Advanced Space Math Activities (Grades 9-12)

Advanced Space Math

This section introduces advanced learners to the wonders of the universe through foundational mathematics. Designed for high school educators and students, from grades 9-12+, these activities apply critical math skills, including algebra, calculus, data analysis, geometry, logarithms, trigonometry, and scientific notation, to real-world NASA missions and astrophysical phenomena.

Table of Contents (Anchor Menu)

To help you easily navigate this extensive library, resources have been subcategorized by Core Math Skills. Use the Table of Contents below to jump directly to the materials that best fit your classroom's needs.

Algebra, Equations & Functions ↓	Calculus ↓	Data Analysis & Graphing ↓	Geometry, Measurements and Formulas↓
Logarithms↓	Rates, Ratios & Conversions↓	Scientific Notation↓	Trigonometry↓

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Algebra, Equations & Functions

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Resource Title & Link	Description
Exponential Functions and Atmospheric 'Scale heights' (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page15.pdf) ↗	In these math problems students are guided in the study of the way a planet's atmosphere changes as its temperature is changed using exponential functions.
SAGE- Light Attenuation Using Exponential Functions (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page96.pdf) ↗	In these three problems students work with the extinction formula for light and see how light dimming is an exponetial process.
SAGE- Three Mathematical Ways to Describe Light Extinction (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page101.pdf) ↗	In these four problems students explore the three common ways that scientists record extinction using base-10 and base-e functions.
SAGE- Investigating Opacity and Extinction (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page106.pdf) ↗	In these two problems students work with the properties of filters to prove that the product of exponentials leads to the sum of their exponents.
Global Warming and the Sun’s Evolving Luminosity (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page65.pdf) ↗	In these five problems students work with two functions that relate the brightness of the sun to its age and the temperature of earth to the suns brightness.
Modeling the Keeling Curve with Excel (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page54.pdf) ↗	In these three math problems students create a mathematical model of the growth curve of atmospheric carbon dioxide using an Excel Spreadsheet, and create a future forecast for 2050.
The Temperature of Earth without Carbon Dioxide (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page63.pdf) ↗	In these two math problems students study a computer model to determine the temperature of Earth if there were no carbon dioxide in the atmosphere.
The 2011 Japan Earthquake Rocks the Earth (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page72.pdf) ↗	In these three math problems, students use a simple physical model to explore the principle by which the Japan Earthquake of 2011 caused Earth's rotation to spin up by 1.8 microseconds.
Kepler 10b - A matter of gravity (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page58.pdf) ↗	In these three math problems tudents use the measured properties of the Earth-like planet Kepler 10b to estimate the weight of a human on its surface.
Estimating the Temperatures of Exoplanets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page14.pdf) ↗	In these four math problems students review the basic properties of ellipses by exploring the orbits of newly-discovered planets orbiting other stars.
The Grail and LRO Encounter in Lunar Orbit (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page48.pdf) ↗	In these four math problems students explore the May 31, 2012 encounter between NASA's Grail and LRO spacecraft in orbit around the moon.
Grail Satellites Create a Gravity Map of the Moon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page28.pdf) ↗	In these four math problems students explore the gravity field of the moon, and the behavior of simple pendulum clocks in places on the moon where the local gravity is slightly different.
Tidal Forces: Let 'er rip! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page49.pdf) ↗	In these three math problems students explore tidal forces and how satellites are destroyed by coming too close to their planet.
The Volume of a Hypersphere (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page89.pdf) ↗	In these four math problems students understand volume of higher-dimensional spheres and their unusual properties in dimensions 4 through 10.
How Hot is That Planet? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page61.pdf) ↗	In these three math problems students use a simple function to estimate the temperature of a recently discovered planet called CoRot-7b.
Stellar Temperature; Size and Power- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page44.pdf) ↗	In these four math problems students work with a basic equation to explore the relationship between temperature, surface area and power for a selection of stars.
Exploring Artificial Gravity (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page59.pdf) ↗	In these three math problems students work with centrifugal forces to calculate the acceleration of County Fair rides, rotating spacecraft, and the acceleration of rockets to see if artificial gravity can be created.
The Higgs Boson and the Mystery of Mass (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page86.pdf) ↗	In these four math problems students explore how the mass of this particle is believed to depend on the energies used to form it by studying a simple quartic polynomial.
The Energy of Empty Space (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page87.pdf) ↗	In these eight math problems students explore the energy of 'empty space' and its relationship to the mass of the Higgs Boson using a simple quartic polynomial.
Oscillating Spheres (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page6.pdf) ↗	In this math activity students use a mathematical model to calculate the period of oscillation of a star, a planet, and a neutron star from the estimated densities of these bodies.
Calculating the Thickness of a Neutron Star Atmosphere (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page78.pdf) ↗	In these three math problems students determine the thickness of the carbon atmosphere of the neutron star Cas-A using Earth's atmosphere and a set of scaling relationships.
Asteroids and Ice (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page154.pdf) ↗	In these two math problems students calculate how much ice may be present on the asteroid 24-Themis based on recent discoveries by NASA.
The Closest Approach of Asteroid 2005YU55 - III (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page27.pdf) ↗	In these five math problems students work with the equation of a circle and line to find the orbit intersection points, midpoint, and closest distance to earth.
Close Encounters of the Asteroid Kind! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page26.pdf) ↗	In these two math problems students use a simple formula to calculate the brightness of these asteroids from their distance and size.
Computing the Orbit of a Comet (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page156.pdf) ↗	In these four math problems students use data from the orbit of Halley's Comet to determine the equation for its elliptical orbit.
Pluto's Fifth Moon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page3.pdf) ↗	In these three math problems students explore Kepler's Third Law and estimate the orbit period of a hypothetical sixth moon using the distance,period law.
MESSENGER Explores the Mass of Mercury (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page45.pdf) ↗	In these four math problems students use the orbit of NASA's MESSENGER spacecraft to determine the mass of Mercury.
The Most Massive Stars Known (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page22.pdf) ↗	In these three math problems students study the lifespans of the most massive stars known.
The Radioactive Dating of a Star in the Milky Way! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page5.pdf) ↗	In these four math problems students explore Cayrel's Star using a radioisotope dating technique involving the decay of uranium-238.
