Department of Aerospace Engineering

AE 442 | Course Introduction and Application Information

Course Name

Applications of General Relativity to Space Engineering

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
AE 442	SPRING	2	2	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	Q&A Problem Solving Lecturing / Presentation
National Occupational Classification Code	-
Course Coordinator	Dr. Öğr. Üyesi Fabrizio Pinto
Course Lecturer(s)	Dr. Öğr. Üyesi Fabrizio Pinto
Assistant(s)	-

Course Objectives

The main objective of this course is to provide an introduction to the general theory of relativity, which explains the emergence of gravity as a geometrical consequence of the curvature of space and time, and its applications.

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 mathematical properties of the theories of special and general relativity.					X
LO2	Use tensor algebra in relativistic problems.					X
LO3	Solve Einstein’s field equations.					X
LO4	Explain the solar system tests of general relativity.					X
LO5	Discuss black holes and gravitational waves.					X
LO6	Analyze cosmological models described by general relativity.					X

Course Description

The discussions in this course will involve the topics of fundamental importance to the theory of gravitation. After developing the bases of the tensor formalism, Einstein’s field equation will be introduced, and the Schwarzschild solution to the field equations will be obtained. Observational proofs of the theory will be presented, and two important consequences of the theory will be investigated, namely, black holes and gravitational waves. Elaborations will be made on quantum gravity and cosmology.

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	Review of Special Relativity Theory (SRT)	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 4-5; L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 1-3	LO1
2	Non-Euclidean geometry; Equivalence	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 3, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 4	LO1
3	Tensor Formalism in General Relativity Theory (GRT)	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 8, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 10	LO2
4	Einstein’s Field Equations	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 9, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 11	LO3
5	The Schwarzschild Solution	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 9, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 11	LO5
6	Solar System Tests of General Relativity 1	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 9, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 11	LO4
7	Midterm		-
8	Hydrostatic Equilibrium	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 9, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 11	LO5
9	Solar System Tests of General Relativity 2	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 9, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 11	LO3
10	Collapse, white dwarfs, neutron stars, black holes	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 9, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 11	LO5
11	Project 1		-
12	Gravitational waves	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 9, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 11	LO5
13	Space engineering and general relativity	M. G. Millis and E. W. Davis, Frontiers of Propulsion Science (AIAA, Reston, 2009). ISBN: 978-1563479564, Ch. 15	LO4
14	Project 2	J. B. Hartle, Gravity (Addison-Wesley, San Francisco, 2003). ISBN: 978-0805386622 Ch. 17-18, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975). ISBN: 978-0750627689 Ch. 12	-
15	Semester Review		-
16	Final Exam		-

Course Notes/Textbooks	L. D. Landau E. M. Lifshitz The Classical Theory of Fields (Pergamon Press Oxford 1975). ISBN: 978-0750627689
Suggested Readings/Materials	J. B. Hartle Gravity (Addison-Wesley San Francisco 2003). ISBN: 978-0805386622 M. G. Millis and E. W. Davis Frontiers of Propulsion Science (AIAA Reston 2009). ISBN: 978-1563479564S. Weinberg Gravitation and Cosmology (John Wiley & Sons Inc. New York 1972). ISBN: 0471925675

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5	LO6
Project	1	40	X	X	X	X	X	X
Midterm	1	20	X	X		X
Final Exam	1	40	X	X	X	X	X	X
Total	3	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	2	32
Laboratory / Application Hours	16	2	32
Study Hours Out of Class	14	3	42
Field Work	-	-	-
Quizzes / Studio Critiques	-	-	-
Portfolio	-	-	-
Homework / Assignments	-	-	-
Presentation / Jury	-	-	-
Project	2	8	16
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	12	12
Final Exam	1	16	16
		Total	150