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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Nonlinear feedback solution for minimum-time injection into circular orbit with constant thrust acceleration magnitude
Solution for minimum fuel guidance from hyperbolic to circular orbit
Attitude stability of a spinning passive satellite in circular orbit
Equilibrium shape of radio astronomy satellite antenna array in circular orbit
Analysis of launch windows from circular orbits for representative Mars missions
Minimum fuel multiple impulse orbital rendezvous for fixed transfer time near circular orbits
Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.
Preliminary circular orbit determination from single state of range-only data
A particular type of three-impulse transfer between two circular orbits is analyzed. The possibility of three plane changes is recognized, and the problem is to optimally distribute these plane changes to minimize the sum of the individual impulses. Numerical difficulties and their solution are discussed. Numerical results obtained from a conjugate gradient technique are presented for both the case where the individual plane changes are unconstrained and for the case where they are constrained. Possibly not unexpectedly, multiple minima are found. The techniques presented could be extended to the finite burn case, but primarily the contents are addressed to preliminary mission design and vehicle sizing.
The Upper Atmosphere Research Satellite (UARS) is a three-axis stabilized Earth-pointing spacecraft in a low-Earth orbit. The UARS onboard computer (OBC) uses a Fourier Power Series (FPS) ephemeris representation that includes 42 position and 42 velocity coefficients per axis, with position residuals at 10-minute intervals. New coefficients and 32 hours of residuals are uploaded daily. This study evaluated two backup methods that permit the OBC to compute an approximate spacecraft ephemeris in the event that new ephemeris data cannot be uplinked for several days: (1) extending the use of the FPS coefficients previously uplinked, and (2) switching to a simple circular orbit approximation designed and tested (but not implemented) for LANDSAT-D. The FPS method provides greater accuracy during the backup period and does not require additional ground operational procedures for generating and uplinking an additional ephemeris table. The tradeoff is that the high accuracy of the FPS will be degraded slightly by adopting the longer fit period necessary to obtain backup accuracy for an extended period of time. The results for UARS show that extended use of the FPS is superior to the circular orbit approximation for short-term ephemeris backup.
Study of optimum low-thrust transfers between neighboring coplanar circular orbits for a simplified system model
Approximate analytical solution for minimum impulse transfer between circular orbit and given hyperbolic velocity vector at infinity
Central angle of travel and time from retrofire as function of circular orbit altitude for reentry
Dynamic stability analysis of two point-mass rotating vehicles tethered in circular orbit
Noncoplanar transfers between neighboring circular orbits are presented for spacecraft using their own low-thrust blow down propulsion system. It is assumed that the out-of-plane angle between the decaying thrust vector and the current orbit plane remains constant for each extended burn. Switching conditions are derived for the cutoff and relight of the propulsion system in order to carry out a given transfer with inclination change. Furthermore the location where the thrust acceleration is initially applied with respect to the line of nodes of the two orbits is uniquely determined. Finally an analytic derivation of the linearized coplanar motion for stationkeeping and terminal rendezvous studies is also presented and a scheme for deriving the second order correction shown.
Existing expressions are used to obtain the minimum propellant fraction required for return from a circular orbit as a function of vacuum trajectory range. trajectory are matched to those of the atmospheric trajectory to obtain a complete return from orbit to earth. The results are restricted by the assumptions of (1) impulsive velocity change, (2) nearly circular transfer trajectory, ( 3) spherical earth, atmosphere, and gravitational field, (4) exponential atmospheric density variation with attitude, and (5) a nonrotating atmosphere. The solutions for the parameters of the vacuum Calculations are made t o determine the effects of longitudinal and lateral range on required propeUant fraction and reentry loading for a nonrotating earth and for several orbital altitudes. the single- and two-impulse method of return is made and the results indicate a "trade off" between propellant fraction required and landing- position accuracy. A comparison of An example of a return mission from a polar orbit is discussed where the initial deorbit point is the intersection of the North Pole horizon with the satellite orbit. Some effects of a rotating earth are also considered. It is found that, for each target-orbital-plane longitudinal difference, there exists a target latitude for which the required propellant fraction is a minimum.
Probability distributions for errors in parameters of near-earth circular orbits with Apollo application
The minimum velocity change rendezvous solutions, when the motion may be linearized about a circular orbit, fall into two separate regions; the phase-for-free region and the general region. Phase-for-free solutions are derived from the optimum transfer solutions, require the same velocity change expenditure, but may not be unique. Analytic solutions are presented in two of the three subregions. An algorithm is presented for determining the unique solutions in the general region. Various sources of initial conditions are discussed and three examples presented.