Transfer orbit

Abstract: This two-part series studies the anatomy of the endgame problem, the last part of the spacecraft trajectory before the orbit-insertion maneuver into the science orbit. The endgame provides large savings in the capture A v, and therefore it is an important element in the design of ESA and NASA missions to the moons of Jupiter and Saturn. The endgame problem has been approached in different ways with different results: the ν ∞ -leveraging-maneuver approach leads to high-Δ ν, short-time-of-flight transfers, and the multibody technique leads to low-Δν, long-time-of-flight transfers. This paper series investigates the link between the two approaches, giving a new insight to the complex dynamics of the multibody gravity-assist problem. In this paper we focus on the multibody approach using a new graphical tool, the Tisserand-Poincare graph. The Tisserand-Poincare graph shows that ballistic endgames are energetically possible and it explains why they require resonant orbits patched with high-altitude flybys, whereas in the ν ∞ -leveraging-maneuver approach, flybys alone are not effective without impulsive maneuvers in between them. We then use the Tisserand-Poincare graph to design quasi-ballistic transfers. Unlike previous methods, the Tisserand-Poincare graph provides a valuable energy-based target point for the design of the endgame and begin-game and a simple way to patch them. Finally, we present two transfers. The first transfer is between low-altitude orbits at Europa and Ganymede using almost half the Δν of the Hohmann transfer; the second transfer is a 300-day quasi-ballistic transfer between halo orbits of the Jupiter-Ganymede and Jupiter-Europa. With approximately 50 m/s the transfer can be reduced by two months.

Abstract: A periodic orbit between Earth and Mars has been discovered that, after launch, permits a space vehicle to cycle back and forth between the planets with moderate maneuvers at irregular intervals. A Space Station placed in this cycler orbit could provide a safe haven from radiation and comfortable living quarters for astronauts en route to Earth or Mars. The orbit is largely maintained by gravity assist from Earth. Numerical results from multiconic optimization software are presented for a 15-year period from 1995 through 2010.

Abstract: The problem of optimal low-thrust transfer between inclined orbits is reformulated within the framework of optimal control theory. The original treatment considered the time-constrained inclination maximization with velocity as the independent variable allowing the use of the theory of maxima. Because the independent variable is double valued for some transfers, two expressions for the inclination change involving inverse-sine functions are needed to describe all possible transfers. The present analysis casts this problem as a minimum-time transfer between given noncoplanar circular orbits and obtains a single analytic expression for the orbital inclination involving a single inverse-tangent function, uniformly valid for all transfers. The D V penalty with respect to the exact transfer solution using the full six-state dynamic equations with optimized thrust proe le during the transfer is shown to be small. I. Introduction A NALYTIC solutions of the low-thrust transfer problem are very useful in preliminary mission analysis as well as spacecraft systems designandoptimization.The overalldesign of asolarelectric transfer vehicle or even an integrated spacecraft requires extensive parametric analyses for optimum sizing of the various power, propulsion, and thermal management systems to maximize delivered payload to the destination orbit. These parametric studies require hundredsofiterations, precluding theuseofthe numerically generated transfer solutions. The analytic solutions are also desirable for future onboard autonomous guidance applications, especially for smaller spacecraft such as in the mini- and microsatellite category where the application of low-thrust technology for orbit maintenance and control is most efe cient. In the early 1960s, Edelbaum 1;2 derived analytic expressions for the maximum change in inclination between two circular orbits of given size with continuous constant acceleration and e xed transfer time. Conversely, he derived an analytic expression for the total 1V needed to carry out the transfer between given inclined circular orbits.ThistheorywaslatergeneralizedbyWieselandAlfano, 3 who allowed for the variation of the out-of-plane or thrust yaw angle during each revolution, unlike Edelbaum, who used the simpler constant yawproe le.Thus, the (a,i)semimajor axisand inclination space was mapped by direct numerical integration of the simplie ed differential equations in a and i, such that the minimum time for a given transfer is read directly from the solution map. InRefs.4and5,theoptimalthrustpitchandyawproe lesrequired for a given transfer were determined in a semianalytic way by also considering discontinuous thrust due to eclipsing. However, these solutions are not analytic and, therefore, are dife cult to implement in systems design optimization software. In Ref. 6, rapid transfer calculations were demonstrated by analytic modeling of the various transfer parameters including shadowing and solar power degradation effects due to the Van Allen radiation belts. The thrust yaw angleisheldconstantthroughoutthetransfer,andtherequiredvalue is determined by iteration. This is not as optimal as the Edelbaum steering solution, which holds the yaw angle constant during each revolution but varies its value from revolution to revolution in an optimal manner. All of these analyses assume that the orbit remains or is forced to be circular after each cycle or revolution.

Abstract: The relative orbit transfer problem associated with the Hill-Clohessy-Wiltshire equations is considered, and the open-time minimum-fuel problem with impulsive control is formulated. In particular, between two elliptic relative orbits of the in-plane motion, optimal three-impulse controllers are constructed. For the out-of-plane motion, optimal single-impulse strategies are obtained. Based on these results and the null controllability with the vanishing energy of the Hill-Clohessy-Wiltshire equations, a design method of feedback controllers with a total velocity change close to the optimal one is proposed. It is shown by simulation results that asymptotic relative orbit transfer is fulfilled by the proposed feedback controllers.