This paper describes the processes and results of Verification and Validation (V&V) efforts for the General Mission Analysis Tool (GMAT). We describe the test program and environments, the tools used for independent test data, and comparison results. The V&V effort produced approximately 13,000 test scripts that are run as part of the nightly buildtest process. In addition, we created approximately 3000 automated GUI tests that are run every two weeks. Presenting all test results are beyond the scope of a single paper. Here we present high-level test results in most areas, and detailed test results for key areas. The final product of the V&V effort presented in this paper was GMAT version R2013a, the first Gold release of the software with completely updated documentation and greatly improved quality. Release R2013a was the staging release for flight qualification performed at Goddard Space Flight Center (GSFC) ultimately resulting in GMAT version R2013b.

N-tert-Butylsulfonyl and N-tert-butylsulfinyl aziridine undergo alpha-lithiation/electrophile trapping providing a new entry to terminal aziridines. With N-tert-butylsulfinyl aziridine complete asymmetric induction is observed alpha to nitrogen.

Deprotonation of terminal epoxides and aziridines with organolithium/diamine combinations or lithium amides allows the regio- and stereoselective formation of α-lithiated species. Judicious choice of reaction conditions allows these species to operate as nucleophiles, enolate equivalents, vinyl cation equivalents, or carbenes.

One of the most interesting and challenging aspects of formation guidance algorithm design is the coupling of the orbit design and the science return. The effectiveness of the formation as a science instrument is intimately coupled with the relative geometry and evolution of the collection of spacecraft. Therefore, the science return can be maximized by optimizing the orbit design according to a performance metric relevant to the science mission goals. In this work, we present a general method for optimal formation guidance that is applicable to missions whose performance metric, requirements, and constraints can be cast as functions that are explicitly dependent upon the orbit states and spacecraft relative positions and velocities. The approach is fully nonlinear, accommodates orbital perturbations, and is applicable to multiple flight regimes including highly eccentric, hyperbolic, interplanetary, or libration point orbits. Furthermore, the method is applicable to small formations, as well as large formations and constellations. We present a general form for the cost and constraint functions, and derive their semi-analytic gradients with respect to the formation initial conditions. The gradients are broken down into two types. The first type are gradients of the mission-specific performance metric with respect to formation geometry. The second type are derivatives of the formation geometry with respect to the orbit initial conditions. The fact that these two types of derivatives appear separately allows us to derive and implement a general framework that requires minimal modification to be applied to different missions or mission phases. To illustrate the applicability of the approach, we conclude with applications to two missions: the Magnetospheric Multiscale Mission, and the Laser Interferometer Space Antenna. Nomenclature A = upper left 3 3 partition of B = upper right 3 3 partition of C = lower left 3 3 partition of c k = quadrature constant at point k D = lower right 3 3 partition of m = no. of unique sides in the formation N = no. of path constraints n = no. of spacecraft n k = no. of quadrature points r = position vector s ik = vector defining side i at quadrature point k _ s ik = rate vector of side i at quadrature point k s ik = length of side i at quadrature point k _ s ik = rate of change in length of side i at quadrature point k v = velocity vector = orbit state transition matrix Subscripts C = indicates association with constraints i = side index J = indicates association with cost function j = spacecraft index k = quadrature point index ' = spacecraft index p = dummy index

While there is growing interest in implementing future NASA Earth Science missions as Distributed Spacecraft Missions (DSMs), there are currently very few tools available to help in the design of DSMs. The objective of our project is to provide a framework that facilitates DSM Pre-Phase A investigations and optimizes DSM designs with respect to a-priori Science goals. Our Trade-space Analysis Tool for Constellations (TAT-C) enables the investigation of questions such as: "Which type of constellations should be chosen? How many spacecraft should be included in the constellation? Which design has the best cost/risk value?". This paper provides a description of the TAT-C tool and its components.