David Arnold Research
Custom design and analysis of Retroreflector arrays
Laser tracking of satellites
This website traces my involvement in the design of the Lageos and Lares
satellites that are the core satellites used for determination of the
International Terrestrial Reference Frame (ITRF).
Contents:
1a. Lageos-1
1b. Lageos-2
1c. Correlation method
2a. Lares-1
2b. Lares-2
2c. Initial plan, minimal changes
2d. Proposal for a new design
3. Authorship and intellectual property
4. Funding problems
4a. Legal and contractual problems
4b. Design vs analysis
4c. Work done under my SAO contract
4d. Resignation from SAO
4e. Best use of my expertise
4f. Complaints filed
5a. The security of SAO - the insecurity of self employment.
5b. My pay scale
6a. Complaint to ASI
6b. Lawsuit against SAO and/or Dr. Pearlman
8. Design of Lares-2 - the "next generation" Lageos
9. Lares-2 and space geodesy
10. Summary of work on geodetic satellites
11. Other work
12. Hollow Retroreflectors
13. My expertise and experience in satellite tracking
14a. The Tethered Satellite System TSS
14b. Positive energy tethered satellite system in a bound orbit
15. Development of the retroreflector array analysis programs
16. Curriculum Vita and Bibliography
1a. Lageos-1
Lageos-1 satellite, radius 30 cm
Lageos-1 was built and launched by the U.S. in 1976.
In order to optimize the performance of Lageos-1, I wrote software for
calculating the range correction and cross section of a retroreflector array.
This software is unique. To the best of my knowledge no one else has developed
software for analyzing an array of retroreflectors. This software is essential
to the design process.
This software is documented in the report below.
SAO Special Report 382
Examples of transfer functions that have been computed for various satellites
are given in the report "Retroreflector Array Transfer Functions" presented at
at the 13th International Workshop on Laser Ranging, Washington, DC, USA,
October 7-11, 2002. The reference below is the only complete version of the paper.
It includes the appendices describing how the various analysis programs work.
Transfer
This software was used in the design of the Lageos satellite. The report below
dated April, 1973 is the final report for the design of Lageos by the principal
investigator Dr. George Weiffenbach. My analysis is presented in the tables and
figures in section 5.3 "Retroreflector Array", page 24.
Use of a Passive Stable Satellite for Earth Physics Applications
Additional information on the work done on the design of Lageos is given in
the report below.
Lageos Support
This software was also used to calculate the transfer function of Lageos.
The analysis is given in the report below.
Lageos Transfer Function
Hand drawn contour plots for a single incidence angle on the satellite were
shown for both linear and circular polarization for the far field cross section
matrix (pages 88 and 96) and the centroid matrix (pages 143 and 141). The cross
section shows a dumbbell shape for linear polarization and a circular shape for
circular polarization. The symmetry for the centroid is unclear.
Some calculations for Lageos were presented at the 2002 ILRS International Workshop.
Transfer. Section 4A, Fig. 3 shows the same cross section
and centroid matrices from
the 1978 report using modern graphics. The structure of the patterns is much easier
to see.
Physical reasoning says that the average cross section and centroid patterns for
circular polarization should be circular. To test this hypothesis, the average cross
section and centroid patterns have been computed over 16 orientations and plotted
in Fig. 4 of the 2002 report. The centroid shows approximate circular symmetry.
However, running a larger number of orientations was impractical due to the amount
of computer time required. The centroid matrices were averaged over a large number
of orientations in Fig. 4 of the 2017 Lageos-2 paper in the next section. The centroid
shows good circular symmetry that is not apparent in the pattern for a single incidence
angle.
1b. Lageos-2
An exact copy of Lageos-1 was built by ASI and launched by the Shuttle in 1992.
The 2017 report below gives an analysis of the Lageos-2 satellite. Lageos-2 is
is identical to Lageos-1. However, the advances in computer speed and graphics
made it possible to do much more extensive simulations and present them in a
much better way visually. This analysis was requested by Dr. Antonio Paolozzi,
the chief engineer for the design of Lares-2. This report was never published.
