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Introduction to Orbital Mechanics for Engineering Students

4.5 Filled star Filled star Filled star Filled star Half star
Based on 279 ratings
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Cherish Qualls, PhD

This course covers material typically found in the first half of a university-level Orbital Mechanics or Astrodynamics course.  You'll learn all the fundamentals of elliptical orbits.  We'll go through and derive equations like the trajectory equation, Kepler's equation and more. 

Once you finish this course you'll be able to determine the position and velocity of orbiting bodies, understand the 6 orbital elements, apply Newton's root-finding method to Kepler's equation and much more.

Topics we'll cover

Read more

This course covers material typically found in the first half of a university-level Orbital Mechanics or Astrodynamics course.  You'll learn all the fundamentals of elliptical orbits.  We'll go through and derive equations like the trajectory equation, Kepler's equation and more. 

Once you finish this course you'll be able to determine the position and velocity of orbiting bodies, understand the 6 orbital elements, apply Newton's root-finding method to Kepler's equation and much more.

Topics we'll cover

  • Relative 2-body equation

  • Angular momentum

  • Polar coordinates and energy

  • Trajectory equation

  • Elliptical orbits

  • Kepler's laws

  • Kepler's equation

  • Newton's root finding method

  • Orbital elements

  • Conversion from position and velocity vectors to orbital elements

  • Conversion from orbital elements to position and velocity vectors

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What's inside

Learning objectives

  • Two-body relative motion equation and polar coordinates
  • Trajectory equation
  • Kepler's laws & kepler's equation
  • Elliptical & circular orbits
  • Orbital elements
  • Conversion of position and velocity vectors to orbital elements
  • Conversion of orbital elements to position and velocity vectors

Syllabus

Introduction
Relative 2 Body Equation & Angular Momentum
Polar Coordinates & Energy
Trajectory Equation
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Covers material typically found in the first half of a university-level Orbital Mechanics or Astrodynamics course, providing a solid academic foundation
Explores Kepler's equation and Newton's root-finding method, which are essential tools for solving problems in orbital mechanics
Teaches how to determine the position and velocity of orbiting bodies, a core skill for aerospace engineers and related fields
Focuses on elliptical orbits, which are a fundamental concept in understanding the motion of celestial bodies
Requires learners to apply Newton's root-finding method, which may necessitate a strong foundation in calculus and numerical methods
Examines the conversion between position/velocity vectors and orbital elements, which is crucial for spacecraft navigation and mission planning

