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Flight Projects Sciences and Exploration. Engineering, Technology, and Applications of Science Engineering Design Problem A Practical Application of Vector Dot and Cross Products Students work with coordinate vectors describing the corners of the roof of a house, calculate the area of the roof using dot products; calculate the normal vector to the roof using cross products; and the amount of sunlight striking the roof using dot products to determine how much solar power could be generated by solar panels on the roof.

Problem VAP- Telemetry Math Students work with data rates for the spacecraft and determine how much data needs to be stored.

Problem VAP- Working with Areas of Rectangles and Circles Students use the formulas for simple rectangle and circle areas to determine the areas of the holes in a satellite panel. Problem 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.

Problem 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. Problem 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.

Problem 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 mathemartical model that predicts the declining solar power produced by Junos solar panels as the spacecraft travels from Earth to Jupiter. By determining the scale of each image, they estimate average speeds during the first 4 seconds after lift-off.

Students use a spectacular time-lapse photo of the launch of the STEREO mission obtained by photographer Dominic Agostini in to study parabolic curves.

Problem The Space Shuttle: Fly me to the moon? Students discuss the popular misconception that the Space Shuttle can travel to the moon by examining the required orbit speed change and the capacity of the Shuttle engines to provide the necessary speed changes.

Students determine the form of a function that predicts the changing apparent size of the comet as viewed from the spacecraft along its trajectory. They determine the cratering rate and use this to predict how many impacts the solar panels on the International Space Station experiences each day.

Problem The Ares-V Cargo Rocket Students work with the equations for thrust and fuel loss to determine the acceleration curve of the Ares-v during launch. Problem Some Famous Unit Conversion Errors Students examine three famous unit conversion errors that led to catastrophic failures and near-death experiences.

Problem ISS - Orbit 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. Problem Satellite Drag and the Hubble Space Telescope Satellite experience drag with the atmosphere, which eventually causes them to burn up in the atmosphere.

Students study various forecasts of the althtiude of the Hubble Space Telescope to estimate its re-entry year.

Problem The Mathematics of Ion Rocket Engines- Students learn about the basic physics of ion engines, calculating speeds. Problem Can You Hear me now? Problem Light Travel Times- Students determine the time it takes light to reach various objects in space.

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Problem The Dawn Mission - Ion Rockets and Spiral Orbits- 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. Problem Fly Me To the Moon! Problem Extracting Oxygen from Moon Rocks- Students use a chemical equation to estimate how much oxygen can be liberated from a sample of lunar soil. Problem The Dollars and Cents of Research - Students work with dollar amounts, hourly salary rates, percentages to explore various models of the cost of scientific research as seen by the individual scientist.

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Problem Space Shuttle Launch Trajectory - I - Students use the parametric equation for the altitude and range for an actual Shuttle launch to determine the speed and acceleration of the Shuttle during launch and orbit insertionh [Grade: Topics: Algebra; Calculus; Parametric Equations; Differentiation. Problem How Big is It?

Students work with an image taken by the Mars Orbiter satellite of the Spirit landing site. They determine the image scale, and calculate the sizes of various surface features from the image. Problem Ice on Mercury? Since the 's, radio astronomers have mapped Mercury.

An outstanding curiosity is that in the polar regions, some craters appear to have 'anomalous reflectivity' in the shadowed areas of these craters. One interpretation is that this is caused by sub-surface ice.

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In this activity, students will measure the surface areas of these potential ice deposits an calculate the volume of water that they imply. Students will learn about NASA's Magnetospheric Multi-Scale MMS satellite mission, and how it will use four satellites flying in formation to investigate the mysterious process called Magnetic Reconnection that causes changes in Earth's magnetic field.

These changes lead to the production of the Northern and Southern Lights and other phenomena. From the volume formula for a tetrahedron, they will calculate the volume of several satellite configurations and estimate the magnetic energy and travel times for the particles being studied by MMS.

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This problem asks students to use the periods of the five satellites to figure out when all 5 satellites will be lined-up as seen from Earth. They will do this by finding the Greatest Common Multiple of the five orbit periods, first for the case of 2 or 3 satellites, which can be easily diagrammed with concentric circles, then the case for all five satellites together.

Problem 96 Hinode Satellite Power - Students will study the design of the Hinode solar satellite and calculate how much power it can generate from its solar panels. Problem 95 A Study on Astronaut Radiation Dosages in SPace - Students will examine a graph of the astronaut radiation dosages for Space Shuttle flights, and estimate the total dosages for astronauts working on the International Space Station.

Students use a graph of the wall thickness versus dosage, and determine how thick the walls of a hollow cubical satellite have to be to blackuce the radiation exposure of its electronics. Students calculate the mass of the satellite and the cost savings by using different shielding.

Students use exponential functions to model the density of a planetary atmosphere, then evaluate a definite integral to calculate the total radiation shielding in the zenith straight overhead direction for Earth and Mars. Problem 88 Atmospheric Shielding from Radiation- II - This is the second of a three-part problem dealing with atmospheric shielding.

Students use the formula they derived in Part I, to calculate the radiation dosage for radiation arriving from straight overhead, and from the horizon. Students also calculate the 'zenith' shielding from the surface of Mars. Problem 87 Atmospheric Shielding from Radiation- I - This is the first part of a three-part problem series that has students calculate how much radiation shielding Earth's atmosphere provides. In this problem, students have to use the relevant geometry in the diagram to determine the algebraic formula for the path length through the atmosphere from a given location and altitude above Earth's surface.