Lageos-2 Transfer Function
1c. Correlation method.
At the Technical Workshop in Riga, Latvia in 2017, I developed and presented a paper
on using the correlation method to determine the center of mass of a set of range
measurements. Instead of taking the average of the set of measurements, the set
of range measurements is moved from one side of the histogram of the retroreflector
array to the other side, computing the product of the range measurements with the
histogram at each position. The point where the product is a maximum is taken as the
center of mass (CoM). This removes the effect of data clipping. The paper is shown below.
Correlation Method
and
Correlation Method ILRS Workshop 2017
2a. Lares-1
Lares-1 satellite built by ASI and launched in 2012, radius 18.2 cm
Lares-1 is a smaller version of Lageos using the same type of retroreflectors.
I was asked to work on the design of Lares in 2006. I worked at INFN-LNF on
three occasions from 2006 to 2007. I gave the presentation below at the
First International LARES Science Workshop held in Rome - 3-4 July 2009.
Presentation on design of Lares in 2009
The report below gives the full transfer function of the Lares satellite.
An abbreviated version was presented as a poster at the 19th International
Workshop on Laser Ranging held at Annapolis in 2014.
Lares Transfer Function
2b. Lares-2
Lares-2 satellite built by ASI and launched in 2022, radius 21.2 cm
A general description of Lares-2 is given on the ESA website
ESA website
The section "cube corner reflectors" describes the changes to the retroreflectors.
The last three references (28,29,30) are to my publications.
The work I did on the design of Lares-2 was done under a long-standing contract
with SAO whose terms include the following:
INTELLECTUAL PROPERTY RIGHTS IN WORK PRODUCT:
The Contractor acknowledges that any and all copyrightable work done for the
Smithsonian hereunder will be "work for hire" under the U.S. Copyright Law
(17 U.S.C.101) and hereby assigns to the Smithsonian all right, title, and interest
in all work product created under the contract, including patents, copyrights,
and other intellectual property rights. As a result the Smithsonian will retain
full ownership of any product or service that the Contractor provides to the
Smithsonian.
The contract between ASI and Sapienze University states that the design of Lares-2
is protected by Article 10 of the contract. The redesign of Lares-2 uses a design
that I invented and published in Advances in Space Research 65 (2020) pages 2276-2289.
In 2016, I was asked to participate in the design of a second Lares satellite to be
built by ASI and launched on the test flight of the VEGA-C rocket in 2019/2020.
The request was made by Dr. Erricos Pavlis at the University of Maryland. Dr. Pavlis
is a co-investigator on the project.
Dr. Erricos Pavlis
Chair, ILRS Analysis Standing Committee
Editor, The European Physical Journal Plus
Assoc. Editor, Celestial Mechanics & Dynamical Astronomy
Joint Center for Earth Systems Technology, (JCET/UMBC)
University of Maryland, BC & NASA Goddard 61A
TRC #182
1000 Hilltop Circle
Baltimore, Maryland
U S A 21250
He made the request on behalf of the principal investigator Dr. Ignazio Ciufolini, and
the chief engineer Dr. Antonio Paolozzi. Dr. Michael Pearlman at SAO, Director of the
Central Bureau of the ILRS (International Laser Ranging Service), agreed to fund my
work under a long-standing contract that I have with SAO that has paid me $12,000/year
since 2003. The funding comes from NASA. I had no contract with ASI. Sapienza
Universtiy paid me 5000 Euros for some analysis.
This is the first upgrade of the basic Lageos design in almost 50 years. It will be the
beginning of a new era in earth physics studies.
Below is a brief description of the work I did on the design.
Design of Lares-2
The design was first published in 2017 at the ILRS worksop in Riga.
2017 Lares-2
A description of the design without reference to Lares-2 was presented at the 2018 ILRS
workshop in Canberra.
2018 Thermal-optical design of a geodetic satellite
2018 Thermal-optical design of a geodetic satellite presentation
The basic principles of the design are published in Advances in Space Research.
2020 Design of geodetic satellite
A summary of the design process is given in the paper below.