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Reviews summary

Fundamental orbital mechanics for engineers

According to learners, this course provides a solid foundation in orbital mechanics, covering the essential derivations and orbital elements needed for engineering studies. Many found the instructor's explanations to be clear and concise, particularly praising the step-by-step approach to complex concepts. However, a significant point raised by some students is the high level of mathematical rigor and the pace, suggesting it assumes a strong prior background in physics and calculus. While the provided examples are useful, several learners requested more practice problems to reinforce understanding. Overall, the course is seen as highly relevant for its target audience of engineering students but may be challenging for those without adequate prerequisites.
Good examples, but students want more.
"Could use more practice problems."
"The examples provided were good but limited."
"Some examples could be more varied or complex."
"More practice problems would be a great addition."
Covers fundamentals essential for the field.
"Fantastic introduction to the subject!"
"Solid foundation in orbital mechanics. Covers the fundamentals well."
"Excellent course! The content is exactly what I needed for my aerospace engineering studies."
"Perfect course for getting the fundamental concepts down."
"The content is solid and foundational."
Instructor breaks down complex topics well.
"The derivations were clear and easy to follow. The instructor does a great job breaking down complex topics."
"I appreciated the step-by-step approach to derivations."
"Instructor is knowledgeable and presents the material clearly."
"The way the derivations are explained made them finally click for me."
Requires strong math/physics background.
"I struggled with the pace and assumed math background."
"The prerequisites aren't clearly stated enough; this is NOT for beginners to physics/math."
"It definitely requires a strong understanding of calculus and physics."
"The mathematical rigor was higher than expected. It's thorough but not very accessible for someone just starting..."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Introduction to Orbital Mechanics for Engineering Students with these activities:
Review Physics Fundamentals
Reinforce your understanding of fundamental physics concepts like Newtonian mechanics, energy, and momentum to better grasp the principles behind orbital motion.
Browse courses on Newtonian Mechanics
Show steps
  • Review relevant chapters in a physics textbook.
  • Work through practice problems on kinematics and dynamics.
  • Focus on concepts related to forces, energy, and momentum.
Read 'Fundamentals of Astrodynamics' by Bate, Mueller, and White
Supplement the course material with a detailed textbook on astrodynamics to gain a deeper understanding of the subject.
View Fundamentals of Astrodynamics: Second Edition... on Amazon
Show steps
  • Read the chapters corresponding to the course topics.
  • Work through the example problems in the book.
  • Compare the book's explanations with the course lectures.
Solve Kepler's Equation Problems
Practice solving Kepler's equation using Newton's method to improve your ability to determine the position of orbiting bodies.
Show steps
  • Find a set of practice problems involving Kepler's equation.
  • Implement Newton's method in a programming language or spreadsheet.
  • Solve the problems and verify your solutions.
Three other activities
Expand to see all activities and additional details
Show all six activities
Read 'Orbital Mechanics for Engineering Students' by Howard Curtis
Use this textbook as a reference to deepen your understanding of orbital mechanics concepts and problem-solving techniques.
View Orbital Mechanics for Engineering Students:... on Amazon
Show steps
  • Read the chapters that align with the course syllabus.
  • Work through the example problems and exercises.
  • Use the book to clarify any concepts that are unclear in the course lectures.
Orbital Visualization Tool
Develop a tool to visualize orbits based on orbital elements to solidify your understanding of how these elements define an orbit.
Show steps
  • Choose a programming language and graphics library.
  • Implement the equations to convert orbital elements to position vectors.
  • Create a visualization that displays the orbit in 2D or 3D.
  • Add features to adjust the orbital elements and see the orbit change in real-time.
Simulate a Satellite Orbit
Develop a simulation of a satellite orbiting the Earth to apply your knowledge of orbital mechanics and gain hands-on experience.
Show steps
  • Choose a programming language and simulation environment.
  • Implement the equations of motion for a satellite in orbit.
  • Incorporate orbital elements to define the satellite's initial conditions.
  • Run the simulation and visualize the satellite's trajectory.