Star Light...Star Bright (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page104.pdf) ↗	In these four math problems students use a simple polynomial function is used to determine the temperature of a star from its brightness at two different visible wavelengths.
Kepler probes the interior of red giant stars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page80.pdf) ↗	In these three math problems students use the properties of circular arcs to explore sound waves inside stars.
HST - Exploring Two Nearby Stars to the Sun. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page118.pdf) ↗	In these two math problems students explore two nearby stars Ross 128 and Gliese 445 and determine when they will be the nearest stars to our sun by working with quaddratic equations that model their distances.
Estimating the Size and Mass of a Black Hole (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page81.pdf) ↗	In these three math problems students use a simple formula to estimate the size of a black hole located 3.8 billion light years from Earth, recently studied by NASA's Chandra and Swift satellites.
Black Holes - Hot Stuff! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page79.pdf) ↗	In this math problem students explore the temperature of matter falling into a black hole using a simple equation to calculate the gas temperature at different distances.
A Black Hole - Up Close (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page86.pdf) ↗	In these three math problems students explore how the color of a light bulb changes as it gets close to a black hole, demonstrating the principle of the gravitational 'red shift'.
Exploring Tidal Forces; Black holes and Saturns rings (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page46.pdf) ↗	In these three math problems students use the equation for tidal disruption to explore the stability of a star encountering a black hole, and a satellite of Saturn.
Black Holes - I (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page27.pdf) ↗	In these five math problems students learn about the most basic component to a black hole - the event horizon.
Black Holes - II (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page29.pdf) ↗	In these seven math problems students learn about how gravity distorts time and causes problems even for the Global Positioning System satellites and their timing signals.
Black Holes - III (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page30.pdf) ↗	In these six math problems students learn about how gravity distorts time near a black hole and other massive bodies.
History of Winter - Exploring Energy and Temperature (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/91Mod11Prob1.pdf) ↗	In these three math problems students learn about the relationship between temperature and the kinetic energy of particles.
Rates and Slopes: An astronomical perspective- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page74.pdf) ↗	In these two math problems students determine the slopes for two linear graphs and make the connection to rates with mixed units.
Compound Interest - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/3Page31.pdf) ↗	In these three math problems students use the 'compound interest' formula to examine rates of growth for space mission costs, and the salaries of astronomers, with allowance for inflation.
The Limiting Behavior of Functions- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page52.pdf) ↗	In this math problem students work with two complex formulae to determine their limiting behavior as the independent variables approach infinity and zero.
NASA Juggles Four Satellites at Once! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page8.pdf) ↗	In these three math problems students calculate the volume of several satellite configurations and estimate the magnetic energy and travel times for the particles being studied by MMS.
The Launch of the Mars Science Laboratory (MSL) in 2011 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page29.pdf) ↗	In these eight math problems students use a sequence of launch images to determine the Atlas V's launch speed and acceleration.
The Night Launch of STEREO in 2006 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page28.pdf) ↗	In these four math problems students use a spectacular time-lapse photo of the launch of the STEREO mission to study parabolic curves.
The Ares-V Cargo Rocket (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page40.pdf) ↗	In these three math problems students work with the equations for thrust and fuel loss to determine the acceleration curve of the Ares-v during launch.
Exploring the Ares 1-X Launch: Parametrics (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page74.pdf) ↗	In these three math problems students learn about parametric equations to determine the path of the Ares 1-X rocket.
Exploring the Ares 1-X Launch: Energy Changes (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page75.pdf) ↗	In these five math problems students learn about kinetic and potential energy while studying the Ares 1-X rocket launch.
Exploring the Ares 1-X Launch: The Hard Climb to Orbit (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page76.pdf) ↗	In these five math problems students learn about the energy required to send a payload into orbit by studying the Ares 1-X rocket launch.
Investigating Juno's Elliptical Transfer Orbit (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/JUNO2.pdf) ↗	In these seven math problems students use the Standard Formula for an ellipse to study the elliptical orbit of the Juno spacecraft.
Exploring the Most Distant Galaxies with Hubble (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page25.pdf) ↗	In these four math problems students use recent Hubble Extreme Deep Field data and a polynomial to determine the light travel time between distant galaxies and Earth.
Rotation Velocity of a Galaxy (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page106.pdf) ↗	In these five math problems students examine a simple model of the rotation of a galaxy to investigate how fast stars orbit the centers of galaxies in systems such as the Milky Way and Messier-101.
How Many Quasars are There? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page107.pdf) ↗	In these four math problems students use a piecewise function that estimates how many quasars are found in a given area of the sky.
X-rays from hot gases near the black hole SN1979c (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page54.pdf) ↗	In these three math problems students use two functions to estimate the size of a black hole from the gas emitting x-rays which is flowing into it.
Supercomputers; Modeling colliding neutron stars! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page82.pdf) ↗	In these three math problems students use a series of time-lapse images calculated using a supercomputer to determine the speed of collision of two neutron stars.
Seeing the Distant Universe Clearly (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7page44.pdf) ↗	In these three math problems students calculate the angular sizes and scales of distant objects to study how different sized telescopes see details with varying degrees of clarity.
The Cosmological Redshift - Changing the light from a galaxy. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7page45.pdf) ↗	In these three math problems students learn about the redshift unit of measurement in astronomy, and solve a simple linear equation to explore how the light from very distant galaxies.
Fermi Detects Gamma-rays from the Galaxy Messier-82 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page117.pdf) ↗	In these four math problems students work with a log-log plot to show that straight lines on this plot represent power-law functions.
Hubble Detects More Dark Matter (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page52.pdf) ↗	In these three math problems students learn about how astronomers estimate the amount of invisible dark matter in a cluster of galaxies.
WISE; F(x)G(x); A Tale of Two Functions (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page109.pdf) ↗	In these four math problems students use WISE satellite data to study a practical application of the product of two functions by graphing them individually, and their product.
WISE and Hubble; Power Functions; A question of magnitude (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page135.pdf) ↗	In these four math problems students learn about the stellar magnitude scale used by astronomers to rank the brightness of stars.

