.
Theory of the motion of an artificial Earth satellite   总被引：1，自引：0，他引：1  
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ 4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions.  相似文献   

6.
The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods.  相似文献   

7.
Some general properties for the motion of a particle in a central force field with a general power law drag are derived. Exact and approximate solutions of the equations of motion are found in various cases. Emphasis is placed on inverse square gravitation and drag that varies with the square of the speed and inversely with the distance from the center of attraction. For this model two results stand out. The first is a particular solution in closed form that demonstrates the decay of an initially circular orbit under drag. The second, found from an approximation of the equations of motion when the radial speed is small compared with the tangential speed, demonstrates the decay of an initially elliptic orbit that is not highly eccentric. Formulas for calculation of the time of flight are presented for the two principal results.  相似文献   

8.
A development of an analytical solution for the motion of an artificial Earth satellite subject to the combined effects of Earth gravity and air drag is presented. The atmospheric model takes into account a linear variation of the density scale height with altitude, the rotation and the oblateness of the atmosphere. The perturbation theory is based upon Lie transforms. The secular and long-periodic terms as well as the short-periodic effects are included in the theory which is valid for small to moderate eccentricities and for all values of the inclination.Belgian National Fund for Scientific Research  相似文献   

9.
An exact similarity solution is presented for developing mixed convection flows of electrically conducting fluids over a semi-infinite horizontal plate with vectored mass transfer at the wall which are subjected to an applied transverse magnetic field. This solution is given for the case of a wall temperature that is inversely proportional to the square root of the distance from the leading edge. By application of appropriate coordinate transformations, the governing momentum and energy boundary-layer equations are expressed as a set of coupled ordinary differential equations that depend on a magnetic parameter, the buoyancy parameter, and the Prandtl number. The shear stress, the total heat transfer, and the displacement thickness are calculated for different values of both buoyancy and magnetic parameters.  相似文献   

10.
Modeling the effects of atmospheric drag is one of the more important problems associated with the determination of the orbit of a near-earth satellite. Errors in the drag model can lead to significant errors in the determination and prediction of the satellite motion. The uncertainty in the drag acceleration can be attributed to three separate effects: (a) errors in the atmospheric density model, (b) errors in the ballistic coefficient, and (c) errors in the satellite relative velocity. In a number of contemporary satellite missions, the requirements for performing the orbit determination and predictions in near real-time has placed an emphasis on density model computation time as well as the model accuracy. In this investigation, a comparison is made of three contemporary atmospheric density models which are candidates for meeting the current orbit computation requirements. The models considered are the analytic Jacchia-Roberts model, the modified Harris-Priester model, and the USSR Cosmos satellite derived density model. The computational characteristics of each of the models are compared and a modification to the modified Harris-Priester model is proposed which improves its ability to represent the diurnal variation in the atmospheric density.This investigation was supported by the NASA Goddard Spaceflight Center under contract NAS5-20946 and Contract NSG 5154.  相似文献   

11.
The electronic version of an extensive catalogue of the results of the fireball physics inverse problem solution for the precise observational data of the Prairie Network Fireballs (DTHM-values) obtained by local-ballistic method of a variably-sliding path-segment contains a set of the physical parameters for the 480 fireball images of the 248 cosmic body entries into the Earth's atmosphere (PNVK-values). The parameters are: the fireball velocity with the corresponding values of the mass to cross-section area ratio for the fireball-generating body a teach measured point of the fireball path, the ablation factor and the ratio of the luminous fireball energy to the drag work for the body in the Earth's atmosphere using a factor inversely proportional to the density of the body. The catalogue of all PNVK-values, about 3.1 Mbytes in ASCII is accessible from ftp://ftp2.mao.kiev.ua/pub/astro/pnvk, files pnvk.cat and pnvks.cat This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

12.
Some inhomogeneous viscous fluid cosmological models in the presence of an electromagnetic field for cylindrical symmetry are obtained. To get a determinate solution, it is assumed that the coefficient of shear viscosity is proportional to the rate of expansion. The paper also discusses the behaviour of the model when viscosity is absent and comments on some other physical properties.  相似文献   

13.
An approximate semi-analytic solution of a two-body problem with drag is presented. The solution describesnon-lifting orbital motion in a central, inverse-square gravitational field. Drag deceleration is a non-linear function of velocity relative to a rotating atmosphere due to dynamic pressure and velocity-dependent drag coefficient. Neglected are aerodynamic lift, gravitational perturbations of the inverse-square field, and kinematic accelerations due to coordinate frame rotation at earth angular rate. With these simplifications, it is shown that (i) orbital motion occurs in an earth-fixed invariable plane defined by the radius and relative velocity vectors, and (ii) the simplified equations of motion are autonomous and independent of central angle measured in the invariable plane. Consequently, reduction of the differential equations from sixth to second-order is possible. Solutions for the radial and circumferential components of relative velocity are reduced to quadratures with respect to radial distance. Since the independent variable is radial distance, the solutions are singular at zero radial velocity (e. g., for circular orbits). General atmospheric density and drag coefficient models may be used to evaluate the velocity quadratures. The central angle and time variables are recovered from two additional quadratures involving the velocity quadratures. Theoretical results are compared with numerical simulation results.Presently affiliated with AVCO Systems Division, Wilmington, MA 01887, U.S.A.  相似文献   

