VIRTUAL CONFERENCE ictcm.com | #ICTCM 32 nd International Conference - PowerPoint PPT Presentation

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE ictcm.com | #ICTCM

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Introduction to Using the Space Program to Engage and Excite Students in Undergraduate Mathematics

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Contact Information Frank Wattenberg United States Military Academy Frank.Wattenberg@westpoint.edu Marianna Bonanome New York City College of Technology City University of New York MBonanome@citytech.cuny.edu

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Disclaimer: The views expressed here do not necessarily reflect the views of the United States Military Academy, the United States Army, or the United States Government

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM The mechanics of spaceflight offer a rich source of real-world applications from which to draw when teaching mathematics across almost all levels. Here, we use rocket propulsion – an interesting application of Newton’s third law and the conservation of momentum to inspire students of calculus and differential equations.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM We begin with a typical question your students might ask Spacecraft typically have to make midcourse corrections. As an example, we ask about midcourse corrections on the way to Mars. A spacecraft halfway to Mars would be traveling at about 25 km/sec and closer to Mars traveling at about 21 km/sec. Suppose we need to make a midcourse correction, changing its direction by 0.1 degree. Guess how much fuel would be required as a fraction of the spacecraft’s mass. Does the answer depend on sharply we turn?

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM A rocket gets its thrust by burning fuel and • exhausting gas, and by Newton’s third law, the gas exerts an equal and opposite force on the rocket, propelling it forward. No need for tires and pavement! • Developing an equation which describes • the motion of a rocket is a great exercise for a Calculus I course.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM We begin with a typical question your students might ask Spacecraft typically have to make midcourse corrections. As an example, we ask about midcourse corrections on the way to Mars. A spacecraft halfway to Mars would be traveling at about 25 km/sec and closer to Mars traveling at about 21 km/sec. Suppose we need to make a midcourse correction, changing its direction by 0.1 degree. Guess how much fuel would be required as a fraction of the spacecraft’s mass. Does the answer depend on sharply we turn?

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM A typical effective exhaust velocity is 3050 m/sec.

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Key relationship: Fuel used = 1.3% for 0.1 degree 12% for 1 degree

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Numeric Verification

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM

32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Contact Information Frank Wattenberg United States Military Academy Frank.Wattenberg@westpoint.ed u Marianna Bonanome New York City College of Technology City University of NewYork MBonanome@citytech.cuny.edu