The Math of Space Travel: Orbits and Conic Sections with Hidden Figures

Journeys in Film

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Hidden Figures has been a popular success, filling theaters all over the country and receiving many award nominations. Its subject is a previously unheralded group of women whose brilliance and dedication provided a foundation for the space program—the black women known as “human computers” who worked at the NASA Center in Langley, Virginia. Faced with obstacles to their own education and to job prospects because of race and gender, these women succeeded in earning places, and eventually respect, in a workplace dominated by male supervisors and colleagues and marked by segregated facilities, from office to restroom, that reflected life in the pre-civil rights era.

Mathematics is at the heart of the film Hidden Figures. It is mathematics that supports the ambitions of the three principal characters, mathematics that fills their days in West Computing, and mathematics that brings John Glenn and later astronauts back from their missions. Calculating orbits was particularly important, and so was the ability to handle immensely large numbers in a manageable way. This lesson gives students the opportunity to strengthen their skills in both calculating orbits and managing huge numbers.

Lesson 5 begins with an investigation of calculations that involve exponents, and from there leads students to apply those rules to calculations involving large numbers. The intention is that students will see the need for scientific notation when dealing with astronomical distances and develop an intuitive understanding of the notation through several mental arithmetic exercises.

Exponential arithmetic and scientific notation are together in the same lesson in order to highlight the connections between the two. When students struggle with scientific notation, it is often because they have learned exponential arithmetic by rote, and because they have not been led to see the connections between scientific notation and exponents.

The first part of the lesson is a sequence of problems that lead the students through some (but not all) of the calculation rules for exponential expressions. Scientific notation is nominally a middle school standard in most schools. However, discomfort with exponents, and in particular with scientific notation, is widespread at all ages. Scientific notation is used throughout Lessons 5 and 6. It is recommended that you start with the problems at the beginning of Lesson 5. 

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