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Revisiting the DSST Standalone Orbit

Propagator

Paul J. Cefola

1

, Zachary Folcik

2

, Romain Di-Costanzo

3

,

Nicolas Bernard

3

, Srinivas Setty

4

and Juan Félix San Juan

5

1

Department of Mechanical and Aerospace Engineering

State University of New York at Buffalo

Amherst, NY, USA

2

Arlington, MA, USA

3

CS Communications & Systemes

31506 Toulouse Cedex 5, France

4

Deutsches Zentrum fur Luft- und Raumfahrt (DLR),

German Space Operations Center (GSOC)

5

Universidad de La Rioja, Logrono, Spain

Paper AAS 14-411

AAS/AIAA Space Flight

Mechanics Meeting

Santa Fe, New Mexico 26-30 January 2014

AAS Publications Office, P.O. Box 28130, San Diego, CA 92198

Rev 8

1

REVISITING THE DSST STANDALONE ORBIT PROPAGATOR

Paul J. Cefola,

*

Zachary Folcik,

†

Romain Di-Costanzo,

‡

Nicolas Bernard,

§

Srinivas Setty

**

, and Juan Félix San Juan

††

The goal of the Draper Semi-analytical Satellite Theory (DSST)

Standalone Orbit Propagator is to provide the same algorithms as in the

GTDS orbit determination system implementation of the DSST, without

GTDS’s overhead. However, this goal has not been achieved. The 1984

DSST Standalone included complete models for the mean element mo-

tion but truncated models for the short-periodic motion. The 1997 up-

date included the short-periodic terms due to tesseral linear combinations

and lunar-solar point masses, 50 x 50 geopotential, and J2000 coordi-

nates. However, the 1997 version did not demonstrate the expected im-

proved accuracy. Three projects undertaken by the authors since 2010

have led to the discovery of additional bugs which are now resolved.

*

Adjunct Professor, Department of Mechanical and Aerospace Engineering, State University of New York at Buf-

falo, Amherst, NY, USA, paulcefo@buffalo.edu; also Consultant in Aerospace Systems, Spaceflight Mechanics,

and Astrodynamics, Vineyard Haven, MA, USA.

†

53 Maynard Street, Arlington, MA, USA, zjfolcik@mit.edu; Zachary Folcik is currently Technical Staff at the

MIT Lincoln Laboratory

‡‡

CS Communications & Systemes, 5 rue Brindejonc des Moulinais, 31506 Toulouse Cedex 5 (France),

Email: romain.di-costanzo@c-s.fr

§

CS Communications & Systemes, 5 rue Brindejonc des Moulinais, 31506 Toulouse Cedex 5 (France),

Email: nicolas.bernard@c-s.fr

**

Ph.D Student, Space Situational Awareness, Deutsches Zentrum fur Lüft- and Raumfahrt (DLR), Ger-

man Space Operations Center (GSOC), Müncher Str. 20, 82234 Wessling, Germany, Email:

Srinivas.Setty@dlr.de

††

Professor,

Department of Mathematics and Computation,

Universidad de La Rioja, Logroño, Spain, Email:

juanfelix.sanjuan@unirioja.es

(Preprint) AAS 14-411

Rev 8

2

INTRODUCTION

Development of the DSST started in the mid 1970’s at the Computer Sciences Corporation in

Maryland with focus on the mean element motion due to conservative perturbations –

geopotential and lunar-solar point masses. This development employed the GTDS orbit determi-

nation system as the host environment. Development later continued at the Charles Stark Draper

Laboratory in Cambridge, Massachusetts. All of these developments employed the non-singular

equinoctial elements.

The Draper development initially focused on the following areas:

• Numerical averaging concepts for the mean element motion due to the non-

conservative perturbations – atmospheric drag and solar radiation pressure

• Coupling between oblateness and atmospheric drag

• Analytical short-periodic motion models for the zonal harmonics, tesseral m-

dailies, tesseral linear combination terms, lunar-solar point masses, and J2-

secular/tesseral m-daily coupling

• Interpolation strategies for evaluating the mean elements and the short periodic

Fourier coefficients at times off their respective integration grids

• Refinement of tesseral resonance models including consideration of the Hansen

coefficients

• Semi-analytical theory for the partial derivatives of the perturbed motion

• Weighted least squares concept to directly estimate precise mean elements from

tracking data

• Kalman Filter concepts to recursively estimate precise mean elements directly

from tracking data

The initial development of the Draper Semi-analytical Satellite Theory discussed above used

the IBM mainframe GTDS orbit determination system as the development environment. Howev-

er, users external to the Draper Laboratory wanted access to the Semi-analytical Satellite Theory

without the ‘overhead’ of GTDS. In this context, ‘overhead’ related to the learning curve associ-

ated with GTDS.

