Department of Aerospace Engineering

AE 424 | Course Introduction and Application Information

Course Name

Special Topics in Astrophysics and Orbital Mechanics

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
AE 424	SPRING	3	0	3	5

Prerequisites	None
Course Language	English
Course Type	ELECTIVE_COURSE
Course Level	First Cycle
Mode of Delivery	Face-to-face
Teaching Methods and Techniques of the Course	-
National Occupational Classification Code	-
Course Coordinator	Dr. Öğr. Üyesi Fabrizio Pinto
Course Lecturer(s)	Dr. Öğr. Üyesi Fabrizio Pinto
Assistant(s)	-

Course Objectives

The aim of this course is to explore a range of subjects of timely importance to astrophysics and orbital mechanics by means of high performance computing (HPC) approaches, especifically leveraging competitive features available in modern Fortran, as well as employing a broad suite of free open source software (FOSS) tools to explore complex astrophysical systems and to simulate and visualize results useful in the digital design and analysis of next generation spacecraft trajectories and operations.

Learning Outcomes

The students who succeeded in this course;

Name	Description	PC Sub	* Contribution Level
Name	Description	PC Sub	1	2	3	4	5
LO1	Describe the astrophysical systems and the orbital mechanics problems under study.				X
LO2	Define the relationship between measured and observed parameters and the final outcome of analysis and simulations.				X
LO3	Import into computing algorithms data available from observations or laboratory experiments published in the refereed literature and catalogs.				X
LO4	Employ HPC programming, particularly modern Fortran, to solve numerically intensive mathematical problems.					X
LO5	Employ FOSS tools to create advanced visualizations, simulations and enhanced multidimensional representations of the results.					X

Course Description

This course introduces the study of high performance computing for the analysis of complex astrophysical systems and realistic orbital mechanics problems dictated by next generation propulsion and navigation technologies. Simplifications typically introduced in introductory courses are removed and analysis is carried out on multiple length and time scales and involving the simultaneous interaction of various physical principles thus introducing the need for HPC with modern Fortran and representation of complex results with other FOSS tools.

Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses	X
	Supportive Courses
	Media and Managment Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
1	Introduction to the gravitational N-body problem, analytical 2-body solution, Kepler equation, applications to spacecraft trajectory, solar system dynamics, binary stars, galaxies	R. Bate et al., Fundamentals of Astrodynamics (Dover Publ., New York, 1971). ISBN: 0486600610. J. Binney and S. Tremaine, Galactic Dynamics (Princeton Univ. Press, Princeton, 1987). ISBN: 0-691-08444-0. H. Goldstein, C. Poole, and J. Safko, Classical Mechanics (Addison-Wesley, San Francisco, 2002).	cdcb580a
2	Perturbed 2-body problem and solvable cases of the full 3-body problem. Numerical approaches: symplectic and adaptive algorithms.	R. Bate et al., Fundamentals of Astrodynamics (Dover Publ., New York, 1971). ISBN: 0486600610. P.J. Teuben, The Stellar Dynamics Toolbox NEMO, Astronomical Data Analysis Software and Systems IV, PASP Conf Series 77, 398, (1995).	52473b35
3	Introduction to Modern Fortran. FOSS tools review: CygWin, Jupyter, gnuplot, Sage, gfortran. LaTeX. Applications to the N-body problem (N>>1). History, strategies, and parallelization.	Janet A. Nicholson, Introduction to Programming using Fortran 95 (2011). (electronic document). W. H. Press et al., Numerical Recipes in Fortran, FORTRAN 77 and Fortran 90, (Cambridge University Press, Cambridge). ISBN: 0-521-43064-X.	b95109fd
4	Project 1: student presentations		dc4f1a0a
5	Analytical solutions of the polytropic models. Emden-Lane equation. King’s models and globular clusters. Gravitational and atomic charge potential models.	J. Binney and S. Tremaine, Galactic Dynamics (Princeton Univ. Press, Princeton, 1987). ISBN: 0-691-08444-0. S. Chandrasekhar, An Introduction to the Study of Stellar Structure (Dover Publ., New York, 1967). Library of Congress Catalog: 58-162. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Butterworth-Heinemann, Oxford, 2002). ISBN: 0-08-029140-6.	b95109fd
6	Star formation and structure. Numerical solutions of equilibrium stellar structure. Equations of state. Relativistic astrophysics. White dwarfs, neutron stars.	E. Brown, Stellar Astrophysics (Open Astrophysics Bookshelf, 2021). (git version6f0150ea). S. Chandrasekhar, An Introduction to the Study of Stellar Structure (Dover Publ., New York, 1967). Library of Congress Catalog: 58-162. S. Weinberg, Gravitation and Cosmology (John Wiley & Sons, Inc., New York, 1972). ISBN: 0471925675.	52473b35
7	Numerical solutions of dynamical stellar structure. Variable stars, structural instabilities, novae and supernovae.	S. Chandrasekhar, An Introduction to the Study of Stellar Structure (Dover Publ., New York, 1967). Library of Congress Catalog: 58-162.	cdcb580a
8	Midterm		52473b35
9	Spacecraft trajectory optimization: low thrust missions.	J. Aziz et al., Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation, J. of Astronaut. Sci., 65, 205-228 (2018). O. Golan et al., Minimum Fuel Lunar Trajectories for a Low-Thrust Power-Limited Spacecraft, Dynamics and Control, 4, 383-394 (1994).	b95109fd
10	Autonomous spacecraft navigation and Kalman filters	M. Rhudy, A Kalman filtering tutorial for undegraduate students, International Journal of Computer Science & Engineering Technology (IJCSET), 8, 1-18 (2018). R. Faragher, Understanding the Basis of the Kalman Filter Via a Simple and Intuitive Derivation, IEEE Signal Processing Magazine, 29, 128-132 (2012).	8aeee991
11	Autonomous landing	Z. Bojun, High-Precision Adaptive Predictive Entry Guidance for Vertical Rocket Landing, Journal of Spacecraft and Rockets, 56, 1735-1741 (2019). L. Ocampo, Solving the optimization control problem for lunar soft landing using minimization technique, University of Texas, 2013.	8aeee991
12	Project 2: student presentations		8aeee991
13	General relativistic spacecraft trajectories, trajectories in the Schwarzschild and Kerr metrics, Post-Newtonian approximations.	S. Weinberg, Gravitation and Cosmology (John Wiley & Sons, Inc., New York, 1972). ISBN: 0471925675.	52473b35
14	Interstellar travel: relativistic navigation technologies, artificial intelligence, and simulations.	C. Bayler-Jones, Lost in space? Relativistic interstellar navigation using an astrometric star catalogue, ArXiv:2103.10389v1 (2021). I. Crawford, “Direct Exoplanet Investigation using Interstellar Space Probes,” The Handbook of Exoplanets (Springer International Publishing, 2018). ISBN: 978-3-319-55333-7.	52473b35
15	Review of the Semester		cdcb580a
16	Final Exam		52473b35

