Paper AAS 03-236 rev-
Comparison of the DSST and the USM SemiAnalytical Orbit Propagators P. J. Cefola1, V. S. Yurasov2, Z. J. Folcik 1, E. B. Phelps1, R. J. Proulx3, A. I. Nazarenko 4 1
MIT/ Lincoln Laboratory 244 Wood Street MIT Lexington, MA 02420-9108
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Space Research Center “Kosmos” Magadanskaya str. 10-59 Moscow 129345, Russia
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The Charles Stark Draper Laboratory 555 Technology Square Cambridge, MA 02139-3563
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Center For Program Studies 84/32 Profsoyuznaya ul Moscow 117810, Russia
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13 AAS/AIAA AAS/AIAASpace SpaceFlight Flight MechanicsMeeting Meeting Mechanics Ponce, Puerto Rico
9-13 February 2003
AAS Publications Office, P.O. Box 28130, San Diego, CA 92198
AAS 03-236 rev --
Comparison of the DSST and the USM Semi-Analytical Orbit Propagators1 Dr. Paul J. Cefola2, Technical Staff MIT/Lincoln Laboratory 244 Wood Street Lexington, MA 02420-9108
Dr. Vasiliy S. Yurasov3 Principal Scientist Space Research Center “Kosmos” Magadanskaya str 10-59 Moscow 129345, Russia
Zachary J. Folcik4 Assistant Technical Staff MIT/Lincoln Laboratory 244 Wood Street Lexington, MA 02420-9108
Dr. Eric B. Phelps5 Technical Staff MIT/Lincoln Laboratory 244 Wood Street Lexington, MA 02420-9108
Dr. Ronald J. Proulx6 Principal Member, Technical Staff The Charles Stark Draper Laboratory 555 Technology Square Cambridge, MA 02139
Prof. Andrey I. Nazarenko7 Chief Scientist Center for Program Studies 84/32 Profsoyuznaya ul Moscow 117810, Russia
This paper begins an effort to compare the accuracy and timing characteristics of the Draper Semianalytical Satellite Theory (DSST) developed in the USA and the Universal Semianalytical Method (USM) developed in Russia. The DSST and the USM share several characteristics: Both employ the Generalized Method of Averaging (GMA) Perturbation Theory Both employ non-singular orbital elements Both include comprehensive force modeling Both consider numerical approximation of the slowly varying quantities However, the development of these two theories has proceeded completely independently over more than 20 years up to the current time and there are many differences in the theories, as well.
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The work of the MIT Lincoln Laboratory authors is sponsored by the Air Force under Air Force Contract F19628-00-C-0002. “Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government.” 2 Also, Lecturer in Aeronautics and Astronautics, MIT. E-mail:
[email protected] 3 E-mail:
[email protected] 4 E-mail:
[email protected] 5 E-mail:
[email protected] 6 E-mail:
[email protected] 7 E-mail:
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AAS 03-236 rev --
INTRODUCTION The current paper begins an effort to compare the accuracy and timing characteristics of the Draper Semianalytical Satellite Theory (DSST) (Refs. 1-6 and 23) developed in the USA and the Universal Semianalytical Method (USM) (Refs. 7, 8) developed in Russia. The DSST was initially implemented as an orbit propagator option within the GTDS Orbit Determination Program (Ref. 9). Subsequently in 1983, the DSST was implemented in a standalone orbit propagator package. This standalone allowed the astrodynamical user to access the DSST without incurring the overhead required to support the larger GTDS program. The long-term goal of the current DSST/USM comparison is to understand which elements of the two theories can be combined to provide an improved Semianalytical Satellite Theory. A very accurate and efficient satellite motion model is of strong interest in orbit and constellation design where recent efforts employ complete perturbation models, together with parallel processing and nonlinear optimization techniques such as genetic algorithms and simulated annealing (Refs. 10 - 12). Such approaches to orbit design take advantage of the computational richness that is currently available. In these approaches, each iteration of the design may require thousands of long-term orbit propagations. An accurate and efficient satellite motion model is also of strong interest in applications designed to provide near real-time corrections to the atmosphere density (Refs. 13 –16); in these applications orbit determination results from multiple satellites and multiple time intervals are combined. The DSST and the USM share several characteristics: •
Both employ the Generalized Method of Averaging (GMA) Perturbation Theory
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Both employ non-singular orbital elements
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Both include comprehensive force modeling
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Both consider numerical approximation of the slowly varying quantities
The development of these two theories has proceeded completely independently over more than 20 years and there are many differences in the theories. The theories were initially implemented in different computing environments and with different compilers8. The algorithmic differences between the USM and DSST include the following: •
Different choices for the nonsingular elements that give the orientation of the orbit plane
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Different integration coordinate systems employed in the numerical solution of the mean element equations of motion
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Different approaches to the efficient computation of the slowly varying quantities in the mean element equations of motion and in the short-periodic perturbations
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Differences in the treatment of the second order J2 terms in the mean element equations of motion and in the short-periodic perturbations; specifically, the USM models approach closed form with respect to eccentricity
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Different representations for the inclination functions and the Hansen coefficients employed in the gravitational perturbation models
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Different representations of the lunar and solar ephemerides required in the models for the perturbations due to the attraction of the Moon and Sun
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We expect the range of issues to be experienced in the DSST/USM comparison to be the same as those usually experienced in comparing precision orbit determination programs (Ref. 17).
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AAS 03-236 rev -•
Use of an analytical averaging concept (with the GOST atmosphere density model, Ref. 18) for the atmosphere drag in USM vs. the use of a numerical averaging (quadratures) concept in DSST
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Use of an analytical averaging concept for the solar radiation pressure in USM vs. the use of a numerical averaging (quadratures) concept in DSST
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Different architectures within the mean element equation of motion and short-periodic model software
The perturbations included in the USM and DSST are summarized in Table 1 (Ref. 7) and Table 2, respectively.
Table 1. The Characteristic Perturbations Considered In USM
Perturbation factors
Short-periodical perturbations
Mean element equations of motion
Second-degree zonal harmonic
• First-order terms in a, ξ, η, P, Q, λ; • Second-order terms in a.
First and second order terms relative to the second-degree zonal gravitational coefficient c20
Harmonics lm of geopotential (2