14.
Some Bianchi type IX viscous fluid cosmological models are investigated. To get a solution, a supplementary condition between metric potentials is used. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density, whereas the coefficient of shear viscosity is considered as proportional to scale of expansion in the model. The cosmological constant Λ is found to be positive and is a decreasing function of time, which is supported by results from recent supernovae observations. Some physical and geometric properties of the models are also discussed.  相似文献   

15.
The trajectory and attitude dynamics of an orbital spacecraft are defined by a unified state model, which enables efficient and rapid machine computation for mission analysis, orbit determination and prediction, satellite geodesy and reentry analysis. The state variables are momenta — a general form for attitude, and a parametric form for orbital motion. The orbital parameters are the velocity state characteristics of the orbital hodograph. The coordinate variables are sets of four Euler parameters, which define the rotation transformation by the quaternion algebra. The unified state model possesses many analytical properties which are invaluable for dynamical system synthesis, numerical analysis and machine solution: regularization, unified matrix algebra, state graphs and transforms. The analytic partials of position and velocity with the state and coordinate variables are presented, as well as representative perturbation functions such as air drag, gravitational potential harmonics, and propulsion thrust.  相似文献   

16.
In this paper, a spatially homogeneous and anisotropic Bianchi type-V cosmological model is considered in a scalar-tensor theory of gravitation proposed by Saez and Ballester (in Phys. Lett. A 113:467, 1986) when the source for energy momentum tensor is a bulk viscous fluid containing one dimensional cosmic strings. The field equations being highly non-linear, we obtain a determinate solution using the plausible physical conditions (i) the scalar of expansion of the space-time is proportional to shear scalar (ii) the baratropic equation of state for pressure and density and (iii) the bulk viscous pressure is proportional to the energy density. It is interesting to observe that cosmic strings do not survive in this model. Some physical and kinematical properties of the model are also discussed.  相似文献   

17.
Gas-surface interactions and satellite drag coefficients   总被引：1，自引：0，他引：1  
Information on gas-surface interactions in orbit has accumulated during the past 35 years. The important role played by atomic oxygen adsorbed on satellite surfaces has been revealed by the analysis of data from orbiting mass spectrometers and pressure gauges. Data from satellites of special design have yielded information on the energy accommodation and angular distributions of molecules reemitted from satellite surfaces. Consequently, it is now possible to calculate satellite drag coefficients from basic physical principles, utilizing parameters of gas-surface interactions measured in orbit. The results of such calculations are given. They show the drag coefficients of four satellites of different compact shapes in low-earth orbit with perigee altitudes in the range from about 150 to 300 km, where energy accommodation coefficients and diffuse angular distributions have been measured. The calculations are based on Sentman's analysis of drag forces in free-molecular flow. His model incorporates the random thermal motion of the incident molecules, and assumes that all molecules are diffusely reemitted The uncertainty caused by the assumption of diffuse reemission is estimated by using Schamberg's model of gas-surface interaction, which can take into account a quasi-specular component of the reemission. Such a quasi-specular component is likely to become more important at higher altitudes as the amount of adsorbed atomic oxygen decreases. A method of deducing accommodation coefficients and angular distributions at higher altitudes by comparing the simultaneous orbital decay of satellites of different shapes at a number of altitudes is suggested. The purpose is to improve thermospheric measurements and models, which are significantly affected by the choice of drag coefficients.  相似文献   

18.
The orbit-averaged differential equations of motion of dust particles under gravity, radiation pressure and Poynting-Robertson drag were given by Wyatt and Whipple (1950). An integral of motion enables the system of two equations in semi-major axis a and eccentricity e to be reduced to one equation, the solution of which is presented here in terms of analytical formulae. An efficient numerical algorithm to compute the solution is given. Listings of two FORTRAN routines are included.  相似文献   

19.
The interaction between a large meteoroid and the atmosphere is modeled as its destruction into a cloud of fragments and vapors moving with a common shock wave. Under the action of aerodynamic forces the shape of this cloud is deformed—it is expanded in the direction transverse to the motion and compressed in the longitudinal direction. With allowance for the pressure distribution over the surface of a body varying its shape (it is assumed that the sphere is transformed into a flattened spheroid), the relation for the rate of increase in the midsection radius of a fragmented meteoroid has been obtained. This rate significantly depends on the degree of the meteoroid flattening which leads to a significantly smaller increase in the transverse size of the meteoroid along the trajectory as compared to similar models used in the literature where the influence of the body shape was not considered. The proposed model also takes into account the change in the density of the cloud of fragments due to an increase in gaps between them. An approximate analytical solution of equations of the physical theory of meteors with drag and heat transfer coefficients varying along the trajectory has been obtained for a fragmented meteoroid. The interaction of the Chelyabinsk meteoroid with the atmosphere is modeled and the solution obtained for the energy release curve is compared with the observational data.  相似文献   

20.
We have constructed a model in Lyra manifold and time varying cosmological constant with perfect fluid using LVDP (Linear Varying Deceleration Parameter). Bianchi type-III metric is used as source of investigation. To get a deterministic solution of the field equation the expansion scalar (θ) is considered as proportional to the shear scalar (σ). The cosmological constant is found to be positive which satisfies the result obtained by supernova Type-Ia Observations [1999]. Here we analyse the behaviour of pressure and deceleration parameter by using different form of dark energy(DE). In addition to it, some physical and geometrical properties of the solutions are studied.  相似文献   

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