Course Notes/Textbooks

J. Aziz et al. Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation J. of Astronaut. Sci. 65 205-228 (2018)
R. Bate et al. Fundamentals of Astrodynamics (Dover Publ. New York 1971). ISBN: 0486600610
C. Bayler-Jones Lost in space? Relativistic interstellar navigation using an astrometric star catalogue ArXiv:2103.10389v1 (2021)
J. Binney and S. Tremaine Galactic Dynamics (Princeton Univ. Press Princeton 1987). ISBN: 0-691-08444-0
E. Brown Stellar Astrophysics (Open Astrophysics Bookshelf 2021). (git version6f0150ea)
Z. Bojun High-Precision Adaptive Predictive Entry Guidance for Vertical Rocket Landing Journal of Spacecraft and Rockets 56 1735-1741 (2019)
S. Chandrasekhar An Introduction to the Study of Stellar Structure (Dover Publ. New York 1967). Library of Congress Catalog: 58-162 I. Crawford “Direct Exoplanet Investigation using Interstellar Space Probes ” The Handbook of Exoplanets (Springer International Publishing 2018). ISBN: 978-3-319-55333-7
R. Faragher Understanding the Basis of the Kalman Filter Via a Simple and Intuitive Derivation IEEE Signal Processing Magazine 29 128-132 (2012)
O. Golan et al. Minimum Fuel Lunar Trajectories for a Low-Thrust Power-Limited Spacecraft Dynamics and Control 4 383-394 (1994)
H. Goldstein C. Poole and J. Safko Classical Mechanics (Addison-Wesley San Francisco 2002)
L. D. Landau and E. M. Lifshitz Quantum Mechanics (Butterworth-Heinemann Oxford 2002). ISBN: 0-08-029140-6
Janet A. Nicholson Introduction to Programming using Fortran 95 (2011). (electronic document)
L. Ocampo Solving the optimization control problem for lunar soft landing using minimization technique University of Texas 2013
W. H. Press et al. Numerical Recipes in Fortran FORTRAN 77 and Fortran 90 (Cambridge University Press Cambridge). ISBN: 0-521-43064-X
P.J. Teuben The Stellar Dynamics Toolbox NEMO Astronomical Data Analysis Software and Systems IV PASP Conf Series 77 398 (1995)
M. Rhudy A Kalman filtering tutorial for undegraduate students International Journal of Computer Science & Engineering Technology (IJCSET) 8 1-18 (2018)
S. Weinberg Gravitation and Cosmology (John Wiley & Sons Inc. New York 1972). ISBN: 0471925675.

Suggested Readings/Materials

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5
Project	2	40			X	X	X
Midterm	1	20	X	X	X
Final Exam	1	40	X	X		X	X
Total	4	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	3	48
Laboratory / Application Hours	-	-	-
Study Hours Out of Class	14	3	42
Field Work	-	-	-
Quizzes / Studio Critiques	-	-	-
Portfolio	-	-	-
Homework / Assignments	-	-	-
Presentation / Jury	-	-	-
Project	2	14	28
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	14	14
Final Exam	1	18	18
		Total	150