Exploring Space through Math

1. First Moon Landing 1969 (one minute 44 seconds)
President Kennedy’s vision became reality on July 20, 1969, when Apollo 11
commander Neil Armstrong stepped onto the Moon’s surface. With, “this one small
step for man; one giant leap for mankind,” Neil Armstrong became the first man to
set foot on the Moon.
On January 14, 2004, 34 years after Apollo 11’s historic mission, President George W.
Bush announced a bold new vision for NASA and the future of space exploration.
President Bush’s vision for space exploration includes:
“…completing the International Space Station, developing a new exploration
vehicle…and extending human presence across the solar system starting with a
human return to the Moon by the year 2020, in preparation for human exploration of
Mars and other destinations.”

2. NASA’s Constellation Program represents the future and
the next generation of spacecraft for human exploration.
The Orion spacecraft will carry a new generation of
explorers back to the Moon, Mars, and beyond. As part of
the Constellation Program, Orion will succeed the space
shuttle as NASA’s primary vehicle for human space
exploration.
“Over the past decade, fifteen nations have come together
to design, assemble, occupy, and conduct research inside
and outside of the largest and longest inhabited object to
ever orbit the Earth – the International Space Station (ISS).
Now NASA is working with U.S. industries to develop
commercial spaceflight capabilities to the ISS while building
America’s new human space exploration vehicle, the Orion
Multi-Purpose Crew Vehicle. Using its new space launch
system, Orion will have the capability to take astronauts on
exploration missions farther than any previous missions.
When paired with additional propulsion and life support
systems, Orion will eventually be able to take humans to
Mars.”

4. 7 minute youtube video

5. 1. What is the name of the new spacecraft?
2. Why do we need a new spacecraft?
3. What vehicle does the Orion design resemble?
4. Name some places where NASA intends to travel using Orion.

6. Space exploration incorporates new and existing
technology to continually evolve and change.
Orion’s improved, larger blunt-body is similar to
the shape of the Apollo capsule.
With an outside diameter of 5 meters, Orion will have about three times the volume of an
Apollo capsule. While the Apollo capsule carried three astronauts, Orion is designed to carry
four to six astronauts into space. Although NASA’s intention was not to make the Orion
spacecraft similar to the Apollo capsule, experts found that this design not only met the
requirements but was also the most effective within the safety goals.

7. Determine the area of the largest vertical cross-section of the Orion Crew Exploration
Vehicle (CEV).
This will give you a sense of the surface area inside the Orion CEV. Keep in mind that the
Orion dimensions are 140% of the Apollo capsule.

8. To get a sense of the room inside the crew module, use the model on the graph
paper to estimate the vertical cross-sectional area by counting squares and
multiplying the number of squares by 0.032 m².

9. Using the figure,
decompose the
model of Orion into
familiar geometric
shapes and then
name the shapes.
Use your tablet and
the PicsArt app to use
different colored
highlighters for each
geometric shape to
show the
decomposition into
smaller parts.
Record the shapes
and their
corresponding area
formulas in Table 1.

10. Table 1

11. Based on your calculations in Table 1, what is the total vertical cross-sectional area
of the crew module?
If the actual largest vertical cross-sectional area of the crew module is 11.665 m²,
how far off was your estimate from the graphing method in question 1? Express
your answer in terms of a percent (percent error). Round your answer to the
nearest percent.
If the actual largest vertical cross-sectional area of the crew module is 11.665 m²,
how far off was your estimate decomposition estimate? Express your answer in
terms of a percent (percent error). Round your answer to the nearest percent.
In your groups, discuss which estimation method was closest to the actual area.
Also discuss your approach and methods used to estimate the area with one other
group. Compare your answers.