This paper assumes a requirement for an unmanned multiunit satellite to be assembled in orbit. The requirement to be met is to bring the satellites together so tha t they do not collide but actually rendezvous. The equations of motion of the rendezvous satellite in a relative coordinate system are derived and used to compute a final injection velocity which would effect collision after a time r. The velocity is corrected periodically by a command guidance system and just before impact retrothrust is applied. A terminal infrared homing sj^stem is required to actually accomplish physical contact and joining of the satellites. The first satellite placed in orbit is the "control satellite" and controls all the satellites to be assembled and contains the ccmputer, command guidance equipment, precision orientation equipment, and other features necessary to effect rendezvous. The succeeding satellites contain a propulsion system, a rough at t i tude control system, and a command receiver plus whatever scientific equipment they carry to perform their basic mission. This paper presents the following:

Terminal Guidance System for Satellite Rendezvous

Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

Search for New Physics with Atoms and Molecules

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Studies in Surface Science and Catalysis

Atomic clocks have been instrumental in science and technology, leading to innovations such as global positioning, advanced communications, and tests of fundamental constant variation. Timekeeping precision at 1 part in 10 18 enables new timing applications in relativistic geodesy, enhanced Earth- and space-based navigation and telescopy, and new tests of physics beyond the standard model. Here, we describe the development and operation of two optical lattice clocks, both using spin-polarized, ultracold atomic ytterbium. A measurement comparing these systems demonstrates an unprecedented atomic clock instability of 1.6 × 10 –18 after only 7 hours of averaging.

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An atomic clock with $10^{-18}$ instability

Chern-Simons Modified General Relativity

This is a modern textbook that guides the reader trough the theory and practice of satellite orbit prediction and determination. Starting from basic principles of orbital mechanics, it covers elaborate force models as well as precise methods of satellite tracking. Emphasis is on numerical treatment and a multitude of algorithms adopted in modern satellite trajectory computation are described in detail. Numerous exercises and applications are provided and supplemented by a unique collection of computer programs with associated C++ source codes included on the accompanying CD-ROM. These programs are built around a powerful spaceflight dynamics library well suited to the development of inividual applications. An extensive collection of Internet resources is provided through WWW hyperlinks to detailed and frequently updated online information on spaceflight dynamics. The book addresses students and scientists working in the field of navigation, geodesy and spaceflight technology, as well as satellite engineers and operators focusing on spaceflight dynamics.

Satellite Orbits: Models, Methods and Applications

Review and comparison of active space debris capturing and removal methods

Reduced dynamic orbit determination using GPS code and carrier measurements

The three-dimensional nature of Global Positioning System (GPS) measurements provides a unique opportunity for accurately determining the position and velocity of satellites in low Earth orbit (LEO). For optimum results a reduced dynamic technique is commonly preferred, which combines the merits of kinematic positioning techniques with those of a fully dynamic trajectory modeling. As part of the present study two different approaches to reduced dynamic orbit determination are compared, both of which involve the estimation of empirical accelerations on top of a precise deterministic force model. In the batch least-squares estimator piece-wise constant accelerations are adjusted in consecutive sub-intervals that are sufficiently short compared to the orbital period. The extended Kalman filter/smoother approach, on the other hand, estimates the empirical accelerations using a first-order Gauss–Markov process noise model. Software implementations of both estimation methods have been used with GPS measurements of the GRACE mission to assess the individual merits of the different filtering schemes. Both approaches are shown to provide accurate and compatible results, which match an external reference solution to better than 5 cm when processing dual-frequency data and better than 10 cm when using single-frequency measurements. While the extended Kalman filter/smoother requires less computer resources in terms of memory and processing time, the batch least-squares estimator ensures a better smoothness of the resulting trajectory and was found to be more robust in case of data gaps.  2005 Elsevier SAS. All rights reserved. Zusammenfassung Die drei-dimensionale Natur von Messungen des Global Positioning System (GPS) schafft eine ideale Voraussetzungen zur genauen Bestimmung der Position und Geschwindigkeit eines Raumfahrzeuges im niedrigen Erdorbit (LEO). Beste Ergebnisse lassen sich dabei mit reduziert-dynamischen Verfahren erzielen, die die Vorteile einer kinematischen Positionierung mit denen einer streng-dynamischen Bahnmodellierung verbinden. Im Rahmen der vorliegenden Studie werden zwei verschiedene Ansatze zur reduziert-dynamischen Bahnbestimmung verglichen, die beide auf der Schatzung empirischer Beschleunigungen in Kombination mit einem prazisen Kraftemodell basieren. Bei Ausgleichung nach der Methode der kleinsten Quadrate werden abschnittsweise konstante Beschleunigungen in Intervallen geschatzt, die ausreichend klein gegenuber der Bahnperiode sind. Beim “Extended Kalman-Filter/Smoother” werden die Beschleunigungen direkt unter Annahme eines Gauss–Markov-Prozesses erster Ordnung geschatzt. Implementierungen beider Verfahren wurden zur Prozessierung von GPS-Daten der GRACE Mission eingesetzt, um die jeweiligen Vorteile zu bewerten. Beide Ansatze liefern genaue und kompatible Ergebnisse, die mit externen Referenzlosungen bei Nutzung von Zweifrequenzmessungen auf besser als 5 cm und bei Einfrequenzmessungen auf besser als 10 cm ubereinstimmen. Wahrend der “Extended Kalman-Filter/Smoother” geringere Speicher-Resourcen und Rechenzeit

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Reduced dynamic orbit determination using GPS code and carrier measurements Reduziert-dynamische Bahnbestimmung mit GPS Code- und Phasenmessungen

PRISMA is a technology demonstration mission for satellite formation ﬂying and in-orbit servicing. The space segment comprises the fully maneuverable Main minisatellite and the smaller Target satellite in a low Earth orbit at 700-km altitude. A key mission objective is to demonstrate onboard, fully autonomous, robust, safe, and precise formation ﬂying of spacecraft. This is accomplished by spaceborne global positioning system navigation, guidance, and control functionalities for the maintenance of the relative motion between the two spacecraft. An innovative estimation approach employs a common Kalman ﬁlter for the absolute states of Main and Target, which accounts for the interdependency of absolute and relative navigation without the need for an explicit relative state. As a result, the onboard navigation system provides absolute and relative orbit information in real time with a position accuracy of 2 and 0.1 m, respectively. The formation control achieves accuracies of a few tenths of meters with minimum usage of thrusters. The guidance and control concept is detailed with emphasis on a relative eccentricity and inclination vector separation strategy. The paper derives estimates of the expected relative orbit control performances based upon realworld simulations using typical global positioning system receiver and propulsion system characteristics.

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Eberhard Gill

Papers

Satellite Orbits: Models, Methods and Applications

Review and comparison of active space debris capturing and removal methods

Reduced dynamic orbit determination using GPS code and carrier measurements

Reduced dynamic orbit determination using GPS code and carrier measurements Reduziert-dynamische Bahnbestimmung mit GPS Code- und Phasenmessungen

Autonomous Formation Flying for the PRISMA Mission