2022 Summary of the design of Lares-2
2c. Initial plan, minimal changes
The primary mission is relativity studies. This does not require greater accuracy.
Although the satellite is being built by Italy, NASA has a strong vested interest in
the satellite since it can be used for earth physics being done by NASA and for
the determination of the ITRF (International Terrestrial Reference Frame). More
satellites are needed for accurate determination of the ITRF. The accuracy goal is
is higher for the earth physics studies.
Initially the plan was to use the same type of retroreflectors used on Lageos. This was
similar to the way Lares-1 was designed. The only change was to the size and weight of
the satellite to accommodate the mission requirements. I had worked on the design of
Lares-1. It did not require a large amount of analysis or funding since there was no
change to the type of retroreflector and mounting cavity.
The work to be done initially is given below.
Initial work
2d. Proposal for a new design.
The analysis I had done on the design of Lageos-1 in the early 1970s showed that better
accuracy could be obtained by using a larger number of smaller cube corners. Since
this would be more expensive and was not needed for the accuracy goal of 5 millimeters,
this alternate design was not used.
My analysis of smaller cubes was never published. The only person I told about this
alternate design for Lageos was the Principal Investigator Dr. George Weiffenbach.
I proposed using smaller cubes on the second Lares in order to increase the accuracy.
This would require using a larger number of cubes to obtain the needed cross section.
The higher cost could be avoided by using inexpensive COTS cubes. The cubes would
need to be tested to make sure they were of sufficient quality. This could be done
by Dr. Ludwig Grunwaldt and Dr. Reinhart Neubert at GFZ.
Dr. Antonio Paolozzi asked Reinhart Neubert and Ludwig Grunwaldt to participate in
the design. The testing of the COTS cubes showed that the quality is comparable to
custom manufactured cubes. They can be obtained quickly in order to meet the launch
date with a larger number of cubes.
The terms and conditions of my employment were clarified in a set of emails dated
March 4-6, 2017 shown in the file
Terms and Conditions
There were a lot of negotiations going on with ASI about changing the design
as described in the email from Erricos Pavlis dated March 6, 2017.
Erricos email
The proposal to use smaller COTS cubes was discussed with Dr. Giuseppe Bianco who
is an official of ASI. In an email dated September 15, 2017, I answered his questions
regarding the advantages of using this new design. The email is below.
Bianco email
Dr. Pearlman wrote a letter to the President of ASI supporting the new design.
Pearlman letter supporting the new Lares-2 design
In that letter, Mike Pearlman stated "The newer technologies, with kilohertz lasers,
solid state detectors and very fast event timers have improved to the point where
the satellite design is now a major limitation in reaching the 1 mm goal."
This statement may not be entirely correct. The stations do not yet have the ability to
range to millimeter accuracy especially with respect to the atmospheric correction.
For this reason there is no way to verify the accuracy of Lares-2 using the tracking
data. Unless there is prelaunch testing, the claim of 1 mm accuracy rests entirely on
my theoretical calculations.
The decision was made to use 1.0 inch COTS cubes. Below is the email from Ignazio
Ciufolini dated October 16, 2017.
Design accepted by ASI.
The only remaining item was "It is not yet clear if the design of the mounting system
that Antonio and you have proposed, will be accepted by ASI."
The possibility of getting a free launch for Lares-2 on the test flight of the Vega-C
and the availability of inexpensive COTS cubes opened up the possibility of creating
a satellite that could make a significant contribution to science by providing the one
millimeter accuracy that is the current goal for the earth physics studies and the
ITRF.
Changing the cube size affected every aspect of the design. What would have been a
routine effort now became a major effort that would have to be done very quickly
and efficiently to meet the launch deadline. I felt it could be done successfully.
What followed was an intense design effort involving myself, Reinhert Neubert, Ludwig
Grunwaldt, and the Lares-2 team. All the problems were successfully resolved within
the time frame needed to meet the launch date. This new design will make Lares-2
the most accurate satellite used for geodetic studies.
The satellite was put into orbit in a flawless launch on July 13, 2022.