Problem 83 Luner Meteorite Impact Risks - In , scientists identified 12 flashes of light on the moon that were probably meteorite impacts. They estimated that these meteorites were probably about the size of a grapefruit. How long would lunar colonists have to wait before seeing such a flash within their horizon?

Students will use an area and probability calculation to discover the average waiting time.

Problem 80 Data Corruption by High Energy Particles - Students will see how solar flares can corrupt satellite data, and create a timeline for a spectacular episode of data loss recorded by the SOHO satellite using images obtained by the satellite.

Students will also calculate the speed of the event as particles are ejected from the sun and streak towards earth. Problem 79 Correcting Bad Data Using Partity Bits - Students will see how computer data is protected from damage by radiation 'glitches' using a simple error-detection method involving the parity bit. They will reconstruct an uncorrupted sequence of data by checking the '8th bit' to see if the transmitted data word has been corrupted.

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By comparing copies of the data sent at different times, they will reconstruct the uncorrupted data. Problem 76 Radon Gas in the Basement - This problem introduces students to a common radiation problem in our homes.

They will calculate the orbit decay rates, and investigate why this might be happening. Problem A Simple Gauge in a Tank - II Students work with the formula for the volume of a conical solid to design a gas tank gauge. Problem Calculating the Volume of the J-2x Rocket Engine Bell Students explore conical volumes by examining the diemnsions of a large rocket engine.

Problem Volumes of Solids - Packing for a trip to the Moon Students calculate volumes of rectangular solids and pack a volume-limited travel kit used by astronauts.

Problem The Launch of LADEE to the Moon Students plot the altitude, range and speed of the LADEE rocket launch and investigate rates of change including acceleration by graphing the tabular data and determining the slope of the graph using the definition of the slope of a line between two points. Problem Gravity and Escape Speed Students calculate the escape speed for various planets using a simple 'square root' equation.

Problem Reading a Speed vs Time Graph - acceleration Students read a graph to determine how speed is related to acceleration as the area under a curve. Problem Exploring Artificial Gravity 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. Problem The Physics of Rock Throwing Students study the motion of a thrown rock to explore the parabolic shape of the rocks motion.

Problem Distance Traveled Under Free Fall by Gravity Students explore accelerated motion and distance traveled using an equation that related distance to time-squared, and solve the equation under various conditions. Problem Gravity and Falling Bodies Students work with simple linear equations to study the speed of falling bodies under gravity.

Problem Exploring the Launch of the Falcon 9 Students use data from the launch of the Falcon 9 booster to determine its speed and acceleration.

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They create a mathematical model that fits the data, and use this to make their own prediction of the re-entry date. Problem The Last Flight of the Space Shuttle Endeavor Students use tabular data and graphing to determine the launch speed and acceleration of the Space Shuttle from the launch pad. Problem Apollo Lanuch from Lunar Surface Students use a sequence of images to determine the speed of ascent of the Apollo capsule from the lunar surface.

Problem Space Shuttle Atlantis - Plume Speed Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image.

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Problem Space Shuttle Atlantis - Exhaust Speed Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. Problem Space Shuttle Atlantis - Launch Speed Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image.

Problem Space Shuttle Atlantis - Ascent to Orbit Students use a sequence of images from a video of the launch to determine speed from the time interval between the images, and the scale of each image. Problem Space Shuttle Launch Trajectory - I - Students use the parametric equation for the altitude and range for an actual Shuttle launch to determine the speed and acceleration of the Shuttle during launch and orbit insertion [Grade: Topics: Algebra; Calculus; Parametric Equations; Differentiation.

Problem Buying a Telescope Students compare several telescopes and select the one with the best performance and lowest cost. Problem How do Telescopes Magnify? Students use a simple ratio formula to calculatethe magnification of a telescope.

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Problem How Telescopes Work Students compare hwo much light a telescope can gather compared to the human eye. Problem The Scale of an Image with a Telescope Students desigh digital cameras for telescopes given information about the image scale of the telescope and the pixel dimensions.

Problem Digital Camera Math Students learn about digital cameras and how to interpret formats, megapixels and angular resolution. Problem Designing a Telescope System Students design two telescopes given information about the desired properties for conducting research. Problem Telescope Resolution - How much detail can you see? Students determine the resolving power of a telescope and the limit to the finest details that can be see for a telescope of a specific diameter.

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Problem Telescope Field of View - How much can you see? Problem Telescope Light Gathering Ability - Seeing Faint Stars Students calculate the light gathering ability of various telescopes compared to the human eye. Problem Calculating the Magnification of a Telescope Students fill in missing numbers in a table using proportions and evaluating a simple equation for magnification. Problem Exploring Parabolas - The shape of a satellite dish Students use the equation for a parabola to determine the focus location for a solar cooker and a sound amplifier dish given their diameters and depths.

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Problem Exploring Light Brightness and the Inverse Square Law Students collect data and explore the inverse square law using a light meter. They deduce the formula for the brightness of a lamp given its distance and wattage.

Problem The Most Important Equation in Astronomy 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. Students work with vectors to determine a spacecrafts orientation relative to Earths magnetic field.

They compute the expected strength of the magnetic field parallel and perpendicular to the spacecraft motion vector. Problem VAB-Navigating in a Magnetic Field Using Linear Equations Students model spacecraft motion and the local magnetic field direction using two linear equations, then determine the line perpendicular to the spacecraft motion and the angle of motion relative to the magnetic field.