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Calculus

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Resource Title & Link	Description
Lunar Crater Frequency Distributions (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page105.pdf) ↗	In these three math problems students use LRO satellite image of the Apollo-11 landing area to determine safety in landing.
The Volume of a Lunar Impact Crater (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page19.pdf) ↗	In these three math problems students use calculus to determine the volume of a crater whose depth is defined by a fourth-order polynomial
Differentiation- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page39.pdf) ↗	In these six math problems students explore partial derivatives by calculating rates of change in simple equations taken from astrophysics.
Collapsing Gas Clouds and Stability- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page37.pdf) ↗	In this math problem students use the derivative to find an extremum of an equation governing the pressure balance of an interstellar cloud.
Meteor Impacts – How Much Stuff? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page113.pdf) ↗	In these two math problems students integrate a powerlaw function to estimate the number of tons of meteoritic debris that Earth collects every year.
Estimating the mass of Comet Hartley 2 using calculus. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page48.pdf) ↗	In these two math problems students use a recent image of the nucleus of Comet Hartley 2 to calculate the volume of the comet's head and its total mass.
Deep Impact Comet Flyby (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Deep2.pdf) ↗	In these four math problems students determine the form of a function that predicts the apparent size of the comet as viewed from the Deep Impact spacecraft that flew by the Comet Tempel-1 in 2005.
From Dust Grains to Dust Balls (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page80.pdf) ↗	In these six math problems students create a model of how dust grains grow to centimeter-sized dust balls as part of forming a planet based on a simple physical model.
From Dust Balls to Asteroids (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page81.pdf) ↗	In these six math problems students calculate how long it takes to form an asteroid-sized body using a simple differential equation based on a very simple physical model.
From Asteroids to Planets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page82.pdf) ↗	In these six math problems students explore how long it takes to form a small planet from a collection of asteroids in a planet-forming disk of matter.
How to Grow a Planet or a Rain Drop (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page20.pdf) ↗	In these two math problems students use calculus to slove for the growth in mass of a body, and solve the equation for the case of a raindrop and a planet like Earth.
The Io Plasma Torus- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page47.pdf) ↗	In these five math problems students approximate the Io radiation belts as a cylinder to determine its volume, and the mass of the particles within it.
The Close Encounter to the Sun of Barnards Star (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page18.pdf) ↗	In these three math problems students use parametric equations and calculus to determine the linear equation for the path of Barnards Star, and then determine when the minimum distance to the sun occurs
Modeling a Planetary Nebula - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page34.pdf) ↗	In these five math problems students use calculus to create a mathematical model of a planetary nebula
Estimating Maximum Cell Sizes (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Astro14.pdf) ↗	In these four math problems students estimate the maximum size of spherical cells based on the rates with which they create waste and remove it through their cell walls.
Calculating Arc Lengths of Simple Functions- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page31.pdf) ↗	In these four math problems students work with the differential form of the Pythagorean Theorem to determine the basic integral formula for arc length, then evaluate it for a parabola, logrithmic spiral and normal spiral.
The Ant and the Turntable: Frames of reference - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page32.pdf) ↗	In these five math problems students predict the motion of an ant crawling from the center of a spinning CDrom to the edge. They also use calculus to estimate the length of the spiral path seen by a stationary observer.
Optimization- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page60.pdf) ↗	In these four math problems students determine the optimal dimensions of an hexagonal satellite to maximize its surface area given its desired volume.
Fluid Level in a Spherical Tank - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page45.pdf) ↗	In these three math problems students explore the relationship between volume, and the height of fluid in a spherical tank as fluid is being drained at a constant rate.
Space Shuttle Launch Trajectory - I - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page40.pdf) ↗	In these three math problems students use the parametric equation for the altitude and range to determine the speed and acceleration of the Shuttle during launch and orbit insertion.
The Dawn Mission - Ion Rockets and Spiral Orbits- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page33.pdf) ↗	In these three math problems students determine the shape of the trajectory taken by a spacecraft using a constant-thrust ion motor using differential and integral calculus for arc lengths.
The Big Bang - Cosmic Expansion - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page38.pdf) ↗	In these four math problems students explore the expansion of the universe predicted by Big Bang cosmology