3. Authorship and intellectual property
I had been planning to present a paper at the International Workshop on Laser Ranging
in Canberra, Australia in November, 2018 describing the work I had completed on the
design of Lares-2.
On Aug 3, 2018 I received the email below
Email from the Journal of Geodesy
On August 18, 2018 sent an email to Antonio and Ignazio about an abstract I had
submitted to the ILRS workshop.
Workshop paper
On August 22, 2018, I received the email below from the Principal Investigator
objecting to the use of the word "design" in the title.
Email from Ignazio Ciufolini
I refused an offer to be a coauthor on one of his papers.
The mechanical design was done by Dr. Antonio Paolozzi, the chief engineer on the
Lares-2 project. The thermal optical design was done my myself.
To avoid any problems with authorship and use of the word design, I decided to change
the paper to a general description of the techniques used in the design. The report
below describes the basic principles used in the design of Lares-2.
New Design for a Geodetic Satellite
Since I had decided not to attend the workshop in Canberra, Dr. Erricos Pavlis
agreed to present the paper on my behalf.
A revised version of the paper to correct an error in section 6 is below.
Revised version of the paper.
In order to provide background on the Lageos and Lares satellites a third
version of the paper has been written.
WORD version of the paper.
The design has also been published in "Advances in Space Research"
Design of geodetic satellite
This publication in a peer reviewed journal establishes that I invented the
therml optical design used on Lares-2.
4. Funding problems
The only funding I had received during the work on Lares-2 was $12,000/year from a
contract with SAO that goes back to 2003. I did about 15 months of work on Lares-2.
No provision had been made for the funding needed to do an extensive redesign of the
satellite. This was no surprise. Neither the availability of a free launch or an
extensive design effort could have been anticipated. I expected that the funding issue
would be addressed retroactively.
The $12,000/year paid by SAO could only cover a very small part of the work that I
had done. After the work was finished, I pointed out to my contract monitor that
I had not been paid for all the work I did. His response is given below.
Contribution to science
4a. Legal and contractual problems
In November of 2017, Mike Pearlman asked for more money for the Lares-2 work. The
request was refused.
Email from Dr. Pearlman
I requested full payment from Dr. Stephen Merkowitz who manages all the NASA funding
for the ILRS (International Laser Ranging Service).
I received the unexpected reply below from Dr. Merkowitz dated November 6, 2018.
Reply from Dr. Merkowitz
Dr. Pearlman claimed that an exception had been agreed to for working on Lares-2.
Exception for working on Lares-2
However, Dr. Pearlman never presented any proof that such an agreement exists.
4b. Design vs analysis
The Principal Investigator and the contractor hired to do the design of Lares-2 denied
that I had worked on the design.
Design vs Analysis
In a public email dated November 24, 2018, Ignazio and Antonio state That the design
is protected by Article 10 of the agreement between ASI and Sapienza University.
Antonio.
A description of my activities is given in the paper
2022 Summary of the design of Lares-2
I am an internationally recognized expert as certified in the document
Relazione per assegnazione prestazione occasionale Dr. David Arnold
The tranlation to English is Translation to English
Reinhart Neubert and Ludwig Grunwaldt played a critical role in the design of
Lares-2 by showing that COTS retroreflectors have the same optical quality as
expensive custom made retroreflectors. In an email to Dr. Giuseppe Bianco, an
official of ASI, Reinhart confirms that Lares-2 uses the conceptual design
that I proposed. Dr. Bianco already knew this since he was involved in the decision
to use 1.0 inch COTS cubes.
Email from Dr. Neubert to Dr. Bianco
Below is a copy of the email dated June 2, 2017 in which I proposed a new design that
eliminates the problems with the 1.5 inch retroreflectors used on Lageos-1, Lageos-2,
and Lares-1.
Propose new design
4c. Work done under my SAO contract.
The reports below dated July 31, 2017 and September 27, 2018 show that I was working
on Lares-2 under my contract with SAO.
Annual report
Contract report
In the email dated October 20, 2018, Mike Pearlman denies ever having asked me
to work past $12,000/year.
