L e s s o n
5
(MATHEMATICS)
71
J o u r n e y s i n F i l m
: H i d d e n F i g u r e s
The Math of Space Travel:
Orbits and Conic Sections
Enduring Understandings
•
In many cases, the orbits of planets and of spacecraft
can be described as ellipses or hyperbolas.
•
Circles and ellipses are related by scaling. Circles,
ellipses, parabolas, and hyperbolas can be generated
by slicing certain 3D figures.
•
Distances in space are enormous, far beyond everyday
human experience. Scientific notation is an effective
way to make calculations with the large numbers
inherent to orbital calculations.
•
Essential Questions
•
How can the orbits of planets and manmade satellites
be represented mathematically? What physical
representations can we make of orbital paths?
•
How do dilations and scale factors relate geometric
shapes to each other and also enable the visualization
of large distances?
•
How can the large numbers inherent in orbital
calculations be handled in an efficient manner?
Notes to the Teacher
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

72
J o u r n e y s i n F i l m
: H i d d e n F i g u r e s
The second part of the lesson is designed as a “from first-
principles” investigation of ellipses and how they relate to
German mathematician and astronomer Johannes Kepler’s
first and second laws. The goal in many cases is not to
construct a mathematical proof of the claims made, but
only to examine why they might be reasonable. For a more

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- Winter '17
- Mrs. Manternach
- English