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Data Analysis & Graphing

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Resource Title & Link	Description
The Arctic's Vanishing Ozone Layer (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page21.pdf) ↗	In these math problems, students use ozone data for the Arctic region between 1979 and 2011 to graph the tabulated data, perform simple regression analysis, and forecast trends into the future.
The Changing Pace of Global Warming (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page61.pdf) ↗	In these four math problems students work with a table of global temperatures to forecast the temperature change by 2050 using a linear extrapolation.
Scientists Track the Rising Tide (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page60.pdf) ↗	In these two math problems students use a graph of sea level rise since 1900 to fit linear functions and perform simple forecasting for the year 2050 and beyond.
The Global Warming Debate and the Arctic Ice Cap (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page100.pdf) ↗	In these three math problems students use graphical data on the Arctic Polar Cap in September to compare with surveys of what people believe about global warming.
The Declining Arctic Ice Cap During September (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page19.pdf) ↗	In these five problems students graph the change in Arctic ice surface area, and perform linear and quadratic regressions to model and forecast trends.
Volcanos are a Blast; Working with simple equations- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page77.pdf) ↗	In these math problems students examine famous events using three equations that describe the height of the plume and initial velocity.
Alpha Centauri Bb - a nearby extrasolar planet? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page17.pdf) ↗	In these three math problems, students plot data for the orbiting planet and determine its orbit period, distance, and surface temperature.
Satellite Drag and the Hubble Space Telescope (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page13.pdf) ↗	In these two math problems students study various forecasts of the altitude of the Hubble Space Telescope to estimate its re-entry year
Benford's Law (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page18.pdf) ↗	In these three math problems students explore a relationship called Benford's Law, which is used by the IRS to catch fradulent tax returns, but also applies to astronomical data and other surprising situations.
Why are hot things red? - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page36.pdf) ↗	In this math activity students explore the Planck Function using graphing skills, and calculus for experts, to determine the relationship between temperature and peak wavelength.
History of Winter - What is a Snowballs Chance on Mars? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/93Mod11Prob3.pdf) ↗	In these two math problems students explore the phase diagrams for water and carbon dioxide and discover whether astronauts would be able to create dry-ice snowballs on mars.
A Mathematical Model of Water Loss from Comet Tempel-1 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page49.pdf) ↗	In these three math problems students use data from the Deep Impact spacecraft to create a simple empirical model for predicting the rate of water loss from a comet based on actual data.
Deep Impact: Approaching Comet Hartley-2 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page41.pdf) ↗	In these three math problems students use data for the brightness of Comet Hartley-2 measured by the Deep Impact spacecraft to create a linear equation for its approach distance.
Comparing the Heat Output of Mars and Earth (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight12.pdf) ↗	In these four math problems students learn about the heat flow formula and use it to explore the properties of Earth and Mars in terms of their crust composition.
Modeling the Atmospheric Re-entry of UARS (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page17.pdf) ↗	In these three math problems students graph the altitude of the UARS satellite in the weeks before re-entry to explore the accelerating effects of atmospheric drag.
Exploring the Ares 1-X Launch: Downrange Distance (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page73.pdf) ↗	In these two math problems students learn about the path of the Ares 1-X test launch and calculate its downrange landing distance in the Atlantic Ocean.
Radio Communications with Earth – The Earth-Sun Angle (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight6.pdf) ↗	The earth-sun angle is given in tabular form in degrees. Students graph the data and find the dates when transmissions to Earth cannot occur.

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Geometry, Measurement & Formulas