Deny work over $12,000/year
Mike Pearlman agreed to cover my work under his contract, at least initially. The email
dated March 21, 2016 is below.
Initial payment
Dr. Pavlis gave assurance that "If successful, there will be more funding for him down
the road".
4d. Resignation from SAO.
The design was completed in the fall of 2018. I received the email from Dr. Merkowitz
stating that I would not be paid on November 6, 2018. On November 10, 2018 I resigned
from my SAO contract.
4e. Best use of my expertise.
Almost all the existing laser targets have problems with either accuracy or cross
section. There is usually no feasible method of dealing with this after launch.
The only approach is to design the array to reduce the effects to a level that
meets the project requirements. Lares-2 is the first multi-cube array where thermal
and optical effects have been reduced to a level that can be neglected.
The most effective use of my expertise is in the conceptual design of reflectors.
Dr. George Weiffenbach on the Lageos-1 project and Dr. Giuseppe Colombo on the
tethered satellite project gave me the oppotunity work on new designs. I was well
paid for my services and given credit for my work. This work done while I was a
full-time employee at SAO.
4f. Complaints filed.
I have filed complaints with the NASA OIG, SAO, the American Embassy in Rome, the
Commissioner of ASI, and Steve Merkowitz who manages the NASA funding for ILRS.
5a. The security of SAO - the insecurity of self employment.
As a full time employee, I was protected by all the laws and rules designed to
protect employees. As a contractor it was now my responsibility to protect myself.
I did not understand this and failed to take the steps needed to protect myself.
5b. My pay scale
If I were still a full time employee of SAO I would have been paid salary and benefits
for about 15 months of work at GS pay grade 13, step 10. At the time I left SAO
in 1995 my salary was 65,700/year. This does not include benefits, overhead, etc.
The 2018 pay scale for Boston for GS 13 step 10 was $125,335/year. Inflation has been
about a factor of 2 over the last 25 years since I left SAO. I never got a pay raise from
Mike Pearlman.
6a. Complaint to ASI
I received the email below from the Commissioner of ASI in response to
my complaint about Lares-2.
Response from the Commissioner of ASI
This is very similar to the response I got from Dr. Merkowitz at NASA.
Reply from Dr. Merkowitz
6b. Lawsuit against SAO and/or Dr. Pearlman
I was always treated with respect while I was a full time employee of SAO.
However, the way I was treated as a contractor is unacceptable to me.
What happended took me ompletely by surprise. It did a lot of needless
damage to me, and to the project, and to people depending on the project.
Dr. Michael Pearlman asked me to work on the design of Lares-2. He did not tell
me that he had no legal authority to pay me to work for a foreign agency. I did
not know that until I got the email from Dr. Merkowitz on November 6, 2018.
Government employees have absolute immunity for acts taken as part of their
official duties. I did not know that until I filed a lawsuit for misrepresentation.
This is all perfectly legal. Unfortunately, I am not willing to work for people or
institutions that cannot be held accountable if they do something wrong.
The Declaration filed by Dr. Pearlman is shown below.
Pearlman Declaration.
In Section 7, Dr. Pearlman says he asked me to "assess the Lares-2 satellite
for inclusion in the ILRS". He never made any such request to the best of
my knowledge. The emails in
Terms and Conditions
show that I was asked to help with the new design. I was told "Do whatever you can
to support this work".
My lawsuit was dismissed on the grounds of sovereign immunity. Immunity is not
innocence. The facts were never adjudicated.
The court order is given in the file
Court Order.
As stated in the court order, the Westfall Act "accords federal employees absolute
immunity from common-law tort claims arising out of acts they undertake in the course
of their official duties."
A tort against a federal employee is considered a tort against the United States.
The United States is substituted as the defendant.
The order states, "Arnold's claim of misrepresentation must be dismissed for lack of
subject matter jurisdiction, as the FTCA bars such claims against the federal
government. Absent waiver of sovereign immunity, the federal courts lack subject
matter jurisdiction over torts against the United States." (page 6)
The exceptions to the FTCA are listed in the file
Exceptions.
The transcript of the hearing is given in the file
Transcript.