The DSST Standalone was developed in 1983-84 to provide better access to the DSST (Ref.

1). This version of the Standalone included complete models for the mean element motion (based

on the Mean of 1950.0 integration and the 21 x 21 geopotential conventions then employed in

GTDS) and a portion of the short-periodic models (zonal harmonic and tesseral m-daily terms).

The intent was to provide accuracy for LEO orbits of approximately 200 meters. Analytical

models for the lunar-solar short periodic motion were not initially included in the DSST

Standalone because the GTDS implementation of these models was still being tested (Ref. 2).

Rev 8

3

The development of the Standalone was supported by the Aerospace Corporation; Aerospace

subsequently modified the Standalone to interface with the CDC computers then employed for

astrodynamic applications at Aerospace (Ref. 3). Also, Aerospace interfaced the DSST

Standalone with the MEANELT and the SATPROP programs which were standards in the

Astrodynamics Department (Refs. 4, 5). At the Draper Laboratory, the time-independent lunar-

solar short periodic model (Ref. 2) was added to the DSST Standalone in the late 1980s and these

updates were shared with the Astrodynamics Department at the Aerospace Corporation. At that

point, the accuracy of the Standalone models was assumed to match that of the GTDS DSST

models.

By 1996, extensive improvements to the DSST had been made in the GTDS environment.

These included the expansion of the geopotential to include 50 x 50 fields, the additional of solid

Earth tide models, and J2000 coordinate systems (Refs. 6, 7). In 1997, an effort to extensively

upgrade the DSST Standalone was undertaken (Ref. 8). This effort included:

• 50 x 50 geopotential models

• Solid Earth tide contributions to the mean element equations of motion

• J2000 coordinate systems

• Short periodic motion models for the Tesseral Linear Combination terms

• Improvements to the maintainability of the source code

To improve the maintainability of the source code, the following issues were addressed:

• Conformance to coding standards

• Elimination of COMMON blocks and their replacement with structure records

and modules

• Preparation for FORTRAN 90

While the 1997 upgrade to the DSST Standalone upgrade touched large portions off the source

code, the testing described in Reference 8 only focused on the mean element equations of motion

(see Tables 1 and 2 in Ref. 8).

The DSST Standalone next received significant consideration in 2008-2009 when develop-

ment of Linux and Windows versions of the DSST Standalone was the goal (Ref. 9). The DSST

Standalone was originally installed at MIT LL on the same SGI-UNIX machine used for GTDS

R&D. The code was maintained under version control on a Linux machine at MIT LL. The Intel

FORTRAN Compiler version 9.1 was used to compile the code. On the Windows side, the code

was implemented under Microsoft Visual Studio and Intel Visual Fortran 11; the port was

straight-forward. Comparison testing of GTDS versus the Linux DSST Standalone was initiated

(see Tables 6 and 7 in Ref. 9). These tests included some short periodic geopotential perturba-

tions but the degree and order of the field was limited to 2 x 2. Some discrepancies in the DSST

Standalone were uncovered. The test protocol for Windows DSST Standalone was to use the

Rev 8

4

LLNL SatOrb program (a special perturbations program) to least-squares fit position and velocity

data generated with the Windows DSST Standalone. This latter effort was not completed.

The roadmap of this paper is as follows. In Section 2, we discuss the three demonstration pro-

jects that have contributed to the refinement of the DSST Standalone. Each of the projects has a

test process and discussion of these test processes is emphasized. In Section 3, we discuss the

fixes that have been made to the DSST Standalone and anticipate the impact of these fixes. Sec-

tion 4 gives current numerical results for the comparison of the Orekit java DSST with DSST

Standalone. These results constitute an evolution of the Orekit DSST versus F77 Standalone

DSST comparisons given in February 2013 (Ref. 10). Conclusions and Future Work end the pa-

per.

OPEN SOURCE SOFTWARE SPACE SITUATIONAL AWARENESS

DEMONSTRATION PROJECTS

In 2010, the first author presented a paper with the title “Open Source Software Suite for

Space Situational Awareness for and Space Object Catalog Work”

(Ref. 11). This paper

proposed three demonstration tasks:

1. Creation of a Web interface for the DSST Standalone Orbit Propagator

2. Migration of the DSST Standalone Orbit Propagator from Fortran 77 to an Ob-

ject-Oriented software platform

3. Non-invasive encapsulation of the Linux GTDS R&D Orbit Determination sys-

tem

The top level design of the F77 DSST Standalone is given in Figure 1.

