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The Virtual Telescope for X-ray Observations (VTXO) will use lightweight Phase Fresnel Lenses (PFLs) in a virtual X-ray telescope with $\sim$1 km focal length and with $\sim$50 milli-arcsecond angular resolution. VTXO is formed by using precision formation flying of two SmallSats: a smaller OpticsSat that houses the PFLs and navigation beacons while a larger DetectorSat contains an X-ray camera, a precision start tracker, and the propulsion for the formation flying. The baseline flight dynamics uses a highly elliptical supersynchronous orbit allow the formation to hold in an inertial frame around the 90,000 km apogee for 10 hours of the 32.5 hour orbit with nearly a year mission lifetime. VTXO's fine angular resolution enables measuring the environments close to the central engines of bright compact X-ray sources. This X-ray imaging capability allows for the study of the effects of dust scattering near to the central objects such as Cyg X-3 and GX 5-1, for the search for jet structure near to the compact object in X-ray novae such as Cyg X-1 and GRS 1915+105, and for the search for structure in the termination shock of in the Crab pulsar wind nebula. The VTXO SmallSat and instrument designs, mission parameters, and science performance are described. VTXO development was supported as one of the selected 2018 NASA Astrophysics SmallSat Study (AS$^3$) missions., Comment: 6 pages, 7 figures, corrected version, Proceedings Volume 11444, Space Telescopes and Instrumentation 2020: Ultraviolet to Gamma Ray; 114447V (2020). arXiv admin note: text overlap with arXiv:2006.12174

The formation flying of an occulter with a telescope at the Sun-Earth L2 (SEL2) Libration Point can be a challenging problem. A good knowledge of the Restricted Three Body Problem dynamics is required to understand how these two spacecraft interact with each other in the SEL2 unstable environment, and how other perturbations such as Solar Radiation Pressure (SRP) affect their mutual trajectories. This paper focuses on the transfer trajectories to achieve specific relative positions between two spacecraft as they fly in formation at SEL2, andanalyzes the relevance of SRP in this formation, using the Wide-Field Infrared Survey Telescope (WFIRST) and the Starshade occulter as an example. Given that WFIRST and Starshade have very different area-to-mass ratios, SRP will affect their motion in different ways, and their relative position can be key to reduce the V cost. In this paper we intend on providing an explanation on how the relative position between both spacecrafts affects the transfer V from one observation to the other using dynamical system theory and Floquet modes.

In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.

Innovative trajectory design tools are required to support challenging multi-body regimes with complex dynamics, uncertain perturbations, and the integration of propulsion influences. Two distinctive tools, Adaptive Trajectory Design and the General Mission Analysis Tool have been developed and certified to provide the astrodynamics community with the ability to design multi-body trajectories. In this paper we discuss the multi-body design process and the capabilities of both tools. Demonstrable applications to confirmed missions, the Lunar IceCube Cubesat lunar mission and the Wide-Field Infrared Survey Telescope (WFIRST) Sun-Earth L2 mission, are presented.