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Unformatted text preview: The
Mathematics
of Space
Rendezvous NASA has a variety of classroom activities
designed to accompany the video.
Click here to explore. Overview The NASA video illustrates the use of
algebra and estimation in shuttle flight
and rendezvous.
The accompanying slides demonstrate
the problems that the astronauts pose
and provide extra support as the
problems are worked. NASA has developed a learning guide to accompany this video. Rendezvous
Have you ever missed an appointment? How did it make
you feel? How did it make the
other party feel? Rendezvous What is a rendezvous?
See the video for definitions. How can you plan ahead
to get there on time?
How do astronauts
calculate where and
when to meet in space? Math… The Language
of the Universe Mathematics is
an essential part
of space travel.
Mathematics
even helps us
travel on earth. It is more than numbers and symbols! Math… The Language
of the Universe
What instruments did early space
travelers use to calculate
mathematical equations? What instruments do space
travelers use today to calculate
mathematical equations? Math aboard the
Space Shuttle NASA The Shuttle Design
The Launch
Navigation
The Landing
The Rendezvous Rendezvous… Can you think of
examples of rendezvous? Rendezvous… Is like playing frisbee
catch with a dog. Is like a quarterback
throwing a timing
route pass to a wide
receiver. Questions
First: What question needs to be
answered?
When will the target (the Mir) be at the
When
rendezvous site (over Moscow)?
rendezvous The Target
Gather the known facts: Altitude of 400 kilometers.
Orbit is at 92 minutes.
Incline of the orbit is 51.6’.
Earth revolves once
every 24 hours. NASA Find out more about the Mir. The Target
More facts: Moscow is at 37’ E longitude. Mir’s present longitude is at 105’ E. Questions
Review the questions again: When will the target be at the
rendezvous site? When will it pass over
the rendezvous site? Check out where the space station
is right now on this real time site. Questions
What other information do we need
to solve this problem?
Degrees the earth rotates
in the time it takes Mir
to make one orbit. Set Up the Equations
Recall known and previous given facts: 360° in a full circle or
around the earth.
The earth rotates
once in 24 hours.
Mir’s orbit takes 92
minutes. NASA Set Up the Equations The following ratio determines how far the
Earth rotates with each orbit of the Mir
360°
=
x
24 hours
92 min We need these in common terms, let’s
change the hours into minutes.
(24 hours is 1440 minutes) Here is the problem again:
360°
=
1440 min x
92 min Questions
What other information do we need
to solve this problem? How far it is between Moscow and where the space station is currently. The angular distance between
the Mir’s present location
and its rendezvous point is
105o – 37o or 68o. Questions
What other information do we need
to solve this problem? How long it takes Mir to make one orbit. We were given this information earlier. Mir’s orbit takes
92 minutes. Calculate o X= 92 min x 360 = 23o
1440 min
o The Earth rotates 23 each time Mir
circles it once. To rendezvous at the designated
o
location, the Earth must rotate 68 . Calculate Mir must circle Earth.
23
o
68 ÷ orbit or ≈ 3 orbits
o If it takes 92 min per orbit, then
If
min
3 orbits x 92orbit = 276 min = 4.6 hrs Orbital Altitude
How does orbital altitude affect an
objects travel?
Speed
Orbit
Rendezvous Questions
How fast is Mir
traveling in its
orbit? How fast is the
shuttle traveling? How can be at the
same place and
match speed? NASA Gather the Facts Mir’s altitude is 400 km and
speed is 92 min/revolution. The shuttle’s altitude is 298
km and speed is 89
min/revolution. The Earth’s radius is 6,378
km. Known Facts Orbit is almost a
circle Circumference of
a circle
C = 2Π r NASA Known Facts
Equation for speed
Speed = Distance/Time Mir’s Orbit First the formula:
Speed = C (Mir’s orbit) / R (minutes) Then the facts:
Mir orbits at a distance of
6,378 + 400 km Find Mir’s orbit:
C (Mir’s orbit) = 6,778 km x 2(pi)
= 42,578 km per orbit. Mir’s Speed The formula again:
Speed = C (Mir’s orbit) / R (minutes) Put in Mir’s orbit:
Speed = 42,587 km/92 min Solve the equation:
Speed of Mir = 463 km/min
= 27,780 km/hr Speed of the Shuttle First the formula:
Speed = C (shuttle) / R (minutes) Find the shuttle orbital radius:
637 km x 298 km = 41,947 km Put in the facts:
Speed = 41,947 km / 89 min Calculate:
Speed of the Shuttle = 471 km/min = Slow Down to
Rendezvous The space shuttle must slow down
to rendezvous with Mir. To slow down,
the shuttle will climb
to Mir’s higher orbit. Gather the Facts 0.4 meters per second increase in
velocity equals 1 km increase in
altitude. Present altitude
is 298 km. Need to increase
altitude to 305 km. Question
How many meters per
second does the
shuttle need to
increase to rise 7 km? NASA Set Up the Equations
Desired – current = needed increase in altitude
305 km – 298 km = 7 km
Recall: 0.4 m/s increase in velocity =
1 km increase in altitude .
7 (km) / 1 (km) x .4 (m/s) = 2.8 m/s
An increase of 2.8 m/s will increase the orbit
of the shuttle 7 km and actually slow it down! Shuttle Instruments
Shuttle instruments
can show this
process
graphically. The astronauts can
also see the Mir
through the
windows. NASA
Virtual view of Mir through the
shuttle window. Views from Space NASA The video is showing videos
that were taken by the
astronauts. More videos
and photos are available at
NASA’s
web site. Click on this slide to
see more photos. NASA It takes Math to
Rendezvous in Space
The astronauts use both: Computer calculations Math estimation skills Try another math activity with airplanes. Math of the Universe
Whether it is using scientific notation to
measure the microscopic or astronomic,
whether it is estimation or calculus,
mathematics plays a big part in science. Read more about experiments
performed aboard the shuttle
and space station. Math on Earth
The video is showing some
examples of everyday activities that
need math. Can you think of others? Explore a web site with activities focusing on every day math. Math and Rendezvous The video and slides have illustrated a
few problems that the space shuttle
astronauts need to estimate while on a
single space flight.
Space travel and travel on earth have
similarities. Work with your class to
create earth examples of rendezvous. Math and Rendezvous Math is an important
part of making meetings
in space and on earth
prompt and accurate. The Technology Leadership Institute
(TLI) is funded by the United States
Department of Education's Preparing
Tomorrow's Teachers to use
Technology (PT3) Program (Catalyst
grant  P342A990323). ...
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 Winter '08
 JARVIS
 Math, Algebra, International Space Station, Mir

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