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Resource Title & Link	Description
SAGE- Sunset and Sunrise Geometry (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page97.pdf) ↗	In these three problems students explore the tangent geometry used by the SAGE-III instrument, and work with chords to determine their lengths using the Pyhtagorean formula.
Exploring the new planet Kepler 16b called 'Tatooine' (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page14.pdf) ↗	In these two math problems students use the tangent function to estimate the angular diameter and separation of the two stars in the Kepler 16 binary system as viewed from the planet's surface...if it had one!!
A simple model for the origin of Earth's ocean water (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page22.pdf) ↗	In these four math problems, students create a model of the arrival of water to Earth using three sizes of cometary bodies and their arrival rates.
Exoplanet Orbits and the Properties of Ellipses (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page13.pdf) ↗	In these four math problmes students determine the basic properties of the elliptical orbits for the planets.
Spitzer Studies the Distant Planet Osiris (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page71.pdf) ↗	In these three math problems, students learn about the density of the planet HD209458b, also called Osiris, and compare it to that of Jupiter.
The Moon's Atmosphere! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page26.pdf) ↗	In these four math problems students learn about the moon's very thin atmosphere by calculating its total mass in kilograms using the volume of a spherical shell and the measured density.
The Moon's Density - What's Inside?- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page20.pdf) ↗	In these four math problems students develop a simple mathematical model of the moon's interior using two nested spheres with different densities.
Water on the Moon! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page11.pdf) ↗	In these four math problems students estimate the amount of water on the moon using spacecraft data.
LCROSS Sees Water on the Moon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page66.pdf) ↗	In these four math problems students use LCROSS impactor data to estimate the (lower-limit) concentration of water in the lunar regolith in a shadowed crater.
LRO Makes a Temperature Map of the Lunar South Pole (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page42.pdf) ↗	In these three math problems students use an LRO temperature map to study the scale of the South Polar Region, and estimate the volume of water-ice that may be present in the Shackleton Crater.
Probing the lunar core using seismology (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page56.pdf) ↗	In this math problems students learn about the geometry needed to determine the diameter of the lunar core using a simplified model.
The Apollo-11 Landing Area at High Resolution (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page95.pdf) ↗	In these six math problems students use recent LRO images to estimate distances, crater sizes, and tons of TNT needed to create some of the craters by meteor impact.
A Lunar Transit of the Sun from Space - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/3Page33.pdf) ↗	In these four math problems students will use simple geometry to determine how far the STEREO satellite was from the moon and Earth at the time the photograph was taken.
Cross Sections and Collision Times - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page42.pdf) ↗	In these four math problems students explore the relationship between density, speed and size in determining how quickly particles collide in a gas.
Reading a Speed vs Time Graph - acceleration (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page60.pdf) ↗	In these three math problems students read a graph to determine how speed is related to acceleration as the area under a curve.
Beyond the Blue Horizon - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/3Page19.pdf) ↗	In these six math problems students use geometry, and the Pythagorean Theorem, to determine the formula for the distance to the horizon on any planet.
The Physics of Rock Throwing (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page57.pdf) ↗	In these two math problems students study the motion of a thrown rock to explore the parabolic shape of the rocks motion.
Evaluating Secondary Physical Constants (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page43.pdf) ↗	In these seven math problems students evaluate complicated algebraic quantities that define important constants in physics with both integer and fractional exponents.
Angular Size and Similar Triangles (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page28.pdf) ↗	In these three math problems students review the basic properties of similar triangles for a fixed angle - a critical concept in astronomy is angular size, measured in degrees, minutes or arc-seconds.
The Solar System Beyond the Orbit of Neptune (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page64.pdf) ↗	In these three math problems students compute the volume and density of the Kuiper Belt , and estimate how far apart the objects are located compared to the earth-sun distance.
Mercury and the Moon - Similar but different (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page78.pdf) ↗	In these five math problems students explore the mass and volume of Mercury compared to the moon by using the formula for a sphere and scale changes.
Getting an Angle on the Sun and Moon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page32.pdf) ↗	In these six math problems students explore angular size and scale by comparing two images of the sun and moon which have identical angular size, but vastly different scales.
The Rings of Saturn (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page10.pdf) ↗	In these three math problems students explore the volume and mass of the rings of Saturn to estimate the number of ring particles and their separations.
Estimating the mass and volume of Comet Hartley 2. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page47.pdf) ↗	In these two math problems students use a recent image of the nucleus of Comet Hartley 2 and a simple geometric model to estimate the volume of the comets nucleus, and its total mass.
Making a Model Planet (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Week14.pdf) ↗	In this math activity students make a mathematical model of a planet based on its mass, radius and the density of several possible materials.
How to Build a Planet from the Inside Out (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page72.pdf) ↗	In these five math problems students model a planet using a spherical core and shell with different densities.
The Transit of Mercury (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page4.pdf) ↗	In these five math problems students use images taken by the Hinode satellite, students will create a model of the solar disk to the same scale as the image, and calculate the distance to the sun.
Ice on Mercury? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page23.pdf) ↗	In these six math problems students will measure the surface areas of these potential ice deposits on Mercury and calculate the volume of water that they imply.
Hubble Spies Colliding Asteroids (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page141.pdf) ↗	In this math activity students calculate how often asteroids collide in the Asteroid belt using a simple formula.
MESSENGER Explores the Interior of Mercury (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page49.pdf) ↗	In these three math problems students work with a simple spherical core and shell model to determine the interior structure of mercury and the size of its dense iron core.
Hubble: The Changing Atmosphere of Pluto (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page142.pdf) ↗	In these three math problems students determine the aphelion and perihelion of Pluto's elliptical orbit using the properties of ellipses, then calculate the temperature of Pluto at these distances.
Spitzer Telescope Discovers New Ring of Saturn! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page67.pdf) ↗	In these six math problems students calculate the volume of the ring and compare it to the volume of Earth to check a claim that 1 billion Earths could fit inside the new ring.
Giant Gas Cloud in System NGC 6240 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page37.pdf) ↗	In these three math problems students use scientific notation and volume of sphere to estimate the density of the gas cloud, and the number of hydrogen atoms per cubic meter.
The Eagle Nebula Close-up (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page16.pdf) ↗	In these four math problems students measure a Hubble image of the famous Eagle Nebula 'Pillars of Creation' to determine the sizes of various features compared to our solar system
Interstellar Distances with the Pythagorean Theorem - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page5.pdf) ↗	In this math activity students use the Pythagorean distance formula in 3-dimensions to explore stellar distances for a collection of bright stars.
Star Circles (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page67.pdf) ↗	In these six math problems students use a photograph of star trails around the North Star Polaris to determine the duration of the timed exposure based on star arc lengths.
Chandra Observatory Sees the Atmosphere of a Neutron Star (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page77.pdf) ↗	In these three math problems students determine the mass of the carbon atmosphere of the neutron star Cas-A.
WISE: Exploring Power-law Functions Using WISE Data (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page114.pdf) ↗	In these three math problems students explore a practical application of a power law function to count the number of stars in the sky. An additional calculus-level problem is included for advanced students.
The Remarkable Gamma Ray Burst GRB 130427A (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page39.pdf) ↗	In these two math problems students work with the surface area of a sphere, metric conversions and scientific notation to calculate the total power of this distant supernova event.
Angular Size and velocity- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page61.pdf) ↗	In these six math problems students study a spectacular photo of the ISS passing across the face of the sun, and work out the angular sizes and speeds of the transit.
The Interplanetary Voyage of MSL (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page30.pdf) ↗	In these three math problems students use the properties of ellipses to determine the formula for the Hohmann Transfer Orbit taking the Mars Science Laboratory to Mars in 2012.
Hubble: Seeing a Dwarf Planet Clearly (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page143.pdf) ↗	In these three math problems students use published photos to determine the sizes of the smallest discernible features and compare them to the sizes of the 48-states in the USA.
The Hexagonal Tiles in the Webb Space Telescope Mirror (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page27.pdf) ↗	In these two math problems students learn about the Webb Space Telescopes segmented mirror by studying the geometry of hexagons.
Scaling Up the Webb Space Telescope Mirror (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page31.pdf) ↗	In these two math problems students learn about the Webb Space Telescopes segmented mirror and determine the area of the mirror using the formula for the area of a hexagon.
6-fold Symmetry and the Webb Space Telescope Mirror (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page32.pdf) ↗	In these two math problems students learn about the Webb Space Telescopes segmented mirror and its rotational 6-fold symmetry due to tiling with hexagons.
Exploring Gale Crater with the Curiosity Rover (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page1.pdf) ↗	In these four math problems students explore the Gale Crater landing area and calculate rover distances to various way stations to determine the round trip distance and travel time.
The Distance to the Martian Horizon (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight16.pdf) ↗	In these three math problems students devive a basic equation for the distance to the horizon on a spherical body using the Pythagorean Theorem and a bit of algebra.
Estimating the Mass of a Martian Dust Devil! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight5.pdf) ↗	In these two math problems students estimate the mass of a martian dust devil using the approximation that it is a cylinder with a fixed density of dust.
Exploring the Interior of Mars with Spheres and Shells (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight15.pdf) ↗	In these two math problems students use the volume properties of spheres and shells along with the relationship mass=densityxvolume to create a model of the interior of mars.
Solid Rocket Boosters (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page38.pdf) ↗	In these two math problems students learn how SRBs actually create thrust, and study the Ares-V booster to estimate its thrust.
Solid Rocket Boosters and Thrust (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page39.pdf) ↗	In these two math problems students learn how solid rocket boosters work, and calculate the SRB Thrust Curve using a simple geometric model and 'counting squares'..
SpaceX launches the First Commercial Rocket to the ISS (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page47.pdf) ↗	In these two math problems students detemine the volume of the Dragon capsule using the volume formula for a cone.
The Most Important Equation in Astronomy (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page50.pdf) ↗	In these three math problems students learn about how an instrument's ability to see details depends on its size and its operating wavelength - the key to designing any telescope or camera.
The Milky Way: A mere cloud in the cosmos- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page65.pdf) ↗	In these five math problems students compare the average density of the Milky Way with the density of the universe.
Counting Galaxies with the Hubble Space Telescope (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page14.pdf) ↗	In these three math problems students use an image of a small area of the sky to estimate the total number of galaxies in the universe visible from Earth.
Mapping Dark Matter in a Distant Cluster (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page23.pdf) ↗	In this math problem students explore the changing density of dark matter within a distant cluster of galaxies to see if the density of dark matter is uniform inside the cluster.

