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

5. 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 1.What is the fictitious energy in the parking orbit? 2.What is the fictitious energy in the transfer orbit? 3.What is the fictitious energy in the geostationary orbit? 4.What is the speed in the parking orbit? 5.What is the first delta V? 6.What is the speed at apogee in the transfer orbit? 7.What is the second delta V? 8.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