University of Colorado Denver University of Colorado Denver College of Liberal Arts and Sciences
Alexander Engau

Http: Faculty & Staff Directory

Email: Alexander [dot] Engau
[at] UCDenver [dot] edu

Phone: [+1] (303) 315-1719
Fax: [+1] (303) 315-1704

Office: SCB 4223
1201 Larimer Street
Denver, Colorado 80204

Mail: UCD Math & Stats
C Box 170, PO Box 173364
Denver, CO 80217-3364

Alexander Engau

(You may download my card for contact information only.)

Alexander Engau, Assistant Professor

Math 4779/5779 Math Clinic: Optimal Collision Avoidance for Operational Spacecraft in Near-Real Time

This page describes the Spring 2011 Math Clinic sponsored and conducted jointly with SpaceNav LLC. The problem is highlighted in the recent newsletter article UC Denver Students to Investigate and Fight Collisions in Space. More general information about the mathematics clinics are provided at various sites by the college, department, and myself.

Mathematical Sciences Course Catalog Description

The clinic is intended to illustrate the applicability and utility of mathematical concepts. Research problems investigated originate from a variety of sources: industry, government agencies, educational institutions or nonprofit organizations. Prereq: Permission of Instructor. Semester Hours: 3.

  • Meetings: Tuesday and Thursday, 2:00 pm - 3:15 pm, CU Building, Rooms 626/656

Spring 2011 Clinic Sponsor and Contact

SpaceNav LLC is a Colorado-based aerospace engineering firm providing technical solutions in the areas of Space Situational Awareness, Systems Engineering, and Mission Operations. Their process-driven approach to problem-solving enables to deliver on-time, error free products and services in a variety of functional areas including Systems Engineering & Integration (SE&I), Space Situational Awareness (SSA), Orbit Analysis Mission Operations, and Advanced Concepts Research & Development Cell. The SpaceNav team brings technical expertise and experience from a vast number of programs spanning the U.S. Department of Defense (DoD), National Aeronautics and Space Administration (NASA) and National Oceanic and Atmospheric Administration (NOAA) customer base. Leveraging a passion for space combined with in-depth knowledge of space operations, SpaceNav provides cost-effective solutions to a vast array of technical problems.

  • Contact: Matthew Duncan, President
  • Address: SpaceNav, LLC, 1630a 30th Street, Boulder, Colorado 80301
  • Phone: [+1] (877) 577-2236, Fax: [+1] (303) 648-4548
  • Email: {matthew [dot] duncan, info} [at] space-nav [dot] com

Problem Description

The Optimal Collision Avoidance in 'Near Real-Time' problem is concerned with determining an operational strategy to enable personnel at the Joint Space Operations Center (JSpOC) to minimize the risk of collisions between satellites and space debris, by altering satellite trajectories. The goal of this Math Clinic will be to assist SpaceNav in formulating a tractable optimization model for this problem and to develop an algorithm to make recommendations for collision avoidance maneuvers in real time. Participants of the Math Clinic will perform the following tasks in order to develop a solution this problem.

  • Perform a literature search and review to identify existing methodologies for solving this problem as well as related problems.
  • Formulate and implement a nonlinear optimization model of the problem using analytic approximations of orbits of satellites and space debris.
  • Assess the validity of the model against simulations developed by SpaceNav.

Background and Resources (to be updated regularly)

  • Roger R. Bate, Donald D. Mueller, and Jerry E. White, Fundamentals of Astrodynamics, Dover Publications, 1 edition (June 1, 1971), 455 pages, Paperback, ISBN-10: 0486600610, ISBN-13: 978-0486600611.
  • Oliver Montenbruck and Eberhard Gill, Satellite Orbits: Models, Methods and Applications, Springer, 1st ed. 2000. Corr. 3rd printing, 2000, XI, 369 p. 97 illus., 10 in color. With CD-ROM, Hardcover, ISBN: 978-3-540-67280-7.
  • John E. Prussing and Bruce A. Conway, Orbital Mechanics, Oxford University Press, USA (September 23, 1993), 208 pages, Hardcover, ISBN-10: 0195078349, ISBN-13: 978-0195078343
  • Vladimir A. Chobotov, Orbital Mechanics, Third Edition, The Aerospace Corporation, AIAA Education Series, 2002, Revised, 3rd Edition, 472 pages, Hardcover, ISBN-10: 1-56347-537-5, ISBN-13: 978-1-56347-537-5.
    Students: Log in to the Auraria Library Network to read this book online as eBook.