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Polytechnic University of Valencia (UPV)

Jose A. MorañoSantiago E. Moll

Luis M. Sanchez-RuizNuria Llobregat-GómezTEEM’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 secondsemester. Two blocks: OM & GL.

In OM block there are lots of contents: Astronomy concepts, orbital motion ofsatellites 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-basedlearning model for CP+LP sessions.

We seek with these simulations the effect 'doing and understanding’.

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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

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Introduction

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Method and Tools

• Binding CP and LP facilitates to develop this active methodology by performingsimulations by STK10

• The process:

- The previous week of a CP+LP session and after the theoretical expositionsome questions are proposed (in this way students prepare and meditatethe new concepts, equations and formulas).

- The day of the session an educational platform is used to do anassessment 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 themovement of the simulation in 2D and 3D.

• They can distinguish between different typesof orbits according to their orbital elements.

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To review and understand theoretical concepts

• In the 2D window they can understand the concept of ‘Ground Track’ andthe influence of the satellite elements in this reprensentation

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To do simulations for long periods of time

• Some theoretical concepts seem less important a priori because they are notperceived in real-time simulations but performing simulations for long periods oftime become very remarkable. For example, Sidereal day Civil day.

- Students have to insert two geostationary satellites but they must modify the period of oneof them to 24 hours.

- For short period of simulation both of satellites seem geostationary, but then, they areencouraged to animate the simulation for a long period.

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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 themovement of the ISS (Delay of the element of the ISS)

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To confirm good calculations

• To understand a special type of orbits (Molniya, Tundra,…) students learn, in thetheory-sessions, that the variation of the element depends on i according to theformula:

• 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.

revradip

RC E /1cos523 2

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To confirm good calculations

• To understand a special type of orbits (Molniya, Tundra,…) students learn, in thetheory-sessions, that the variation of the element depends on i according to theformula:

• 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.

revradip

RC E /1cos523 2

2

20

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To know types of reports and graphs

• Performing simulations to study if the coverage (studied in theory) of a group ofsatellites 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 andgraphs 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 teachercan 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 numberseven for a master course.

• It should be noted that the only student that did not take the exam only attendedthe 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 abouttheir opinions on the simulations used in OM.

• Poll was conducted anonymously using a tool from the UPV educationalplatform.

• I consider using STK10 in CP+LP of OM is …

• Do you consider using a simulator orbits as STK10 helps to understand termsand concepts of the lectures?

• Most of students consider using STK10 is essential for learning and helps them alot 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 Engineeringstarted 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 ofthe subject Orbital Mechanics.

We have achieved the effect 'doing and understanding’.

This integration has facilitated a Simulation-based learning boosting theachievement 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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Heid, M.K. and Blume, G.W. 2008. Technology and the development of algebraic understanding. M.K. Heid,G.W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Researchsyntheses, Vol. 1, Charlott, NC (2008), 55–108.

Tall, D. 2000. Cognitive development in advanced mathematics using technology. Mathematics EducationResearch Journal, 12, 3 (2000), 210–230.

Principles and standards for school mathematics. 2000. National Council of Teachers of Mathematics.Reston, VA (2000).

Richards, D. and Taylor, M. 2015. A Comparison of learning gains when using a 2D simulation tool versus a3D virtual world: An experiment to find the right representation involving the Marginal Value Theorem.Computers & Education, 86, (2015), 157-171. doi:10.1016/j.compedu.2015.03.009

Tiana, Y., Liu, H. Yin, J., Luo, M. and Wua, G. 2015. Evaluation of simulation-based training for aircraftcarrier marshalling with learning cubic and Kirkpatrick’s models. Chinese Journal of Aeronautics, 28, 1,(2015), 152–163. doi:10.1016/j.cja.2014.12.002

Tiwari, S.R., Nafees, L. and Krishnan, O. 2014. Simulation as a pedagogical tool: Measurement of impact onperceived effective learning. The International Journal of Management Education, 12, 3, (2014), 260-270.

Zbiek, R.M. and Hollebrands, K. 2008. A research-informed view of the process of incorporatingmathematics technology into classroom practice by in-service and prospective teachers. M.K. Heid, G.W.Blume (Eds.), Research on technology and the teaching and learning of mathematics: Research syntheses,1, (2008), 287–344.

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Thanks!

Orbital Mechanics via a Simulation-based learning