Career center

Learners who complete Introduction to Orbital Mechanics for Engineering Students will develop knowledge and skills that may be useful to these careers:
Astrodynamicist
An astrodynamicist specializes in the study of the motion of celestial bodies, particularly spacecraft. This is a highly mathematical and technical role that draws heavily on orbital mechanics. The 'Introduction to Orbital Mechanics for Engineering Students' course is an essential starting point for anyone considering becoming an astrodynamicist. The course focuses on subjects such as the relative 2-body equation, trajectory equations, and Kepler’s laws. This course’s approach to Kepler's equation and its application using Newton's method are directly beneficial for those entering this career. This course helps build a strong understanding of how to work with orbital elements, convert between positions, velocities, and orbital elements, and to analyze orbital behavior.
See salaries and explore the career path for Astrodynamicist
Satellite Systems Engineer
A satellite systems engineer is involved in the design, development, and operation of satellites. This position requires a comprehensive understanding of orbital mechanics, making this course highly relevant. The 'Introduction to Orbital Mechanics for Engineering Students' course directly addresses key concepts like elliptical orbits, Kepler's equation, and the calculation of orbital elements. A satellite systems engineer must be able to determine the position and velocity of orbiting bodies. This course covers the fundamentals of this process, including how to apply Newton's root-finding method to Kepler's equation. The knowledge gained will be directly transferable to real-world satellite mission planning and analysis.
See salaries and explore the career path for Satellite Systems Engineer
Mission Analyst
A mission analyst plays a critical role in planning and executing space missions. This role involves analyzing mission requirements and designing trajectories. This course, 'Introduction to Orbital Mechanics for Engineering Students', is directly relevant as it teaches the fundamentals of orbital mechanics, including how to calculate orbital elements and predict satellite positions and velocities. A mission analyst must understand how to utilize tools like the trajectory equation and Kepler's laws. This course provides the core knowledge needed to begin analyzing more complex mission scenarios. The course's focus on converting between position/velocity vectors and orbital elements would also be key in a mission analyst's day-to-day tasks.
See salaries and explore the career path for Mission Analyst
Aerospace Engineer
An aerospace engineer designs, develops, and tests aircraft, spacecraft, and related systems. This role requires a strong foundation in orbital mechanics, as many aerospace projects involve orbital trajectories and maneuvers. Specifically, the 'Introduction to Orbital Mechanics for Engineering Students' course helps establish a knowledge of trajectory equations, Kepler's laws, and orbital elements, all fundamental concepts for an aerospace engineer working on spacecraft or satellite design and mission planning. Understanding how to convert between position/velocity vectors and orbital elements is particularly vital for this career path. This course provides the necessary background for more advanced studies and practical applications in aerospace engineering.
See salaries and explore the career path for Aerospace Engineer
Guidance, Navigation, and Control Engineer
A guidance navigation and control engineer focuses on designing the systems required to guide and control spacecraft in orbit. This role directly requires a strong grasp of orbital mechanics. The 'Introduction to Orbital Mechanics for Engineering Students' course teaches the fundamentals of orbital motion and the tools used to describe it. A guidance navigation and control engineer needs a deep understanding of trajectory equations, orbital elements, and how to convert between position/velocity vectors to orbital elements and vice versa, all of which are included in this course. This course helps build a necessary foundation for analyzing and designing the complex systems needed for spacecraft control.
See salaries and explore the career path for Guidance, Navigation, and Control Engineer
Spacecraft Operations Engineer
A spacecraft operations engineer is responsible for the day-to-day operation and maintenance of spacecraft. They need a working knowledge of orbital mechanics to perform tasks such as orbital adjustments and monitoring the health of satellites. The 'Introduction to Orbital Mechanics for Engineering Students' course helps build practical knowledge of orbital elements, Kepler's laws, and the calculations required to track the position of orbiting bodies. A spacecraft operations engineer needs to understand how to predict the location of a spacecraft which is well covered in this course. The practical examples covered within the course would also provide useful context for spacecraft operations.
See salaries and explore the career path for Spacecraft Operations Engineer
Space Debris Analyst
A space debris analyst works to track and characterize space debris objects. This role requires an understanding of orbital mechanics to predict the behavior of space debris and assess collision risks. The 'Introduction to Orbital Mechanics for Engineering Students' course is helpful because it covers the fundamental principles for calculating the position and velocity of objects in orbit. Space debris analysts need to work with trajectory equations, Kepler's Laws, and orbital elements. This course provides the necessary background to begin analyzing and working towards mitigating the potential danger posed by space debris. The techniques covered in this course for converting between position/velocity and orbital elements are also directly applicable.
See salaries and explore the career path for Space Debris Analyst
Propulsion Engineer
A propulsion engineer is responsible for the design, development, and testing of spacecraft propulsion systems. While this role has a strong focus on engine technology, an understanding of orbital mechanics is crucial for analyzing mission requirements and designing effective propulsion strategies. The 'Introduction to Orbital Mechanics for Engineering Students' course is useful as it provides the necessary background in understanding orbital trajectories and maneuvers. A propulsion engineer would need to consider how different propulsion methods affect orbital elements, which are discussed and taught extensively throughout this course. Having a strong grasp of the topics presented in this course, such as the trajectory equation and Kepler's laws, will help a propulsion engineer make informed decisions.
See salaries and explore the career path for Propulsion Engineer
Simulation Engineer
A simulation engineer develops and uses computer models to simulate real-world systems. In the context of aerospace, this can include simulating the behavior of spacecraft and their orbits. The 'Introduction to Orbital Mechanics for Engineering Students' course may help a simulation engineer who is working on projects related to orbital dynamics. The material covered in this course, such as trajectory equations, Kepler's laws, and orbital elements, would inform the development of more accurate simulations. The knowledge of how to calculate positions and velocities of orbiting bodies will be useful in creating these computer models.
See salaries and explore the career path for Simulation Engineer
Remote Sensing Specialist
A remote sensing specialist works with data collected from satellites and other airborne platforms to gain insights about earth. While this role is primarily focused on data analysis, an understanding of orbital mechanics is useful for understanding the context of data acquisition and for potentially designing orbital configurations for data collection. The 'Introduction to Orbital Mechanics for Engineering Students' course, with its focus on trajectory equations, Kepler's laws, and orbital elements, is beneficial for a remote sensing specialist interested in gaining a deeper insight into how the data is collected. This course may assist with understanding the factors such as position, velocity, and orbital parameters that influence the quality of the data they analyze.
See salaries and explore the career path for Remote Sensing Specialist
Aerospace Consultant
An aerospace consultant provides expert advice to organizations in the aerospace industry. This role requires a broad understanding of the technical aspects of aerospace engineering. While not strictly essential, a firm grasp of orbital mechanics helps the consultant in understanding the complexities of spacecraft missions and related projects. The 'Introduction to Orbital Mechanics for Engineering Students' course may help an aerospace consultant looking to help organizations perform mission analysis and planning. This course's concepts, such as trajectory equations, Kepler's laws, and orbital elements, are valuable in offering informed recommendations and analyses to clients.
See salaries and explore the career path for Aerospace Consultant
Research Scientist
A research scientist in the field of astrophysics or space science conducts research on space phenomena. This role often requires an advanced degree. This course, 'Introduction to Orbital Mechanics for Engineering Students' may be useful for a research scientist focusing on topics related to orbital dynamics. The material covered includes the trajectory equation, Kepler's laws, and the conversion between position/velocity and orbital elements. Although research positions are diverse in their demands, the skills provided in this course provide a useful foundation for conducting research related to orbital mechanics, which forms the basis for a variety of analysis and investigation.
See salaries and explore the career path for Research Scientist
Data Scientist
A data scientist analyzes large datasets to extract insights and make predictions. While this role has a different focus than orbital mechanics, a data scientist who works in aerospace may find the course, 'Introduction to Orbital Mechanics for Engineering Students' useful. For example, a data scientist might be asked to analyze satellite data or predict spacecraft positions. The topics from this course, such as the relative two-body equation, Kepler's equation, and orbital elements, may contribute to a deeper understanding of the data. This course may provide valuable context for data analysis in certain aerospace applications.
See salaries and explore the career path for Data Scientist
Robotics Engineer
A robotics engineer designs, develops, and tests robots. While this role does not typically involve orbital mechanics, a robotics engineer who develops robotic systems for space application may find the 'Introduction to Orbital Mechanics for Engineering Students' course useful. This is especially true when dealing with robotic manipulators on satellites or for space exploration. The concepts such as trajectory equations, Kepler's laws and orbital elements can help in developing software for robotic movement. This course may serve as a stepping stone if one is looking to pursue space robotics.
See salaries and explore the career path for Robotics Engineer
Software Engineer
A software engineer develops applications for a variety of purposes. If a software engineer is working in the aerospace industry, particularly on projects involving spacecraft or satellite operation, knowledge of orbital mechanics is useful. The 'Introduction to Orbital Mechanics for Engineering Students' course may provide useful context for software development, especially regarding algorithms for orbital prediction or simulation. For example, software engineers might be involved in creating programs that use trajectory equations, Kepler's laws, or converting orbital parameters. Understanding the underlying science can help software engineers create more effective programs.
See salaries and explore the career path for Software Engineer