In 2011 and 2012, three projects were initiated which address the first two of the three demon-

strations tasks:

1. The DSST Standalone was included on the

Astrody

Tools

Web

Web-Site prototype,

which provided a friendly web interface for DSST (Ref. 12). The

Astrody

Tools

Web

web site was established at the Universidad de La Rioja, Spain. This prototype

has now evolved into a stable platform based on the Drupal open source content

management system (Ref. 13).

2. The DSST was implemented as an orbit propagator in object-oriented java as

part of Orekit open source library for space flight dynamics (Refs. 10 and 14

thru 16).

Rev 8

5

3. The accuracy and computation time characteristics of the DSST Standalone rela-

tive to the requirements of space object catalog maintenance are being evaluated

by the Space Situational Awareness (SSA) Group at the DLR GSOC (Refs. 17

and 18).

WEB DSST

Figure 2 shows the encapsulation process followed by the Astro Web Tools team in order to

integrate DSST in the software repository at the Universidad de La Rioja. The DSST Web inter-

face allows registered users to access and execute the original DSST Standalone through an easy-

to-use graphical user web-interface after completing the appropriate form with the initial values

and parameters. We note that the core DSST Standalone code did not require modification; only

its interface required re-engineering.

At University of Rioja, the DSST Standalone operates under the Linux system CentOS. It is

compiled with the Intel Fortran compiler version 11.1.

Figure 3 illustrates the test processes available for the Web DSST. Basically, the process con-

sists of comparisons between the DSST Standalone executing at the University of Rioja and the

DSST Standalone executing in the USA.

These comparisons are supported by the process originally used to test the Standalone DSST

vs the GTDS DSST which is described in Figure 4.

Referring to Figure 4, the GTDS Cowell orbit propagator can be used to generate ‘truth’ posi-

tion and velocity time history files. These position and velocity files can be used as observation

data in GTDS DSST orbit determination runs, either using the mean element differential correc-

tion (DC) or mean element Kalman Filter estimators. This process is given the name Precise

Conversion of Elements (PCE). If the force models are consistent between GTDS Cowell and

GTDS DSST, we expect the final residuals to be small. We can then compare GTDS DSST with

the DSST Standalone. We can also generate the ‘truth’ position and velocity time histories with

the DSST Standalone. Assuming a preprocessor to transform the DSST Standalone output to an

appropriate format, the GTDS Cowell DC program can process the DSST Standalone output file

as observation data. Again, the final residuals should be small if the force models are compatible.

If the same mean elements are input to the GTDS DSST program and the DSST Standalone

program, then the two programs should produce equivalent mean element time histories and

equivalent Fourier coefficients for the short periodic motion.

Additionally, explicit formulas for the mean element rates and the short periodic formulas in

the DSST were constructed with the Macsyma utility (Refs. 19 and 20). These formulas have

been reproduced with the current open source Maxima utility. The numerical results from such

Rev 8

6

explicit formulas can be compared with results from the recursive code in GTDS DSST and the

DSST Standalone.

OREKIT JAVA DSST

Orekit is a library for space flight dynamics. Orekit started in 2002 as a small in-house prod-

uct developed by CS Systèmes d’Information, Toulouse, France. The ORbits Extrapolation KIT

(Orekit) was intended to be a fundamental asset for CS in addition to serving as a basis for cus-

tom systems developed for customers (Ref. 14). The design goals were to write a tool that is easy

to adapt, up to date with respect to recent space flight dynamics models, and still compatible with

older models. Over several years the library matured from a small set of core components to a

full-fledged collection of core classes and associated algorithms: orbits, time, reference frames,

bodies, propagation, attitude, etc. Orekit was first published under the terms of the Apache li-

cense V2 in July 2008. The Apache license is a ‘permissive’ license – the Orekit source code is

published as open-source but distribution of source code for derived works is not mandated (Ref.

15). In early 2011, a public source-forge site was established for Orekit. The Orekit forge pro-

vides public access to activity, bug reports, source code repository, documentation, and down-

loads (Ref. 16). Open governance was established for Orekit in 2012 using a meritocratic model

(Ref. 16). The most prominent application of the meritocratic model is the Apache Software

Foundation (Ref. 21) (Linux also has a very prominent meritocratic model). An initial meeting of

the Orekit Project Management Committee was held in July 2012 (Ref. 22). This meeting led to

an updated Orekit governance charter which is available at Ref. 23.

