Department and Course Number1:



ASTE 580 Orbital Mechanics

Instructor: Gabor

Syllabus

of a one-semester (15 weeks) graduate course for engineering and science students

ASTE 580 “Orbital Mechanics I Extended Syllabus”

Objective and Purposes

Orbital mechanics is the basis for spacecraft mission design and is a key component of spacecraft engineering and operations. The basic principles of orbits and astrodynamics informs the designer with options for selecting orbits, maneuvers, and mission profiles that impact the eventual spacecraft design. Understanding orbit perturbations, trajectories, and maneuver needs guides the mission planner with selecting optimal orbit maintenance, rendezvous, and transfers to accomplish the ultimate goals of the mission. This information will then be used by the spacecraft and subsystem engineers to ensure that the spacecraft design can satisfy those requirements and achieve mission success. Once a spacecraft is on orbit, orbital mechanics is the foundation for tracking, orbit determination, and computing orbit corrections.

The goal of this course is to provide the student with an understanding of the basic theory, practices, and applications of orbit mechanics. It combines the foundational principles of algebra, geometry, and physics to describe the motion of objects to, in, and from space. The goal of this course is to provide the student with a basic understanding of the satellite tracking problem. It combines orbit mechanics, geometry, tracking systems, perturbation modeling, estimation, error analysis, and the decisions involved in computing orbits.

Determining orbits is not a straight forward activity, even when being done under supposedly “routine” conditions. The analyst needs to understand what tools are available to them when processing orbits and what the trade-offs are when using them. In order to make effective operational decisions, the analyst must understand the nuances of orbits, propagation, and estimation.

At the end of the course, the student should have mastered the basic principles of an object in orbit around a central body, effects of other forces on objects in orbit, and the means for changing orbitsa basic understanding of the satellite tracking problem. The student will be able to take satellite tracking data, compute an initial orbit estimate, and then refine the estimate using orbit determination. The student will have an understanding of the impacts of various processing decisions on the orbit products. These fundamentals will enable the student to learn and master almost any orbit determination analysis related problemsoftware that they will encounter during their professional lives.

Overview

This course begins with a refresher of basic physical laws and derives the equations of motion for an object in orbit. The orbit is described in 3 dimensions in relation to standard coordinate frames. Next, the course describes principles of changing orbits through maneuvers and transferring between orbits. Then a detailed exploration of Lambert’s problem and the Patched Conics method leads to applications to mission design. Finally the course addresses perturbative forces that impact orbital motion about a central body. This course combines the fundamentals of sensor to satellite geometry, orbit perturbations, and orbit determination theory in order to provide a theoretical overview of the satellite tracking process. The course begins with an overview of the satellite tracking problem. With a basic understanding of the problem, the course then delves into theoretical background of sensor to satellite geometry, orbit propagation, and orbit determination. Finally, the course addresses the processing decisions that impact likelihood of processing success and the usability of the product. Homework will reinforce the understanding of the theoretical material while an example satellite trackingspacecraft mission design project will demonstrate mastery of the concepts.

Prerequisites

Graduate standing in engineering or science

Algebra II

Analytical Geometry

Trigonometry

Calculus

Mechanical Physics

Orbit Mechanics I

Probability and Statistics

Course Text

Course notes provided by the instructor

■ Official Text

❑ Orbital Mechanics for Engineering Students, 3rd Edition, Howard D. Curtis, Elsevier Ltd, 2014

■

■ Additional Support

❑ Orbital Mechanics, John E. Prussing and Bruce A. Conway, Oxford University Press, 1993

■

❑ An Introduction to Celestial Mechanics, Forest Ray Moulton, 1914

■

❑ Fundamentals of Astrodynamics and Applications, David A. Vallado, 3rd edition, Hawthorne, California, 2007

■ Vallado Errata:

❑ Fundamentals of Astrodynamics, Roger R. Bate, Donald D. Mueller, and Jerry E. White, Dover Publications, Inc. 1971

■ BMW Errata:

❑ An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition, Richard H. Battin, 1999

