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Module 1
 Words into Mathematics

The Changing Altitude of the International Space Station
 Objectives: Students will learn more about how the orbit of the International Space Station changes as a result of atmospheric drag through reading a NASA press release and viewing a NASA eClips video segment. Then students will read a paragraph describing the increases and decreases in the orbit altitude to calculate the final orbit altitude.

Mathematics Skill or Topic Area:

Words into Mathematics

Next Gen Science Standards PS3: Energy; ETS 2: Links among engineering, technology, science, and society

Common Core ELA for Science: RST.6-8.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions. RST.6-8.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.6-8.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.

Common Core Math Standard: CC.7.EE.3 Solve multi-step real-life problems posed with positive and negative rational numbers in any form (whole numbers, fractions or decimals) using tools strategically.

Video Engagement: Keeping the ISS in Orbit This video shows the actions being taken by NASA to counteract atmospheric drag on the International Space Station to prevent orbit decay and premature re-entry (6 minutes).View Program

 Engage your students with a press release: Higher Altitude Improves Station's Fuel Economy For most of the last decade, as astronauts and cosmonauts orbited the Earth aboard the International Space Station they were circling the globe at an altitude of approximately 220 statute miles, or about 350 kilometers. When the European Space Agency’s resupply ship Johannes Kepler, known also as Automated Transfer Vehicle 2 (ATV2) arrives at the space station later this month, it will bring the fuel needed to boost the station to its normal planned altitude of 248 miles, or 400 kilometers. “The key reason for moving to the higher altitude is to save propellant over the long term as we protect against increased solar activity, said Bill Spetch, of the space station program’s Systems Engineering, Analysis and Integration Office. “As solar activity rises, the atmospheric density in our altitude range increases causing increased drag on the vehicle. This in turn causes us to have to raise the orbit more often.” Even though the space station orbits in what most people on Earth would consider to be the “vacuum of space,” there still are enough atmospheric molecules that they cause a minute but continuous lowering of its altitude, or height above the Earth. To fight this tendency, thrusters on the space station or visiting vehicles such as the space shuttle, Progress resupply vehicles or ATVs are fired periodically to “reboost” the station. These reboosts, however, come at the cost of fuel, or propellant, that must be launched from Earth at significant cost. Press release date line - February 14, 2011 Press release location: [ Click Here ]

Explore math connections with

SpaceMath@NASA

Problem I - ISS Altitude Changes - Students read an essay describing the increases and decreases in the International Space Station orbit, and calculate the final orbit altitude after all the changes are applied. Topics include adding positive and negative numbers. [Open PDF]

Problem II - ISS Altitude Graph - Students use a plot of the altitude of the ISS to predict its atmospheric entry year after the peak of the next solar activity cycle. Topics include extrapolating a simple graph, estimation, and forecasting. [Open PDF]

Write your own problem - Using information found in the Math Connection problems, the press release or the video program, create your own math problem that involves ISS altitude changes and solve it. Explain why you set the problem up this way, and how you might find its answer.

Challenge Problem - The altitude of the ISS on February 22, 2012 was 400 kilometers, and it was decreasing by about 30 kilometers per year. Suppose that there were no reboosts of its orbit. By what year and month would the ISS reach an altitude of 250 kilometers where burn-up is likely? Explain how you arrived at this answer.

Answer: The ISS would need to lose 400 km - 250 km = 150 km of altitude. At a rate of 30 km/yr, the time it would take is about 150 km/(30 km/y) = 5 years, so the burn-up date would be about February, 2017.

NASA / JPL

3-D Solar System

Extend your new knowledge - Use the on-line, NASA/JPL 3-D solar system simulator to measure the altitude of the International Space Station and show its changes over time. [ Open PDF ]

For a real-time view of the ISS altitude you can also visit the NASA Space Flight website.