The wide range of applications of the DSST motivated the inclusion of the DSST in the Orekit

library. The decision to proceed on the development of an Orekit DSST was made in 2011.

Since Orekit employs the java object-oriented programming platform (Refs. 24 and 25), migra-

tion of the DSST to java is necessary for the DSST to be included in Orekit. Migration of the

DSST to an object-oriented programming platform also was identified earlier as a demonstration

task for the Open Source Software Suite for Space Situational Awareness and Space Object Cata-

log project (Ref. 11).

The initial design for the inclusion of the DSST in Orekit was described in (Ref. 10). An

overview is given in Figures 5 and 6. Since February 2013, testing of Orekit DSST has continued

and we report the current results of that testing in this paper.

The options available for testing Orekit DSST are illustrated in Figure 7. The primary ap-

proaches are:

1. Comparison of orbits created with the Orekit numerical integrator with orbits

created with the Orekit DSST

2. Comparison of orbits created with the Orekit java DSST with orbits created with

the F77 DSST Standalone

Rev 8

7

The test results given in this paper are based on this second option.

GSOC EVALUATION OF DSST VERSUS SSA REQUIREMENTS

The purpose of the GSOC study is to find an optimal orbit propagation method which is suita-

ble for space object cataloging.

Figure 8 illustrates the test options available. We note the role of the ODEM Special Perturba-

tion Orbit Determination system and particularly the use of the ODEM least squares estimator to

provide position and velocity vectors compatible with the mean elements assumed in the F77

DSST Standalone.

Refs. 17 and 18 provide initial results of this effort for the LEO, MEO, and GEO flight re-

gimes. This effort has been very helpful in identifying areas for refinement of the F77 DSST

Standalone software, particularly the short periodic motion model

FIXES TO THE F77 DSST STANDALONE SOFTWARE, 2011-2013

The following are the routines in the F77 DSST Standalone that were modified to correct

bugs:

• READ_EPOT.FOR

• NKREAD.FOR

• SPTESS.FOR

• SETSP.FOR

• PTHIRD.FOR

READ_EPOT.FOR was modified to allow the usage of GTDS-style geopotential files with on-

ly one geopotential model.

NKREAD.FOR is the routine for reading the Newcomb operator file. The Newcomb opera-

tors are used to initialize the Hansen coefficient recursions for both the tesseral resonance and the

tesseral linear combination short-periodic terms.

Rev 8

8

SPTESS.FOR is the driver for the DSST tesseral linear combination short periodic terms. The

bug in this routine allowed it to turn off the tesseral resonance terms in the mean element equa-

tions of motion.

SETSP.FOR is the routine that allows convenient selection of moderate or high accuracy con-

figurations for the DSST for the various flight regimes

PTHIRD.FOR primarily is the driver for the third-body mean element rates. However, it is al-

so used in the calculation of the constant terms in the third-body short-periodic expansion in the

eccentric longitude. The bug in PTHIRD.FOR was associated with the constant terms and disa-

bled the third-body short periodic models in the DSST Standalone.

Interestingly, the bugs in SPTESS.FOR and PTHIRD.FOR both seem are associated with the

effort to remove traditional common blocks from the DSST Standalone.

NUMERICAL TEST CASES

We employ four test cases in this paper:

• LEO Sun-synchronous orbit

• GPS 12 hr orbit

• SIRIUS 24 hr elliptical orbit at critical inclination

• Low inclination transfer orbit

Tables 1 though 4 give the initial conditions for the four test cases.

