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Graphs and Functions

RBSP Explores the van Allen Radiation Belts

Objectives: Students will learn about NASA’s Radiation Belt Storm Probes (RBSP), Earth’s van Allen Radiation Belts, and space weather through reading a NASA press release and viewing a NASA eClips video segment. Then students will use simple linear functions to examine the scale of the radiation belts and the strength of Earth’s magnetic field.

Mathematics Skill or Topic Area:

Graphs and Functions

Next Gen Science Standards ESS1: Earth’s Place in the Universe; ESS2: Earth’s Systems; ETS2: 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.8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Video Engagement: Space Weather This NASA video segment looks at space weather and examines the major ramifications space weather can have on Earth (6 minutes). View Program

Engage your students with a press release:

Radiation Belt Storm Probes. T Minus One Year.

August has been a busy month for the Radiation Belt Storm Probes and the scientists and engineers preparing the twin RBSP spacecraft (A and B) for their 2012 launch. On August 3, NASA approved a new launch readiness date of August 15, 2012 – exactly one year from today. With that new target date now officially on the calendar, the RBSP team at the Johns Hopkins Applied Physics Laboratory (APL) has recently achieved several major milestones with the integration and testing of the spacecraft.

“We are nearly there with A, and B is only a few weeks behind,” says Jim Stratton, systems engineer for RBSP at the Applied Physics Lab. “We’re very close to having one complete spacecraft.”

What were once bare black octagonal boxes are now recognizable as full-fledged spacecraft, each laden with propulsion systems, power and avionics systems. They’re also (nearly) fully equipped with identical suites of five instruments – designed to survey the harsh environment of the radiation belts that surround Earth – from teams at the University of New Hampshire, University of Iowa, University of Minnesota, New Jersey Institute of Technology and the National Reconnaissance Office. While the final stages of spacecraft assembly occur in one cleanroom, A’s and B’s solar panels and boom assemblies await installation in a neighboring area.

Though building two identical spacecraft simultaneously has its challenges, it also has some benefits. “Spacecraft A hasn’t always been first [for integration and testing],” Stratton explains. “We have a lot of overlap, and we’re able to generate significant efficiencies and apply a lot of lessons learned.”

These instrument teams “collect data from their instruments just like they will in flight,” he continues. “It’s a great opportunity to check ground systems, hardware, and operations teams working together, and we’ve been very successful.”

Press release date line - August 15, 2011

Press release location: [ Click Here ]

Explore math connections with


Problem I - Satellite Solar Electricity - The RBSP satellites use solar panels to generate electricity. Over time, the radiation in the van Allen Belts will cause the panels to produce less and less electricity. Write a linear equation that predicts the power, P, from these panels as the radiation reduces the power by 2% every year since launch, where T is the elapsed time in years from launch (T=0) and the initial power was 600 watts. [Answer: P = 600 - 12T]

Problem II - Radiation in Space - The RBSP satellites are un-crewed and can withstand much higher radiation levels than humans can withstand before the satellites no longer work reliably. The following ordered pairs (D,S) give the amount of radiation the satellites receive as they pass through the van Allen Belts. What is the linear function, S = mD + b, that best represents the amount of radiation in Sieverts, S, the satellites receive for every day, D, that they are inside the van Allen Belts? Note that for an unshielded human, a lethal dose is about 100 Sieverts! Data: (10.0,5.0), (20.0,8.0), (50.0,17.0). [Answer: S = 0.3D +2.0]

Explain your thinking:

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

Evaluate your understanding:

Challenge Problem: Radiation Exposure and Solar Panel Electricity - From your answers to Problems I and II above, what will be the solar panel output power when the accumulated radiation dose to the spacecraft has reached 1000 Sieverts?

[ Answer: From Problem II, solve for D (in days) with S = 1000.0 to get 1000 = 2 + 0.3D therefore D = 3327 days. From Problem I, we have to convert D to years so T = 3327/365 = 9.1 years, then P = 600 - 12(9.1) and therefore P = 491 watts].



3-D Solar System

Extend your new knowledge - Explore Earth's magnetic field in space using the EOSS simulator and a simple function that relates the strength of Earth's magnetic field to a satellite's distance from the center of Earth. [ Open PDF ]