# National Aeronautics and Space Administration

## Space Math @ NASA - Exploring Jupiter ## Common Core State Standards

Mathematics: Expressions and Equations

(8.EE.c.7) Analyze and solve linear equations and pairs of simultaneous linear equations
(HS.Modeling) Graphing utilities, spreadsheets, computer algebra systems, and dynamic geometry software are powerful tools that can be used to model purely mathematical phenomena as well as physical phenomena
(NGSS.MP.2) Reason abstractly and quantitatively
(NGSS.MP.4) Model with mathematics
(NGSS.HSN.Q.A.1) Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays

ELA/Literacy

(RTS.11-12.1) Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account.
(RTS.11-12.2) Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms.

## Next Generation Science Standards

Science and Engineering Practices

(HS-PS2-1) Analyze data using tools, technology or models (computational, mathematical) in order to make valid and reliable scientific claims
(HS-ESS1-1) Develop a model based on evidence to illustrate the relationships between systems or components of a system
(HS-ESS1-2) Construct an explanation based on valid and reliable evidence obtained from a variety of sources including students own investigations, theories, simulations and peer review
(MS-ESS1-3) Analyze and interpret data to determine scale properties of objects in the solar system. [Clarification Statement: Emphasis is on the analysis of data from Earth-based instruments, space-based telescopes, and spacecraft to determine similarities and differences among solar system objects. Examples of scale properties include the sizes of an object’s layers (such as crust and atmosphere), surface features (such as volcanoes), and orbital radius. Examples of data include statistical information, drawings and photographs, and models.]

## Individual Math Challenges

• Problem 568: Ios Volcanoes and Resurfacing Students examine how volcanic activity on Jupiters satellite Io can lead to fresurfacing the entire moon in less than a million years covering all new craters. [Grade: 6-8 | Topics: Surface area of a sphere; rates; scientific notation]
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• Problem 472: Investigating Juno's Elliptical Transfer Orbit Students use the Standard Formula for an ellipse to study the elliptical orbit of the Juno spacecraft, and relate specific properties of the ellipse to features of the spacecrafts trajectory such as aphelion, perihelion, and ellipticity. [Grade: 9-12 | Topics: formula for an ellipse; semi-major and minor axis]
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• Problem 471: Investigating the Launch of the Juno Spacecraft Students use a series of images from a launch video to determine the scale of each image and determine the speed of the rocket as it leaves the gantry. [Grade: 6-8 | Topics: scale models; speed = distance/times]
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• Problem 135 How Big is It? - Io and Jupiter Students work with an image taken by the Cassini spacecraft of Jupiter and its satellite Io. They determine the image scale, and calculate the sizes of various features in the image. [Grade: 4 - 7 | Topics:image scaling; multiply, divide, work with millimeter ruler]
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• Solar Electricity for a New Spacecraft Students explore how solar panels provide the nearly 500 watts of electricity to power its many instruments with three solar panels. [Grade: 4 - 7 | Topics:area; unit conversion]
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• Investigating the Elliptical Orbit of Juno around Jupiter Students work with the equation for an ellipse to determing the spacecraft's orbit equation and from this determine the period of the orbiot using Keplers Third Law [Grade: 9 - 12 | Topics:algebra; trigonometry]
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• ## More Math Challenges

• Problem 470: The Launch of the Juno Spacecraft - Ascent to orbit Students use tabulated altitude and range data following the launch of the Juno mission, to determine the speed of the rocket as it travels to arth orbit. [Grade: 6-8 | Topics: scale models; speed = distance/time]
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• Problem 469: Solar Energy and the Distance of Juno from the Sun Students use the formula for an ellipse, along with the inverse-square law to create a mathematical model that predicts the declining solar power produced by Junos solar panels as the spacecraft travels from Earth to Jupiter. [Grade: 9-12 | Topics: algebra; trigonometry; distance formula]
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• The Speed of the Juno Spacecraft Students use formulae for the distance and speed of the Juno spacecraft to determine the speed as a function of angular position along the orbit. [Grade: 9-12 | Topics: algebra; trigonometry; algebraic formula; parametric equations]
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• Investigating the Radiation Belts around Jupiter Students use formula for the radiation intensity along the spacecraft orbit to determine the total radiation dose of the spacecraft by adding up the area under the curve through approximations. [Grade: 9-12 | Topics: algebra; trigonometry; algebraic formula]
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