Rev 8

9

Table 1: LEO Sun-synchronous Test Case

Mean Keplerian Element

Epoch 2013 July 23, 3 hr 3 min 5.97 sec UTC

Semi-major Axis

7198.4832626

km

Eccentricity

0.00012750114

Inclination

98.6894245

deg

Right Ascension of the Ascending Node

263.17707959

deg

Argument of Perigee

56.9237741458

deg

Mean Anomaly

303.21338071

deg

TOD Coordinate System

50 x 50 geopotential

Third-body point masses

Atmosphere Drag

Harris-Priester density

Table 2: GPS 12 hr Test Case

Mean Keplerian Element

Epoch 1996 January 1, 1 hr 0 min 0.0 sec UTC

Semi-major Axis

26560.271744

km

Eccentricity

0.00089794449

Inclination

54.905215982

deg

Right Ascension of the Ascending Node

336.831733455

deg

Argument of Perigee

5.54483916534

deg

Mean Anomaly

354.376050766

deg

TOD Coordinate System

8 x 8 geopotential

Third-body point masses

Solar Radiation Pressure

Rev 8

10

Table 3: SIRIUS 24 hr Elliptical Orbit (Critical Inclination) Test Case

Mean Keplerian Element

Epoch 2000 July 3, 0 hr 0 min 0.0 sec UTC

Semi-major Axis

42163.393

km

Eccentricity

0.2684

Inclination

63.435

deg

Right Ascension of the Ascending Node

285.0

deg

Argument of Perigee

270.0

deg

Mean Anomaly

344.0

deg

TOD Coordinate System

8 x 8 geopotential

Third-body point masses

Table 4: Low Inclination Transfer Orbit Test Case

Mean Keplerian Element

Epoch 1996 January 1, 1 hr 0 min 0.0 sec UTC

Semi-major Axis

27348.233234545

km

Eccentricity

0.5236375082382266024377202553175

9

Inclination

5.99985975232

deg

Right Ascension of the Ascending

Node

1.50307478738

deg

Argument of Perigee

177.993508218

deg

Mean Anomaly

162.1050405

deg

TOD Coordinate System

5 x 5 geopotential

Third-body point masses

Solar Radiation Pressure

Rev 8

11

Figures 9 through 14 are the results of comparing Orekit java DSST and F77 DSST

Standalone for the LEO case. The mean equinoctial element histories and differences are given.

Figures 15 through 25 are the results of comparing Orekit java DSST and F77 DSST

Standalone for the GPS case. Both mean Keplerian and mean equinoctial element histories and

differences are given. The interval is 17500 days in length.

Figures 26 through 31 are the results of comparing Orekit java DSST and F77 DSST

Standalone for the SIRIUS case. The mean Keplerian element histories and differences are given.

Figures 32 through 34 are the results of comparing Orekit java DSST and F77 DSST

Standalone for the low inclination transfer orbit case. The mean Keplerian element histories and

differences are given.

In all the cases, the difference between the Orekit java DSST and the F77 DSST Standalone is

very small relative to the element motion over the time interval considered.

CONCLUSION

In the interval from 2011 through 2013, three projects were initiated which together have un-

covered several bugs in the F77 Standalone implementation of the DSST satellite theory.

1. The DSST Standalone was included on the

Astrody

Tools

Web

Web-Site prototype es-

tablished at the Universidad de La Rioja, Spain.

2. The DSST was implemented as an orbit propagator in object-oriented java as

part of Orekit open source library for space flight dynamics

3. The accuracy and computation time characteristics of the DSST Standalone rela-

tive to the requirements of space object catalog maintenance are being evaluated

by the Space Situational Awareness Group at the DLR GSOC.

While each of these projects has its own set of goals and tests, the test cases results taken to-

gether have led to significant overall improvement of the DSST F77 software and a better under-

standing of the associated documentation.

FUTURE WORK

The following tasks are to be addressed in the future:

Rev 8

12

1. Extension of the Web interface for the DSST Standalone Orbit Propagator to in-

clude Orbit Determination processing

2. Inclusion of the DSST short-periodic motion models in the Orekit java DSST li-

brary

3. Extension of the DSST short-periodic motion models included in the F77

Standalone DSST

4. Activating the DSST partial derivative models in the F77 Standalone DSST

5. Development of procedures for applying complex spacecraft geometrical and

material models in the DSST non-conservative forces

6. Non-invasive encapsulation of the Linux GTDS R&D Orbit Determination sys-

tem

7. Development of approaches for applying heterogeneous parallel computing ca-

pabilities (CPU, GPU, and FPGA) in the Linux GTDS R&D Orbit Determination

system

The Web interface for DSST-based orbit determination requires consideration of the estima-

tor(s) to be employed, improvements to Web DSST necessary to process data, the observation

modeling, and the observation database.

The short-periodic motion models in the DSST are more complicated (particularly the closed-

form zonal harmonic and lunar-solar point mass terms) than the analogous mean element equa-

tions of motion models. We expect to be able to apply knowledge gained from the existing java

implementation of the DSST.

We intend to extend the F77 Standalone DSST short periodic models to include:

a. J2-squared terms

b. J2 secular/tesseral m-daily coupling terms

c. Lunar-solar point mass weak-time-dependent (WTD) terms

d. Additional SPSHPER options to provide high accuracy options for LEO-

eccentric, MEO, GEO, and HEO orbits

It is also our intent to reconsider the numerical integration method to be used with the DSST.

