![]() ![]() Cape Canaveral, Florida) and orbital trajectory. One of the earliest papers that Johnson coauthored, “ Determination of Azimuth Angle at Burnout for Placing a Satellite over a Selected Earth Position,” deals with the problem of making sure that a satellite can be placed over a specific Earth location after a specified number of orbits, given a certain starting position (e.g. Placing a Satellite over a Selected Position The movie doesn’t focus much on the math details of the types of problems Johnson and her team dealt with, but for the purposes of this blog, I hope to provide at least a flavor of the approaches one might have used in Johnson’s day compared to the present. Where the movie mentions the solving of differential equations using Euler’s method, I will compare this method with more modern ones in an important problem of rocketry: computing a reentry trajectory from the rocket equation and drag terms (derived using atmospheric model data obtained directly from within the Wolfram Language). ![]() For the orbit calculation, I will first exactly follow what Johnson did and then compare with a more modern, direct approach utilizing an array of tools made available with the Wolfram Language. I will touch on two aspects of her scientific work that were mentioned in the film: orbit calculations and reentry calculations. Computers were in their early days at this time, so Johnson and her team’s ability to perform complicated navigational orbital mechanics problems without the use of a computer provided an important sanity check against the early computer results. The movie focuses heavily on the dramatic civil rights struggle of African American women in NASA at the time, and these struggles are set against the number-crunching ability of Johnson and her coworkers. The movie details the hidden story of Katherine Johnson and her coworkers ( Dorothy Vaughan and Mary Jackson) at NASA during the Mercury missions and the United States’ early explorations into manned space flight. It also deals with an important time in US history, touching on a number of topics, including civil rights and the Space Race. The movie Hidden Figures was released in theaters recently and has been getting good reviews. ![]()
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