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Using Satellite Orbits and Space Travel with Game-Quality Simulations in Math and Physics Classes

Explore the power of game-quality simulations in math and science classes, focusing on near-Earth and interplanetary space exploration. Topics include satellite orbits, interplanetary travel, escape velocity, black holes, and more.

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Using Satellite Orbits and Space Travel with Game-Quality Simulations in Math and Physics Classes

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  1. ICTCM - 2013 Using Satellite Orbits and Space Travel with Game-Quality Simulations in Math and Physics Classes from High School through College Frank Wattenberg Department of Mathematical Sciences United States Military Academy Frank.Wattenberg@usma.edu

  2. ICTCM - 2013 Two Big Themes • Near Earth and Interplanetary Space Exploration in Math and Science Courses from the High School through the Advanced Undergraduate Level. • The Power of Game Quality Simulations for Checking Work • Excitement • Students are More Confident in Right Answers • Students See when Answers are Wrong and Often How • Students Persevere

  3. ICTCM - 2013

  4. ICTCM - 2013

  5. ICTCM - 2013 The Story Physics and mathematics make both near-Earth and interplanetary space possible. Chapters include geostationary and geosynchronous orbits, traveling from Earth orbit to Mars orbit, orbital rendezvous, escape velocity, and black holes.

  6. ICTCM - 2013 The Cast • Gravity • Centripetal and Centrifugal Force • Position, Velocity and Acceleration • Force, Energy, and Work • Conservation of Energy • (optionally) Vectors

  7. ICTCM - 2013 Level • Algebra • Applying formulas • Solving equations • Trigonometry • Calculus • Deriving formulas • Applying formulas and solving equations • Integration and improper integration • Multivariable Calculus/Linear Algebra • Vectors • Matrices and rotations • Data-Fitting

  8. ICTCM - 2013 Gravity Find the Acceleration Caused by Gravity near the Earth’s Surface 9.822 meters per second squared

  9. ICTCM - 2013 Centripetal Acceleration • ... at latitude 42 N • Use formula in Algebra (Look up) • Correct for latitude using trig • Derive formula in calculus then apply

  10. ICTCM - 2013 Derivation of Formula

  11. ICTCM - 2013 The Period of a Circular Orbit

  12. ICTCM - 2013 Speed in a Circular Orbit

  13. ICTCM - 2013 Data-Fitting

  14. ICTCM - 2013 Geostationary Orbits and Geosynchronous Orbits • The period should be one sidereal day • Find the radius • Find the speed • Check your work in simulation • Can look down toward the Earth • Note: Can vary the angle of inclination of the orbit

  15. ICTCM - 2013 Getting There -- Hohmann Transfer

  16. ICTCM - 2013 It’s All About Work and Energy • In Algebra use the formulas • In Calculus derive them and then use them

  17. ICTCM - 2013 Fictitious Energy Circular Orbit

  18. ICTCM - 2013 Elliptical Orbit

  19. ICTCM - 2013 Elliptical Orbit

  20. ICTCM - 2013 Adjust for Level • What is the fictitious energy in the parking orbit? • What is the fictitious energy in the transfer orbit? • What is the fictitious energy in the geostationary orbit? • What is the speed in the parking orbit? • What is the first delta V? • What is the speed at apogee in the transfer orbit? • What is the second delta V? • What is the time interval between the first and second burns?

  21. ICTCM - 2013 Additional Questions • Plan a Hohmann transfer from Earth orbit to Mars orbit. How long will the trip take? • When should the first burn occur if the rocket starts near the Earth and wants to reach Mars orbit near Mars?

  22. ICTCM - 2013 Derivation of Potential Energy • To find escape velocity let • and solve for v • Black holes exist because 1/0 is infinity

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