■

❑ Analytical Mechanics of Space Systems, 2nd edition, Hanspeter Schaub and John Junkins, AIAA, 2009

■

■

❑ Statistical Orbit Determination, Byron D. Tapley, Bob E. Schutz, and George Born, 2004

Recommended textbooks:

Fundamentals of Astrodynamics and Applications, David A. Vallado, 3rd edition, Hawthorne, California, 2007

Orbital Mechanics, John E. Prussing and Bruce A. Conway, Oxford University Press, 1993

Fundamentals of Astrodynamics, Roger R. Bate, Donald D. Mueller, and Jerry E. White, Dover Publications, Inc. 1971.

Statistical Orbit Determination, Byron D. Tapley, Bob E. Schutz, and George Born, 2004

Instructional Strategy

Weekly lectures. The homework assignments are due weekly; the homework sets are distributed at the beginning of each chapter. Typically there are several problems in each set that are illustrative examples, implement mathematical details, or derive an alternate approach to establish and confirm the students’ grasp of the material. Selected problems are discussed in class to illustrate and clarify important or challenging points.

Project

The class project consists of planning an interplanetary mission from the Earth to Jupiter and Saturn to integrate creating a report on a specific sensor system to integrate all concepts from the course. The project will be assigned in parts with the end product being the combination of all parts at the end of the semester. The initial part will focus on setting up the design problem. Subsequent parts will develop the mathematics to describe the problem solution, show the execution of the mathematics, and describe the resultant mission. researching a sensor system of the student’s choice. Subsequent parts will develop the sensor-satellite geometry related to that sensor system, describe the orbit perturbations experienced by target satellites, describe the relevant-orbit determination techniques, and finally provide a processing strategy. Project progress is monitored by section drafts as each part is assigned. Based on instructor feedback, the students will compile all parts into a final report with introduction and conclusion. The final report will be due during week 15 of the course.

Exams

One mid-term exam, and one final exam

Grade Policy

Final grade: Mid-term exam 2030%, Homework 20%, Project 20%, final 4030%

Course Outline

■ Introduction

❑ Course description

❑ Administrivia

❑ Applications of Orbital Mechanics

❑ History of Orbital Mechanics

■ Fundamentals

❑ Trig Identities

❑ Coordinate Systems and Time

❑ Vectors

■ Motion of Objects in Space

❑ N-Body Problem

❑ 2-Body Problem

❑ Describing the Orbit in 2D

❑ Moving the Object in its Orbit

■ Kepler’s Equation

■ f and g functions

■ Solving Kepler’s Equation

❑ Describing the Orbit in 3D

❑ Transformations between COE and Cartesian Coords

■ Changing the Orbit (Maneuvers)

❑ Orbit Adjustments

❑ Orbit Transfers for Non-Intersecting Orbits (Hohmann, bi-elliptic)

❑ Interplanetary Mission Analysis

■ Spheres of Influence

■ Patched Conics

■ Swingbys/flybys/gravity assists

❑ Lambert’s Problem

■ Linear Orbit Theory

❑ Hill’s/CW Equations

❑ Force Free Solution

❑ Perturbed Solution

■ Perturbations

❑ Variation of Parameters

❑ Lagrange Planetary Equations

Syllabus

of a one-semester (15 weeks) graduate course for engineering and science students

ASTE 599 580 “Satellite TrackingOrbital Mechanics”

Week # Topics

Week 1 Introduction: Course Description and References

Description of the problem

Applications of Orbital Mechanics

MethodsHistory of Orbital Mechanics

Industry approaches

Week 2 Review vectors and transformations

Physical Principles

Review Describe Orbit Geometry

Elliptical orbits

Transformations from COE to Cartesian

Time and coordinate systems

Week 3 Sensors

Types (radar, optical, skin-track, transponder, laser, GPS)

