Orbital Mechanics via a Simulation-based learning

1
Polytechnic University of Valencia (UPV)
Jose A. Moraño
Santiago E. Moll
Luis M. Sanchez-Ruiz
Nuria Llobregat-Gómez
TEEM’15 Porto
Orbital Mechanics
via a
Simulation-based learning

 Master in Aeronautical Engineering started at UPV in 2014/15.
 ‘Orbital Mechanics and Guidance Laws’ is a compulsory subject of second
semester. Two blocks: OM & GL.
 In OM block there are lots of contents: Astronomy concepts, orbital motion of
satellites and celestial bodies as well as maneuvers between them in space.
 Only 2 ECTS for this block (1 T; 0.5 CP; 0.5 LP)
7 weeks with two sessions (90’)
Every week: 1 session by a magister class and 1 session combining CP and LP
 To improve the learning skills of students we have applied a simulation-based
learning model for CP+LP sessions.
 We seek with these simulations the effect 'doing and understanding’.
2
Introduction

 Software used is System Tool Kit
– STK10 by AGI
– Free for some types of simulations
 We present here
– The way in which we have integrated this software in CP+LP sessions of OM
– Several examples from in-class work-simulations
– Grades/results obtained by students
– Students opinion about the OM learning with simulations
3
Introduction

4
Method and Tools
• Binding CP and LP facilitates to develop this active methodology by performing
simulations by STK10
• The process:
- The previous week of a CP+LP session and after the theoretical exposition
some questions are proposed (in this way students prepare and meditate
the new concepts, equations and formulas).
- The day of the session an educational platform is used to do an
assessment with a double purpose:
- Reviewing topics already covered
- Serving as a guide for students to achieve the expected competences.
- They use a CAS (Matlab or Mathematica) and STK10

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To review and understand theoretical concepts
• We propose the creation of a scenario with several satellites using
‘Define Properties’ to enter their elements.
• We provided them the steps to activate the
movement of the simulation in 2D and 3D.
• They can distinguish between different types
of orbits according to their orbital elements.

6
To review and understand theoretical concepts
• In the 2D window they can understand the concept of ‘Ground Track’ and
the influence of the satellite elements in this reprensentation

7
To do simulations for long periods of time
• Some theoretical concepts seem less important a priori because they are not
perceived in real-time simulations but performing simulations for long periods of
time become very remarkable. For example, Sidereal day  Civil day.
- Students have to insert two geostationary satellites but they must modify the period of one
of them to 24 hours.
- For short period of simulation both of satellites seem geostationary, but then, they are
encouraged to animate the simulation for a long period.

8
To do simulations with Real Objects
• STK10 allows using real objects from its database.
• Simulating with one of these objects, as the ISS, allow us to understand many of
the effects studied in theory such as the J2 effect (Earth-flattening) on the
movement of the ISS (Delay of the element  of the ISS)

9
To confirm good calculations
• To understand a special type of orbits (Molniya, Tundra,…) students learn, in the
theory-sessions, that the variation of the element  depends on i according to the
formula:
• So they are asked to calculate i for which the  = 0.
• Then, they are encouraged to run simulations with different values of i. So, they
can see how the effect J2 changes the position of the orbit if i  63.4º.
  revradi
p
R
C E
/1cos5
2
3 2
2
20 





 

10
To confirm good calculations
• To understand a special type of orbits (Molniya, Tundra,…) students learn, in the
theory-sessions, that the variation of the element  depends on i according to the
formula:
• So they are asked to calculate i for which the  = 0.
• Then, they are encouraged to run simulations with different values of i. So, they
can see how the effect J2 changes the position of the orbit if i  63.4º.
  revradi
p
R
C E
/1cos5
2
3 2
2
20 





 

11
To know types of reports and graphs
• Performing simulations to study if the coverage (studied in theory) of a group of
satellites over a region and a period of time is correct, is a very useful tool.
• With the simulations student has the ability to generate and analyze reports and
graphs of the coverage.

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To Visualize orbit transfers
• With an adequate license it is possible to use the extra-package called Astrogator.
This package allows to simulate inter-orbital transfers.
• Without this package, students can not generate the simulations but the teacher
can use it in support of his explanations by using a free STK Viewer.

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Grades
• Dropout rate is 2.2% (1/46) and the success rate is 95.7% (44/46), good numbers
even for a master course.
• It should be noted that the only student that did not take the exam only attended
the sessions during the first week.
Dropouts < 5 [5-7[ [7-9[ [9-10]
1 1 11 25 8
2.2 % 2.2 % 23.9 % 54.3 % 17.4 %

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Students’ opinion
• After 7+7 sessions and the classroom assessment test, students are asked about
their opinions on the simulations used in OM.
• Poll was conducted anonymously using a tool from the UPV educational
platform.
• I consider using STK10 in CP+LP of OM is …
• Do you consider using a simulator orbits as STK10 helps to understand terms
and concepts of the lectures?
• Most of students consider using STK10 is essential for learning and helps them a
lot for understanding theoretical terms and concepts.
Expendable Advisable Indispensable NA
0 % 36 % 64 % 0 %
Nothing Little Enough Much NA
0 % 4 % 16 % 80 % 0 %

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Conclusions and References
• Conclusions:
 During the 2014/2015 academic year Master in Aeronautical Engineering
started at UPV and with it the subject ‘Orbital Mechanics and Guidance Laws’.
 The subject has been divided into two blocks (OM+GL).
 7 weeks with two 90’-sessions: 1 T class and 1 combining CP+LP.
 The STK software has been integrated into the educational methodology of
the subject Orbital Mechanics.
 We have achieved the effect 'doing and understanding’.
 This integration has facilitated a Simulation-based learning boosting the
achievement of competences and skills of our students.
 Simultaneously it has linked theoretical content with real environment.
 The results obtained have been excellent with just one dropout.
 The opinion of the student has been very positive.

References
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G.W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Research
syntheses, Vol. 1, Charlott, NC (2008), 55–108.
 Tall, D. 2000. Cognitive development in advanced mathematics using technology. Mathematics Education
Research Journal, 12, 3 (2000), 210–230.
 Principles and standards for school mathematics. 2000. National Council of Teachers of Mathematics.
Reston, VA (2000).
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3D virtual world: An experiment to find the right representation involving the Marginal Value Theorem.
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Orbital Mechanics via a Simulation-based learning

Orbital Mechanics via a Simulation-based learning

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