Rev 8

13

The overall intent is to improve the capability of the F77 Standalone to process observation

data in multiple orbital regimes.

The partial derivative capability was included in the original DSST Standalone (1984) but this

capability is not visible with the current orbit_propagator_services architecture. The partial

derivative capability needs to be activated in order to allow the F77 DSST Standalone to support

orbit determination.

The work of Dr. Bent Fritsche (Ref. 26) is typical of the complex spacecraft geometrical and

material models that we would like to investigate in the DSST context.

For the non-invasive encapsulation of the Linux GTDS R&D Orbit Determination system, we

would like to investigate the LCML and LEGEND concepts developed at MIT (Ref. 27).

We would like to investigate the role of software tools such as OpenACC in the application of

heterogeneous parallel computing capabilities to legacy software such as the Linux GTDS R&D

Orbit Determination system (Ref. 28).

ACKNOWLEDGMENTS

The authors would like to acknowledge the support and encouragement of Mr. Luc

Maisonobe, Mr. Pascal Parraud, Dr. Petr Bazavan, and Mr. Nicolas Frouvelle of CS Communica-

tions & Systèmes, Toulouse, France and Dr. Oliver Montenbruck and Dr. Hauke Fiedler at the

DLR/GSOC, Wessling, Germany.

The authors would like to acknowledge the original developers of the DSST Satellite Theory

and its implementation in Fortran 77 including Mr. Wayne McClain, Mr. Leo Early, Dr. Ron

Proulx, Dr. Mark Slutsky, Dr. David Carter, and Mr. Rick Metzinger, all at the Draper Laborato-

ry, Cambridge, MA. The authors also acknowledge the efforts of Prof. Don Danielson at the Na-

vy Postgraduate School, Monterey, CA, in preparing a single integrated document describing the

as-built DSST. The authors also acknowledge the several MIT Aeronautics and Astronautics De-

partment graduate students who participated in the development, test, evaluation, and application

of the Semi-analytical Satellite Theory at the Draper Laboratory.

The work of Zachary Folcik is sponsored by the Department of the Air Force under contract

FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of

the author and are not necessarily endorsed by the United States Government.

Rev 8

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REFERENCES

1. Leo W. Early, A Portable Orbit Generator using Semi-analytical Satellite Theory,

AIAA preprint 86-2164, presented to AIAA/AAS Astrodynamics Conference, Williams-

burg, VA, August 1986.

2. M. Slutsky, The First-Order Short-Periodic Motion of An Artificial Satellite Due to

Third-Body Perturbations: Numerical Evaluation, AAS paper 83-393, AAS/AIAA

Astrodynamics Specialist Conference, Lake Placid, NY, August 1983.

3. G. B. Green, Semi-Analytic Propagator Alterations, Aerospace Corporation Interoffice

Correspondence, August 1985.

4. R. G. Hopkins, Description of the Astrodynamics Department MEANELT

Stationkeeping and Orbit Propagation Capabilities, Aerospace Corporation, Aerospace

Technical Memorandum #86(9975)-23, January 1986.

5. R. G. Hopkins, A User’s Guide to Program MEANELT, Aerospace Corporation, Aero-

space Technical Memorandum #87(9975)-62, September 1987.

6. Daniel John Fonte, Jr., Implementing a 50 x 50 Gravity Field Model in an Orbit Deter-

mination System, Master of Science Thesis, Department of Aeronautics and Astro-

nautics, MIT, June 1993 (CSDL-T- 1169).

7. Scott Shannon Carter, Precision Orbit Determination from GPS Receiver Navigation

Solutions, Master of Science Thesis, Department of Aeronautics and Astronautics, MIT,

June 1996 (CSDL-T- 1260).

8. Joseph G. Neelon, Paul J. Cefola, and Ronald J. Proulx, Current Development of the

Draper Semi-analytical Satellite Theory Standalone Orbit Propagator Package, AAS

paper 97-731, AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, ID, August

1997.

9. Paul J. Cefola, Donald Phillion, and K. S. Kim, Improving Access to the Semi-Analytical

Satellite Theory, AAS paper 09-341, AAS/AIAA Astrodynamics Specialist Conference,

Pittsburgh, PA, August 2009.