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Introduction to Orbital Mechanics for Engineering Students.
Cover image
Fundamentals of Astrodynamics
Save
Classic and comprehensive resource for astrodynamics. It covers the fundamentals of orbital mechanics in detail, including topics like orbital elements, trajectory analysis, and orbital maneuvers. It is commonly used as a textbook in university-level astrodynamics courses and provides a strong foundation for understanding the concepts presented in this course. It serves as an excellent reference for further study.
Fundamentals of Astrodynamics: Second Edition...
Paperback
$$
Cover image
Orbital Mechanics for Engineering Students
Save
This textbook provides a clear and accessible introduction to orbital mechanics, specifically tailored for engineering students. It covers the fundamental principles and equations, with a focus on practical applications. It includes numerous examples and exercises to help students develop their problem-solving skills. valuable resource for reinforcing the concepts learned in the course and preparing for exams.
Orbital Mechanics for Engineering Students: Revised...
Paperback
$$$
Orbital Mechanics for Engineering Students...
Kindle Edition
$$$
Orbital Mechanics: For Engineering Students
Paperback
$$$

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Course image
Rating
4.5 Filled star Filled star Filled star Filled star Half star
Effort
6 total hours
Via
Udemy
Instructor
Cherish Qualls, PhD
Language
English
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Covers material typically found in the first half of a university-level Orbital Mechanics or Astrodynamics course, providing a solid academic foundation
Explores Kepler's equation and Newton's root-finding method, which are essential tools for solving problems in orbital mechanics
Teaches how to determine the position and velocity of orbiting bodies, a core skill for aerospace engineers and related fields
Focuses on elliptical orbits, which are a fundamental concept in understanding the motion of celestial bodies
Requires learners to apply Newton's root-finding method, which may necessitate a strong foundation in calculus and numerical methods
Examines the conversion between position/velocity vectors and orbital elements, which is crucial for spacecraft navigation and mission planning
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