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Dec 18, 2022 304 likes •482 views

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

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32nd International Conference on Technology in Collegiate Mathematics

ictcm.com | #ICTCM

VIRTUAL CONFERENCE

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

Introduction to Using the Space Program to Engage and Excite Students in Undergraduate Mathematics

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32nd 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

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

Disclaimer: The views expressed here do not necessarily reflect the views

f the United States Military Academy, the United States Army, or the

United States Government

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32nd 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.

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

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

n sharply we turn?

We begin with a typical question your students might ask

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32nd 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

n 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.

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

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

n sharply we turn?

We begin with a typical question your students might ask

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

A typical effective exhaust velocity is 3050 m/sec.

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

Key relationship: Fuel used = 1.3% for 0.1 degree 12% for 1 degree

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

Numeric Verification

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32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM

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32nd 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