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Logarithms

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Resource Title & Link	Description
SCOOL-Cloud Cover; Albedo; Transmission and Opacity (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/83Clouds7.pdf) ↗	In these two math problems students explore the concepts of albedo, transmission and opacity for clouds.
Exploring Logarithms and the Richter Magnitude Scale (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight17.pdf) ↗	In these three math problems students work with a logarithmic scale to estimate how much ground movement occurs for earthquakes of different strengths.
Exploring Power-laws; Meteor impacts (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page71.pdf) ↗	In these two math problems students work with logarithmic functions, power-laws and explore the mass function of meteors.
Exploring Power-laws; Meteor impacts (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page112.pdf) ↗	In these four math problems students estimate a function for logarithmic data that describes the number of meteor impacts on Earth every year.
Spotting an Approaching Asteroid or Comet (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page49.pdf) ↗	In these two math problems students work with a fundamental equation for determining the brightness of an asteroid from its size and distance from Earth.
Exploring Impacts and Quakes on Mars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight13.pdf) ↗	In these four math problems students work with logarithmic scales to explore the relationship between the energy of an marsquake and its logarithmic index.
How Many Stars Are In the Sky? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page103.pdf) ↗	In these three math problems students use a simple polynomial to determine how many stars are in the sky.
Exploring Marsquake Energy with the Moment Magnitude Scale (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight18.pdf) ↗	In these three math problems students are introduced to the Moment Magnitude marsquake scale which gives a logarithmic index for marsquakes of differing energies.
Cassini Sees Earth From Space - How Bright is it? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page15.pdf) ↗	In these two math problems students explore the logarithmic magnitude scale and estimate how bright Earth appears from Saturn as viewed in a recent Cassini image
Taking a Log-Log Look at the Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page12.pdf) ↗	In these four math problems students plot the size and mass of various astronomical objects on a Log-Log graph to explore the various physical scales in the universe, and what combinations are excluded.