Tracking networks

Week 4 Sensor to Target

Geometry

Errors – location, signal, biases, noise, other

Week 5 Orbit Perturbations Part I

Gravity – non-spherical

3rd Body Perturbations

Tides – solid Earth, Ocean, atmospheric

Week 6 Orbit Perturbations Part II

Drag

Solar Radiation Pressure

Relativity

Week 7 Midterm Exam

Week 8 Propagation Part I

Analytical – 2 Body, J2, SGP4

Week 9 Propagation Part II

Numerical – Simple, Complex, numerical integrators

Semi-Analytical

Week 10 Alternate state representations

Mean elements

Two Line Elements

Equinoctial elements

DeLaunay

Empirical and reduced dynamic parameters

Week 11 Orbit Determination Part I

Batch estimator

Week 12 Orbit Determination Part II

Sequential estimator

Initial orbit determination

Realistic Error Modeling – Covariance, Consider parameters, Covariance Scaling

Week 13 Orbit Determination Part III

Application of estimation to satellite problem

Prediction – various propagators, mixing propagators

Week 14 Project Review/Discussion

Week 15 Processing Decisions

Role of observability

Use of the a priori state

Fit span

LUPI

Data editing

Parameterization

Force model selection

Finals Week

Recommended Reading

Graduate course for engineering and science students

ASTE 599 “Satellite Tracking”

Recommended textbooks:

Fundamentals of Astrodynamics and Applications, David A. Vallado, 3rd edition, Hawthorne, California, 2007

Statistical Orbit Determination, Byron D. Tapley, Bob E. Schutz, and George Born, 2004

Week # Course text chapters

Week 1 tbd

Week 2 tbd

Week 3 tbd

Week 4 tbd

Week 5 tbd

Week 6 tbd

Week 7 tbd

Week 8 tbd

Week 9 Midterm Exam,

Week 10 tbd

Week 11 tbd

Week 12 tbd

Week 13 tbd

Week 14 tbd

Week 15 tbd

Finals Week

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|Week # |Subject |Book |Class |Term Paper / HW |

| | |Chapter |Notes | |

| |Introduction | | | |

|1 |Course Description and References. Description of the problem. Methods. Industry | |Set #1 |HW #1 |

| |approaches. | | | |

| |Review Orbit Geometry | | | |

|2 |Elliptical orbits. Transformations from classical orbit elements to Cartesian | |Set #2 |HW #2 |

| |coordinates. Time and coordinate systems. | | | |

| |Sensors | | | |

|3 |Types (radar, optical, skin-track, transponder, laser, GPS). Tracking networks. | |Set #3 |HW #3 |

|4 |Sensor to target geometry. Errors – locations, signal, biases, noise, other | |Set #4 |HW #4 |

| |Orbit Perturbations | | | |

|5 |Gravity – non-spherical. 3rd Body Perturbations. Tides – solid Earth, Ocean, | |Set #5 |HW #5 |

| |atmospheric. | | | |

|6 |Drag. Solar Radiation Pressure. Relativity | |Set #6 |HW #6 |

|7 |Midterm Exam | | | |

| |Propagation | | | |

|8 |Analytical – 2 Body, J2, SGP4 | |Set #7 |HW #7 |

|9 |Numerical – simple, complex, numerical integrators. Semi-Analytical. | |Set #8 |HW #8 |

| |Alternate State Representations | | | |

|10 |Mean elements. Two Line Elements. Equinoctial Elements. DeLaunay Elements. Empirical | |Set #9 |HW #9 |

| |and Reduced Dynamic Parameters. | | | |

| |Orbit Determination | | | |

|11 |Batch Estimator | |Set #10 |HW #10 |

|12 |Sequential Estimator. Initial Orbit Determination. Realistic error modeling – | |Set #11 |HW #11 |

| |Covariance, Consider parameter, covariance scaling. | | | |

|13 |Application of estimation to satellite problem. Prediction – various propagators, | |Set #12 |HW #12 |

| |mixing propagators. | | | |

|14 |Project Review/Discussion | | | |

| |Processing Decisions | | | |

|15 |Role of observability. Use of the a priori state, fit span, LUPI. Data editing. | |Set #13 | |

| |Parameterization. Force model selection. | | | |

| |Final Exam | | | |

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