10. Paul J. Cefola, Barry Bentley, Luc Maisonobe, Pascal Parraud, Romain Di-Costanzo and

Zachary Folcik, Verification of the Orekit Java Implementation of the Draper Semi-

Analytical Satellite Theory, AAS paper 13-398, AAS/AIAA Space Flight Mechanics

Meeting, Lihue,Kauai, Hawaii, 10-14 February 2013.

11. Cefola, Paul J., Brian Weeden, and Creon Levit, Open Source Software Suite for Space

Situational Awareness and Space Object Catalog Work, presented at the International

Conference on Astrodynamic Tools and Techniques (ICATT), ESA/ESAC, Madrid,

Spain, 3-6 May 2010

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15

12. San-Juan, J. F., Lara, M., López, R., López, L. M., Weeden, B. and Cefola, P. J., Using

the DSST Semi-Analytical Orbit. Propagator Package via the

NondyWebTools/AstrodyWebTools, Proceedings of 62

nd

International Astronautical

Congress, Cape Town, SA. 2011.

13. San-Juan, J. F., Lara, M., López, R., López, L. M., Weeden, B. and Cefola, P. J.,

Allocationof DSST in the new implementation of , Proceedings of the

AMOS Advanced Maui Optical and Space Surveillance Technologies Conference, Maui,

Hawaii, USA. September 2012.

14. Pommier-Maurussanet, V., and Mainsonobe, L., Orekit: an Open-source Library for

Operational Flight Dynamics Applications, presented at the International Conference on

Astrodynamic Tools and Techniques (ICATT), ESA/ESAC, Madrid, Spain, 3-6 May

2010.

15. Mainsonobe, L., Cefola, P. J., Frouvelle, N., Herbiniere, S., Laffront, F.-X., Lizy-Destrez,

S., and Neidhart, T., Open Governance of the Orekit Space Flight Dynamics Library,

presented at the International Conference on Astrodynamic Tools and Techniques

(ICATT). ESA/ESTEC, Noordwijk, The Netherlands, 29 May-1 June 2012.

16. Orekit forge, https://www.orekit.org/forge/projects/orekit

17. Srinivas J. Setty, Paul J. Cefola, Oliver Montenbruck, and Hauke Fiedler, Investigating

the Suitability of Analytical and Semi-Analytical Satellite Theories for Space Object

Catalogue Maintenance in Geosynchronous Regime, AAS paper 13-769, AAS/AIAA

Astrodynamics Specialist Conference, Hilton Head, South Carolina, August 2013.

18. Srinivas J. Setty, Paul J. Cefola, Oliver Montenbruck, and Hauke Fiedler, Prediction Ac-

curacies of Draper Semi-analytical Satellite Theory in LEO, MEO and Regime for

Space Object Catalogue Maintenance, AAS paper 14-319, to be presented at the

AAS/AIAA Spaceflight Mechanics Meeting, Santa Fe, New Mexico, 26 -30 January

2014.

19. Zeis E. G., A Computerized Algebraic Utility for the Construction of Nonsingular Sat-

ellite Theories, Master of Science Thesis, Department of Aeronautics and Astronautics,

MIT, September 1978.

20. Kaniecki, J. P., Short Periodic Variations in the First Order Semianalytical Satellite

Theory, Master of Science Thesis, Department of Aeronautics and Astronautics, MIT,

August 1979.

21. Apache meritocracy, http://www.apache.org/foundation/how-it-works.html#meritocracy

22. Minutes of first Orekit Project Management Committee (PMC) meeting,

https://www.orekit.org/forge/attachments/318/PMC_meeting_050712.pdf

23. OREKIT governance charter,

https://www.orekit.org/forge/attachments/317/OREKIT_Governance.pdf

Rev 8

16

24. Maisonobe, Luc, Using Java for numerical computation: a space flight dynamics oper-

ational example, presented at the Data Systems in Aerospace Conference (DASIA 2010),

Budapest, Hungary, 1-4 June 2010.

25. Roberts, Eric S., The Art & Science of Java -- An Introduction to Computer Science,

Addison Wesley (Pearson), Boston, MA, 2008

26. Fritsche, B., and H. Klinkrad, Accurate Prediction of Non-gravitational Forces for Pre-

cise Orbit Determination, Part I Principles of the Computation of Coefficients of Force

and Torque, AIAA preprint 2004-5461, presented at the AIAA/AAS Astrodynamics

Specialist Conference, Providence, RI (August 2004).

27. Evangelinos, C., Lermusiaux, P. F. J., Geiger, S. K., Chang, R. C., and Patrikalakis, N.

M., (2006) Web-enabled Configuration and Control of Legacy Codes: An Application

to Ocean Modeling, Ocean Modeling, 13, 197-220.