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Rates, Ratios & Conversions

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Resource Title & Link	Description
Terra Spies a Major Glacier Break-up (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page23.pdf) ↗	In these four problems students use two images from the Terra MODIS instrument to determine the scale of the glacier and the number of cubic kilometers and gallons of fresh water that were 'calved.'
A Simple Model for Atmospheric Carbon Dioxide (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page51.pdf) ↗	In these six problems students work with the known sources of increasing and decreasing CO2 to create a model of the rate of change of atmospheric carbon dioxide.
Terra Satellite Measures Dangerous Dust (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page39.pdf) ↗	In these two math problems, students determine the number of dust particles inhaled by using a satellite map of the dust concentration and a calculation of the mass of a typical dust grain.
Luner Meteorite Impact Risks - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/3Page18.pdf) ↗	In these seven math problems students will use an area and probability calculation to discover the average waiting time for meteorite imapacts..
Mare Nubium And Las Vegas (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Lunar19.pdf) ↗	In these three math problems students compare two satellite images taken at the same resolution to appreciate how large lunar features are compared to more familiar objects.
Using the TV Program CSI to Explore Matter (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/WeekAI.pdf) ↗	In this math activity students will read about how a mass spectrometer works - the kind used in the TV Series CSI, and learn how to interpret a simple spectrum to find out which elements are present in a mystery sample.
Ice or Water? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Astro1.pdf) ↗	In these three math problems students explore the concepts of specific heat and latent heat of fusion to better understand and quantify the energy required for liquid water to exist under various conditions.
Energy and Mass - Same things but different! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page88.pdf) ↗	In these six math problems students use unit conversions to explore the relationship between mass and energy.
Exploring Heat Flow and Insulation (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight11.pdf) ↗	In these three math problems students explore how insulation works to reduce heat flow.
Water on Planetary Surfaces (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Astro3.pdf) ↗	In these four math problems students work with watts and Joules to study melting ice.
The Comet Encke Tail Disruption Event (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page22.pdf) ↗	In these seven math problems students analyze a STEREO satellite image to determine the speed of a comet tail disruption event.
Extracting Oxygen from Moon Rocks- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page28.pdf) ↗	In these four math problems students use a chemical equation to estimate how much oxygen can be liberated from a sample of lunar soil.
Cassini Delivers Holiday Treats from Saturn (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page32.pdf) ↗	In these three math problems students explore proportions and angular size using images of Saturn's moons Titan and Dione
A Star Sheds a Comet Tail! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page20.pdf) ↗	In these five math problems students use the GALEX image to determine the speed of the star Mira, and to translate the tail structures into a timeline extending to 30,000 years ago.
The Origin of Cosmic Rays (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page27.pdf) ↗	In these four math problems students explore the Fermi Gamma-Ray Observatory's confirmation of the idea that supernova are the sources of cosmic rays in the Milky Way.
XZ Tauri's Super CME! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page21.pdf) ↗	in these four math problems students will examine a sequence of Hubble images of the young star XZ Tauri, and measure the average speed and density of this star's CME event between 1955 and 2000.
History of Winter - Exploring Temperature and States of Matter (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/92Mod11Prob2.pdf) ↗	In these three math problems students learn how to read a simple phase diagram and how states of matter are related to temperature and pressure.
Exploring the DNA of an organism based upon arsenic. (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page57.pdf) ↗	In these two math problems students estimate the increase in the mass of the DNA from an arsenic-loving bacterium in which phosphorus atoms have been replaced with arsenic.
Unit Conversions; Energy; Power and Flux (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page84.pdf) ↗	In these five math problems students work with more complicated unit conversions involving simple powers of quantities and mixed ratios.
ISS - Orbit Altitude Changes (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page30.pdf) ↗	In this math activity students read an essay describing the increases and decreases in the ISS orbit, and calculate the final orbit altitude after all the changes are applied.
The Basic Mathematics of Rocket Engines - I (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page76.pdf) ↗	In these four math problems students learn about and calculate specific impulse and thrust.
Exploring Density; Mass and Volume Across the Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page4.pdf) ↗	In this math problem students calculate the density of various astronomical objects to compare how astronomical objects differ enormously in their densities.
Colliding Galaxies - The future of our Milky Way (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page16.pdf) ↗	In these three math problems students explore the collision of two galaxies and estimate from their present speed, separation and acceleration how long it will be before they have collided.
The Sombrero Galaxy Close-up - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page15.pdf) ↗	In this math actiivty students explore the dimensions of this galaxy as well as its finest details, using simple image scaling calculations.