On page 13, the judge stated "the situation should not have happened as it did, right?
You work - you do work, you should be paid for the work that you do. And my guess is
there's nobody who disagrees with that."
8. Design of Lares-2 - the "next generation" Lageos
The Lageos-1, Lageos-2, and Lares-1 satellites do not meet current requirements.
Lares-2 is the "next generation Lageos". My estimate was about 3 mm for systematic
errors in Lageos. My estimate for Lares-2 is one millimeter.
I am making an effort to document my work on the design. The file below gives a
discussion of the most important aspects of the design. I cannot compute a final
transfer function for the satellite since I was never given the final configuration.
Design of Lares-2
9a. Lares-2 and space geodesy
The primary purpose of Lares-2 is verification of one of the predictions of Einstein's
general theory of relativity.
A secondary use of Lares-2 will be in space geodesy. This is discussed on page 6,
Section 6 of the paper
Lares-2 and Space Geodesy
The paper makes the following points:
1. Satellite Laser Ranging (SLR) now provides uniquely the most accurate definition
of the origin of the International Terrestrial Reference Frame (ITRF) and has an equal
share with VLBI in the definition of its scale.
2. We are far from having the ideal "SLR Constellation", compared to the GNSS ones.
3. The ideal constellation would comprise a number of LARES-class spacecraft.
Lares-2 provides the one millimeter accuracy needed by the ITRF. The design I
invented is commercially valuable. There is a lot of money to be made by building
copies of the design I invented.
10. Summary of work on geodetic satellites
I was involved in the design of the Lageos satellites, Lares-1, and Lares-2. I have
computed detailed transfer functions for Lageos-1, Lageos-2, and Lares-1. Since I no
longer work for ILRS due to a dispute over wages/intellectual property, I will not be
computing a final transfer function for Lares-2.
In the time since I stopped working for ILRS in 2018 I have worked privately on various
designs that could eliminate problems with existing retroreflector targets. These designs
are proprietary.
11. Other Work
The ILRS maintains a file of "Other ILRS Related Publications" on its website.
At the end there are two special sections:
"Articles by John Degnan", and
"Reports by David Arnold"
Other ILRS Related Publications
This website is useful for providing copies of papers that are too long for a journal.
It contains the full version of some of my papers that exceeded the page limit for
the proceedings of the ILRS workshops.
12. Hollow Retroreflectors
I was asked to participate in writing a proposal for a retroreflector on a commercial
Lunar Lander. My participation was funded by my contract with SAO. The PI for the
proposal was Dr. Stephen Merkowitz. The document below contains some general
calculations of the diffraction pattern of a large hollow retroreflector.
Five Inch Hollow Retroreflector
The way that hollow retroreflectors have been constructed for the last 50 years has
never made any sense to me. I proposed a conceptually different way of constructing
a hollow retroreflector. Jim Lyons showed that this method can be implemented with
technology that has existed for a long time. This new method was included in the
proposal.
The proposal was submitted at the end of October, 2018. On November 6, 2018 I received
the email from Dr. Merkowitz stating that I would not be paid for my work on the
design of the retroreflector array for the Lares-2 satellite. I responded by refusing
to do any further work for either ASI or NASA until I am paid for the work I did on
the design of Lares-2. I withdrew from the Lunar Lander proposal.
I never signed any contract or non-disclosure agreement regarding the proposed design
of a Lunar lander. I am free to continue the development of these concepts independently.
I continued to study ways of constructing a hollow retroreflector after I resigned. I
believe there is a way to construct a hollow cube corner that eliminates the problems
with the designs that have been tried so far.
13. My expertise and experience in satellite tracking
I prefer to stay in the background. I like being able to solve problems that no one
else can solve. I find the simple solutions that no one else was able to see. I don't
need praise. I know when I have done a good job. I want to be doing something useful.
I work from basic principles, write my own software, and do not trust anything until I
have cross checked it in 2 or 3 different ways. Then I ask others to check my results.
I have been working in satellite tracking since 1965. I started out measuring satellite
tracking films from the Baker Nunn cameras. I wrote programs for analysis of tracking
films including software for automatic star identification.