28. Wolfe, Michael, (Introduction to GPU Computing with OpenACC, November 2012

(http://www.pgroup.com/lit/presentations/sc12_tutorial_openacc_intro.pdf )

17

Figure 1. Fortran 77 DSST Standalone Program Top Level Design

Figure 2. DSST encapsulation in the

Astrody

Tools

Web

Web-Site

18

Figure 3. Test Process for the DSST encapsulation in the

Astrody

Tools

Web

Web-Site

Figure 4. Test Process for the F77 DSST Standalone

19

Figure 5. Design of Flight Dynamics Applications using the Orekit Library

Figure 6. Orekit DSST Propagator Class Diagram

20

Figure 7. Test Processes for the Orekit java DSST

Figure 8. Test Processes for the GSOC Evaluation of DSST for SSA

21

Figure 9 DSST Mean Semi-major axis Histories and Difference for the LEO orbit over 7500

days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)

Figure 10 DSST Mean Equinoctial Element h Histories and Difference for the LEO orbit over

7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)

22

Figure 11 DSST Mean Equinoctial Element k Histories and Difference for the LEO orbit over

7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)

Figure 12 DSST Mean Equinoctial Element p Histories and Difference for the LEO orbit over

7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)

23

Figure 13 DSST Mean Equinoctial Element q Histories and Difference for the LEO orbit over

7500 days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)

Figure 14 DSST Mean Mean Longitude λ

λλ

λ Histories and Difference for the LEO orbit over 7500

days (Orekit & F77 Standalone) (50x50 geopotential, Drag, & Lunar-Solar point masses)

24

Figure 15 DSST Mean Semi-major axis Histories and Difference for the GPS orbit over 17500

days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

Figure 16 DSST Mean Eccentricity Histories and Difference for the GPS orbit over 17500

days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

25

Figure 17 DSST Mean Inclination Histories and Difference for the GPS orbit over 17500

days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

Figure 18 DSST Mean RAAN Histories and Difference for the GPS orbit over 17500 days

(Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

26

Figure 19 DSST Mean Argument of Perigee Histories and Difference for the GPS orbit over

17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

Figure 20 DSST Mean Mean Anomaly Histories and Difference for the GPS orbit over 17500

days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

27

Figure 21 DSST Mean Equinoctial Element h Histories and Difference for the GPS orbit over

17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

Figure 22 DSST Mean Equinoctial Element k Histories and Difference for the GPS orbit over

17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

28

Figure 23 DSST Mean Equinoctial Element p Histories and Difference for the GPS orbit over

17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

Figure 24 DSST Mean Equinoctial Element q Histories and Difference for the GPS orbit over

17500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

29

Figure 25 DSST Mean Mean Longitude λ

λλ

λ Histories and Difference for the GPS orbit over 17500

days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses, and SRP)

Figure 26 DSST Mean Semi-major axis Histories and Difference for the SIRIUS 24 hr orbit

over 7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)

30

Figure 27 DSST Mean Eccentricity Histories and Difference for the SIRIUS 24 hr orbit over

7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)

Figure 28 DSST Mean Inclination Histories and Difference for the SIRIUS 24 hr orbit over

7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)

31

Figure 29 DSST Mean RAAN Histories and Difference for the SIRIUS 24 hr orbit over 7500

days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)

Figure 30 DSST Mean Argument of Perigee Histories and Difference for the SIRIUS 24 hr or-

bit over 7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)

32

Figure 31 DSST Mean Mean Anomaly Histories and Difference for the SIRIUS 24 hr orbit

over 7500 days (Orekit & F77 Standalone) (8x8 geopotential, Lunar-Solar point masses)

Figure 32 DSST Mean Semi-major Axis Histories and Difference for low inclination 12.5 hr

transfer orbit over 7500 days (Orekit & F77 Standalone) (5x5 geopotential, Lunar-Solar point

masses, solar radiation pressure)

33

Figure 33 DSST Mean Eccentricity Histories and Difference for low inclination 12.5 hr transfer

orbit over 7500 days (Orekit & F77 Standalone) (5x5 geopotential, Lunar-Solar point masses,

solar radiation pressure)

Figure 34 DSST Mean Inclination Histories and Difference for low inclination 12.5 hr transfer

orbit over 7500 days (Orekit & F77 Standalone) (5x5 geopotential, Lunar-Solar point masses,

solar radiation pressure)