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Scientific Notation

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Resource Title & Link	Description
The Sky is Falling? Well...not quite! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page4.pdf) ↗	In these two math problems students investigage the recent report that the upper atmosphere has collapsed is investigated.
Playing Baseball on the Earth-like Planet Kepler-22b! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page31.pdf) ↗	In these four math problems student explores the gravity and mass of an exoplanet, and some implications for playing baseball on its surface!
The Cometary Planet HD209458b (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page8.pdf) ↗	In these four math problems students investigate a planet that is losing its atmosphere.
SCOOL-Working with Rainfall Rates and Water Volume (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/80Clouds4.pdf) ↗	In these three math problems students learn about rainfall rates and how to convert them into the volume of water that falls.
Craters are a Blast! - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page82.pdf) ↗	In these three math problems students measure crater diameters in a photo of the moon, and determine the energy required to create them using a simple quadratic equation.
The Elementary Particle Masses (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page85.pdf) ↗	In these four math problems students compare the masses and mass differences between elementary particles using units common to physics such as the electron Volt.
Significant Figures...Oh My! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page25.pdf) ↗	In these three math problems students work with the basic rules of significant figures to evaluate a formula. Exercises also ask students to state the number of SFs in some simple numbers for review.
Exploring Angular Size (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page39.pdf) ↗	In these four math problems students examine the concept of angular size and how it relates to the physical size of an object and its distance using Chandra data.
The Many Faces of Energy- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page80.pdf) ↗	In these four math problems students convert between several different energy units.
Fermi Observatory Measures the Lumps in Space (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page79.pdf) ↗	In these three math problems students use timing data obtained by the Fermi Observatory of a powerful gamma-ray burst 10 billion light years away to determine how lumpy space is.
Exploring the Large Hadron Collider (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page90.pdf) ↗	In these six math problems students explore unit conversions related to energy and mass to understand the Large Hadron Collider
How Saturns Moon Mimas Created the Cassini Division (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/10Page31.pdf) ↗	In these three math problems students calculate the acceleration of gravity in Cassini's Division and estimate the number of years to eject these particles.
Deep Impact Comet Encounter (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page48.pdf) ↗	In these four math problems students learn about the Deep Impact experiment involving Comet Tempel-1, and how the path of an asteroid can be changed by using the Law of Conservation of Momentum.
Celestial Fireworks Near NGC3603 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page3.pdf) ↗	In these two math problems students explore a young star cluster and its evaporating the clouds of interstellar gas and dust from which it formed.
Webb Space Telescope: Detecting dwarf planets (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page146.pdf) ↗	In these three math problems students use three functions to predict how far from the sun a body such as Pluto could be detected by the Webb Space Telescope.
Black Holes---Part IV (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page31.pdf) ↗	In these three math problems students explore how much energy is generated by stars and gas falling into black holes.
Black Holes---Part V (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page32.pdf) ↗	In these two math problems students explore how Kepler's Third Law can be used to determine the mass of a black hole, or the mass of the North Star: Polaris.
Black Holes---Part VI (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page33.pdf) ↗	In these five math problems students calculate the tidal acceleration between your head and feet while standing on the surface of Earth...and falling into a black hole.
Black Holes---Part VII (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page34.pdf) ↗	In these three math problems students use a simple equation to calculate the free-fall speed as they pass through the event horizon.
Black Holes---Part VIII (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page35.pdf) ↗	In these three math problems students use a simple algebraic formula to calculate the temperature at various places in a black hole accretion disk.
Black Holes - What's Inside? (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page36.pdf) ↗	In these seven math problems students work with the Pythagorean Theorem for black holes and investigate what happens to space and time on the other side of an Event Horizon.
Black Hole Power (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page37.pdf) ↗	In these five math problems students calculate how much power is produced as matter falls into a rotating and a non-rotating black hole including solar and supermassive black holes.
Black Hole Fade Out (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/4Page38.pdf) ↗	In these three math problems students calculate how long it takes light to fade away as an object falls into a black hole.
Calculating Black Hole Power (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page96.pdf) ↗	In these three math problems students use a simple formula to calculate how much power is produced by black holes of various sizes as they absorb matter from nearby stars and gas clouds.
Scientific Notation - An Astronomical Perspective. - (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/2page9.pdf) ↗	In these eight math problems students review how to perform multiplication and division with large and small numbers, using scientific notation on astronomical problems.
IBEX Uses Fast-moving Particles to Map the Sky! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page69.pdf) ↗	In these three math problems students learn about Kinetic Energy and how particle energies and speeds are related to each other in a simple formula.
Exploring the Mass of Mars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/Insight14.pdf) ↗	In these three math problems students calculate the mass of mars by using satellite data and Keplers Third Law.
The Mathematics of Ion Rocket Engines- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page64.pdf) ↗	In these five math problems students learn about the basic physics of ion engines, calculating speeds.
Gravity Probe B; Testing Einstein again! (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page83.pdf) ↗	In these two math problems students learn about the Lense-Thirring Effect, and calculate its magnitude near Earth's orbit using an algebraic equation with integer and fractional exponents.
Finding Mass in the Cosmos- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page68.pdf) ↗	In these two math problems students derive a simple formula, then use it to determine the masses of objects in the universe from the orbit periods and distances of their satellites.
Gamma Ray Bubbles in the Milky Way (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page51.pdf) ↗	In these three math problems students use the recent Fermi image of the gamma ray bubbles in the nucleus of the Milky Way to study their sizes and other properties.
Chandra Sees the Most Distant Cluster in the Universe (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page70.pdf) ↗	Students work with kinetic energy and escape velocity to determine the mass of a distant cluster of galaxies by using information about its x-ray light emissions.
Exploring the Big Bang with the LHC (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/6Page91.pdf) ↗	In these four math problems students compute the temperature and energy of matter soon after the Big Bang, and compare these with energies available at the LHC.
Using a Gravity Lens to Weigh a Cluster of Galaxies (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/8Page36.pdf) ↗	In these two math problems students explore how the geometry of a gravity lens can be used to measure the mass of the object producing the gravity.

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Trigonometry

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Resource Title & Link	Description
Fitting Periodic Functions - Distant Planets- (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/5Page51.pdf) ↗	In these two math problems, students work with data from a newly-discovered extra-solar planet to determine its orbit period and other parameters of a mathematical model.
Deep Impact - Closing In on Comet 103P/Hartley 2 (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/7Page38.pdf) ↗	In these four math problems students estimate the angular size of the comet at closest approach, and the scale of the HRI camera image.
Curiosity Uses X-Ray DIffraction to Identify Minerals on Mars (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page24.pdf) ↗	In these four math problems students learn about diffraction geometry and then estimate the distance between crystal planes in a mars rock sample.
Curiosity Discovers Ancient Mars River (https://assets.science.nasa.gov/content/dam/science/hpd/heat/space-math/9Page9.pdf) ↗	In these four math problems students estimate the speed of an ancient mars river using images from the Curiosity rover.

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Table of Contents (Anchor Menu)

To help you easily navigate this extensive library, resources have been subcategorized by Core Math Skills. Use the Table of Contents below to jump directly to the materials that best fit your classroom's needs.

Algebra, Equations & Functions ↓	Calculus ↓	Data Analysis & Graphing ↓	Geometry, Measurements and Formulas↓
Logarithms↓	Rates, Ratios & Conversions↓	Scientific Notation↓	Trigonometry↓

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