Search results for "Circular orbit"
showing 10 items of 11 documents
Optimal Starting Conditions for the Rendezvous Maneuver, Part 1: Optimal Control Approach
2008
We consider the three-dimensional rendezvous between two spacecraft: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular trave…
Guidance Trajectories for Spacecraft Rendezvous
2007
In a previous paper of Miele et al. (J. Optim. Theory Appl. 132(1), 2007), we employed the single-subarc sequential gradient-restoration algorithm to optimize the three-dimensional rendezvous between a target spacecraft in a planar circular orbit and a chaser spacecraft with an initial separation distance and separation velocity. The achieved continuous solutions are characterized by two, three, or four subarcs depending on the performance index (time, fuel) and the constraints. In this paper, based on the solutions in Miele et al. (J. Optim. Theory Appl. 132(1), 2007), we employ the multiple-subarc sequential gradient-restoration algorithm to produce pieced guidance trajectories implementa…
Optimal Trajectories for Spacecraft Rendezvous
2007
The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the ti…
Reflections on the Hohmann Transfer
2004
Walter Hohmann was a civil engineer who studied orbital maneuvers in his spare time. In 1925, he published an important book (Ref. 1) containing his main result, namely, that the most economical transfer from a circular orbit to another circular orbit is achieved via an elliptical trajectory bitangent to the terminal orbits. With the advent of the space program some three decades later, the Hohmann transfer maneuver became the most fundamental maneuver in space. In this work, we present a complete study of the Hohmann transfer maneuver. After revisiting its known properties, we present a number of supplementary properties which are essential to the qualitative understanding of the maneuver.…
Rendezvous Guidance Trajectories via Multiple-Subarc Sequential Gradient-Restoration Algorithm
2009
We consider the three-dimensional rendezvous between a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and an initial separation velocity. We assume that the chaser spacecraft has variable mass and that its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We employ the Clohessy–Wiltshire equations, describing the relative motion of the chaser vis-a-vis the target, and the multiple-subarc sequential gradient-restoration algorithm to produce first optimal trajectories and then guidance trajectories for the following problems: P1—minimum time, fuel free; P2—minimum fuel, ti…
Measurements of relativistic time dilatation for positive and negative muons in a circular orbit
1977
The lifetimes of both positive and negative relativistic (γ = 29.33) muons have been measured in the CERN Muon Storage Ring with the results τ+ = 64.419 (58) µs, τ− = 64.368 (29) µs The value for positive muons is in accordance with special relativity and the measured lifetime at rest: the Einstein time dilation factor agrees with experiment with a fractional error of 2×10−3 at 95% confidence. Assuming special relativity, the mean proper lifetime for μ− is found to be τ0− = 2.1948(10) µs the most accurate value reported to date. The agreement of this value with previously measured values of τ0+ confirms CPT invariance for the weak interaction in muon decay.
GSC 07396-00759 = V4046 Sgr C[D]: A Wide-separation Companion to the Close T Tauri Binary System V4046 Sgr AB
2011
We explore the possibility that GSC 07396-00759 (spectral type M1e) is a widely separated (~2.82', or projected separation ~12,350 AU) companion to the "old" (age ~12 Myr) classical T Tauri binary system V4046 Sgr AB, as suggested by the proximity and similar space motions of the two systems. If the two systems are equidistant and coeval, then GSC 07396--00759, like V4046 Sgr AB, must be a spectroscopic binary with nearly equal-mass components, and V4046 Sgr must be at least ~8 Myr old. Analysis of a serendipitous Chandra X-ray gratings spectrum and light curve as well as XMM-Newton light curves and CCD spectra of GSC 07396-00759 obtained during long exposures targeting V4046 Sgr AB reveals…
Kinematic relative velocity with respect to stationary observers in Schwarzschild spacetime
2013
We study the kinematic relative velocity of general test particles with respect to stationary observers (using spherical coordinates) in Schwarzschild spacetime, obtaining that its modulus does not depend on the observer, unlike Fermi, spectroscopic and astrometric relative velocities. We study some fundamental particular cases, generalizing some results given in other work about stationary and radial free-falling test particles. Moreover, we give a new result about test particles with circular geodesic orbits: the modulus of their kinematic relative velocity with respect to any stationary observer depends only on the radius of the circular orbit, and so, it remains constant.
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
2007
Abstract This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of Epenoy et al. (1997) where the optimal trajectories of the energy minimization problem are approximated using averaging techniques. The averaged Hamiltonian system is explicitly computed. It is related to a Riemannian problem whose distance is an approximation of the value function. The extremal curves are analyzed, proving that the system remains integrable in the coplanar case. It is also checked that the metric associated with coplanar transfers towards a circular orbit is flat. Smoothness of small Riemannian spheres ensures global opti…
Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits
2015
International audience; The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using the standard tools of Riemannian geometry (curvature computations, geodesic convexity), the time minimal case is associated to a Finsler metric which is not smooth. Nevertheless a qualitative analysis of the geodesic flow is given in this article to describe the optimal transfers. In particular we prove geodesic convexity of the elliptic domain.