The aim of this IRAD is to produce a generic launch window analyzer (SWM) that allows for large-scale rapid analysis of a launch window and orbit design\u00a0trade space.\u00a0 This will be \"game-changing\", preventing missions that are in early definition studies, for instance in the Mission Design Lab (MDL), or new business efforts, from going into blind alleys.\u00a0 The domain of applicability will be those missions whose orbit is well-modeled as Keplerian or perturbed Keplerian and includes a vast majority of missions (science, exploration, defense, or commercial), including many involving the new class of low-thrust small satellite platforms.

Using a set of accurate analytic Variation of Parameters (VOP) equations for orbit propagation, and a method for defining and 'mixing-and-matching' various mission constraints, the tool will allow flight projects to e.g. quickly determine launch opportunities, and explore the effects on these of relaxing mission constraints. The basic concepts involve taking advantage of the geometric notion of an orbit, the definition\u00a0of a 'perturbation', and idea of 'geometric proxies'. Let us take these concepts in turn to better describe what SWM does.\u00a0 The notion of an orbit is predicated on the use of Keplerian orbit elements to describe the trajectory of the spacecraft as if it were a 'bead on an elliptically-shaped wire'.\u00a0 That is to say that the semi-major axis and eccentricity describe the shape and size of the wire; the inclination, right-ascension of ascending node, and argument of perigee describe the wire's spatial orientation; and the true anomaly describes where on the wire the bead can be found.\u00a0 The concept of perturbation allows us to think about this elliptically-shaped wire\u00a0as slowly changing its shape, size, and orientation as the spacecraft 'feels' a variety of environmental effects such as higher-order terms in the geopotential, luni-solar gravitational pull, solar radiation pressure, and atmospheric drag.\u00a0 Note that the application of delta-Vs are accomplished by discontinuously changing the orbit using standard methods. These two concepts are traditional 'textbook' ideas.\u00a0 The distinguishing trait of SWM is the marriage of these ideas with the notion of a geometric proxy.\u00a0 To illustrate the idea of a geometric proxy, consider a typical space science mission that wants to place spacecract in situ in the Earth's geomagnetic tail.\u00a0 The geomagnetic tail lies in or near the shadow of the Earth.\u00a0 In SWM, the orbit is then mapped into a geometric coodainte frame which moves as the Earth moves about the Sun such that one of its axes always lies along the Earth-Sun line and another of its axes lies along the ecliptic pole.\u00a0 In this frame the Keplerian elements are 'moving' such that the line-of-apsides advances like the hands of a clock.\u00a0 The action of the perturbations serves to either enhance or retard this motion. Thus the orbit's motion can be mapped into this frame where the geomagnetic tail and the shadow cast by the Earth are essentially fixed.\u00a0 The final step is then use the geometric properties of the orbit and the geometric properties of the geomagnetic tail and the shadow region to simply predict the how much time is spent in the tail compared with the time spent in shadow.\u00a0 Using the geometric proxies, the mission desing space can be quickly explored and, with a few more steps to describe how this orbit is established from launch, a launch window can be generated. \u00a0

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