I switched to analysis of laser tracking data after the Baker Nunn network was closed
down. I wrote my own orbital analysis software for use in special studies. A also
wrote a simulation of the laser tracking system for optimizing the performance of
of the system. I wrote a screening program that can identify the good ranging data
even when most of the data is noise.
14a. The Tethered Satellite System TSS
The "skip rope" problem
I was asked to work on the design of the Tethered Satellite System TSS that was flown
on the Shuttle. I wrote programs for analysis of the dynamics and electrodynamics of
the tether. I worked for many years with Dr. Giuseppe Colombo who invented the concept.
Tethered Satellite System TSS
After Bepi's death I found myself having to deal directly with NASA management. My
analysis discovered the "skip rope" effect that would have caused an instability in the
retrieval. This could have endangered the shuttle. I spent 3 years trying to get
management to deal with the problem. Finally, the astronauts who fully understood
the problem stepped in and a review panel was formed.
The "skip rope" problem.
It was decided to add a damper to stabilize the dynamics on retrieval. I was at mission
control during the first flight as a dynamics expert. The satellite was successfully
retrieved.
14b. Positive energy tethered satellite system in a bound orbit.
One of the most surprising properties of an orbiting tethered satellite system is that
very long tethered systems in a bound orbit can have positive orbital energy.
This appears to violate standard principles of orbital dynamics where bound orbits
(circular and elliptical) have negative energy and escape orbits (hyperbolic)
have positive energy. Parabolic orbits have just barely enough energy to escape and
have zero energy at infinity.
This property was discovered accidentally during a routine study of the energy needed
to retrieve the system. For very long tethers there was a departure from the expected
quadratic dependence of the retrieval energy on tether length.
Dr. Georg Von Tiesenhausen at Marshall Space Flight Center was not satisfied with this
study and wanted an explanation for the deviation from the expected behavior. My study
of this discrepancy showed that very long tethered systems can have positive orbital
energy despite being in a bound circular orbit.
Not surprisingly such orbits are unstable unless the tether remains exactly aligned with
the vertical. If the top mass rotates forward the system escapes from orbit. If it
rotates backward the system falls out of orbit. The report is below.
Positive energy tethered system.
15. Development of the retroreflector array analysis programs
Around 1970 I was asked to work on the design of the retroreflector array for Lageos.
I wrote special software for computing the diffraction pattern of various types of
retroreflectors. This software was incorporated into a program for computing the cross
section and range correction for an array of retroreflectors. This software is needed
for doing parametric analyses to optimize the design of a retroreflector array.
This software is completely unique. The solution is entirely analytic for a hexagonal
retroreflector as described in SAO Special Report 382. No one else has ever written
such a program. Other people who have written diffraction programs use commercial
ray tracing software.
This program for computing the cross section and range correction for a satellite
was written for my own use in the design of Lageos. It is not designed for general use.
There is no user manual. There is no documentation. When I have a question I read the
code. If something needs to be updated I make the necessary changes. Since this program
is unique, I have maintained a working version of the program as the operating systems
and hardware have changed. When I left SAO in 1995 I transferred all the programs to my
home computer. I have continued to keep it updated and have used it to do work for ILRS
on a consulting basis up to the point where NASA decided to not pay me for the work I
did on the design of Lares-2.
I have also written my own software for thermal analysis of a retroreflector rather
than using commercial software. The thermal analysis, ray tracing, and diffraction
programs are written to run in sequence with the output of one program as the input
to the next.
Designing a retroreflector array requires an understanding of the whole process of
of how the data is taken and processed and how the data is used by the scientists.
I have studied all the different parts of the process of laser ranging.
If you wish to contact me, my email is david-arnold@earthlink.net.
16. Curriculum Vita and Bibliography
Curriculum Vita
Bibliography
Other papers by david Arnold can be found on the ILRS website
ILRS website
A paper givng equations for calculating the beam divergence due to
dihedral angle offsets in a cube corner can be found at
Dihedral angle offsets
and
Dihedral angle equations
and
Dihedral angle paper