Latest Space News
Tue, 21 Nov 2017 00:00:00 +0100
We are proud to announce the third annual Maritime Reconnaissance and Surveillance Technology conference will be held in Rome from the 30th-31st January 2018. Download Conference Agenda | Register to attend this Conference Reconnaissance and Surveillance are key to developing clear and accurate maritime situational awareness. In order to maximise their ISR range, Navies and Maritime agencies around the globe are looking beyond the atmosphere to provide new and advanced surveillance capabil...
Mon, 20 Nov 2017 20:47:00 +0100
The propulsion system of the light-weight Angara 1.2 Launch Vehicle Service Module, manufactured by the Khrunichev Space Center (part of ROSCOSMOS State Corporation), completed successful hot-fire testing at the Federal State Enterprise "Rocket & Space Industry Research & Test Center" (RSI RTC) test facility (Peresvet, Moscow Region). The hot-fire tests are the most important and final stage of ground based propulsion system tests prior to flight testing. During the tests, specialists from...
Mon, 20 Nov 2017 17:00:00 +0100
For the first time ever astronomers have studied an asteroid that has entered the Solar System from interstellar space. Observations from ESO's Very Large Telescope in Chile and other observatories around the world show that this unique object was traveling through space for millions of years before its chance encounter with our star system. It appears to be a dark, reddish, highly-elongated rocky or high-metal-content object. The new results appear in the journal Nature on 20 November 2017. ...
Mon, 20 Nov 2017 16:30:00 +0100
Harris Corporation (NYSE:HRS) has partnered with NASA's Johnson Space Center to successfully complete thermal vacuum testing for the James Webb Space Telescope - validating its ability to operate in the frigid space environment. The Webb telescope will be the premier space observatory of the next decade, and will study galaxy, star and planet formation in the universe. Harris' team helped safeguard the telescope in Houston during Hurricane Harvey and ensured uninterrupted testing - including ...
Mon, 20 Nov 2017 14:31:00 +0100
Orbital ATK (NYSE:OA), a global leader in aerospace and defense technologies, contributed to the successful launch of a United Launch Alliance Delta II rocket as it lifted off Saturday from Vandenberg Air Force Base, California, carrying the first Joint Polar Satellite System (JPSS-1) spacecraft. Orbital ATK's contributions to the Delta II include nine Graphite Epoxy Motors (GEM 40) and a large composite fairing for the rocket. This event marks the penultimate launch of the Delta II rocket. It i...
Mon, 20 Nov 2017 00:00:00 +0100
Twice as big as Earth, the super-Earth 55 Cancri e was thought to have lava flows on its surface. The planet is so close to its star, the same side of the planet always faces the star, such that the planet has permanent day and night sides. Based on a 2016 study using data from NASA's Spitzer Space Telescope, scientists speculated that lava would flow freely in lakes on the starlit side and become hardened on the face of perpetual darkness. The lava on the dayside would reflect radiation from th...
Sat, 18 Nov 2017 13:03:00 +0100
Today, NASA launched NOAA's next-generation polar satellite, the Joint Polar Satellite System-1, into space. Two Raytheon (NYSE: RTN) weather programs are mission-critical components of the satellite's mission: the JPSS Common Ground System and the Visible Infrared Imaging Radiometer Suite sensor. Svalbard, Norway, is home to part of a global network of receiving stations that process and distribute polar satellite data to users worldwide. Photo taken at Kongsberg Satellite Services plateau, ...
Sat, 18 Nov 2017 08:00:00 +0100
A United Launch Alliance (ULA) Delta II rocket carrying the Joint Polar Satellite System-1 (JPSS-1) for NASA and National Oceanic Atmospheric Administration (NOAA) lifted off from Space Launch Complex-2 on Nov. 18 at 1:47 a.m. PST. The JPSS program provides the nation's next generation polar-orbiting operational environmental satellite system, delivering key observations for the nation's essential projects and services, including forecasting weather in advance and assessing environmental hazards...
Fri, 17 Nov 2017 00:00:00 +0100
Landing on Mars is difficult and not always successful. Well-designed advance testing helps. An ambitious NASA Mars rover mission set to launch in 2020 will rely on a special parachute to slow the spacecraft down as it enters the Martian atmosphere at over 12,000 mph (5.4 kilometers per second). Preparations for this mission have provided, for the first time, dramatic video of the parachute opening at supersonic speed. The Mars 2020 mission will seek signs of ancient Martian life by investiga...
Thu, 16 Nov 2017 15:07:00 +0100
The U.S. Navy's Communications Satellite Program Office, PMW 146, and Lockheed Martin (NYSE: LMT) handed over full operational control of the fifth Mobile User Objective System (MUOS) satellite to the Naval Satellite Operations Center (NAVSOC). The October 11 milestone followed the successful completion of the MUOS-5 satellite's on-orbit testing and delivery of all operational products needed to "fly" the satellite. In April, the Navy, working with Army Forces Strategic Command (ARSTRAT), con...
Thu, 16 Nov 2017 14:04:00 +0100
As part of ESA's strategy to foster commercial competitiveness in Europe while focusing on its core aims, the agency has transferred ownership of several ground tracking stations for reuse by external organisations. By the end of 2017, ESA will have transferred three stations to national organisations in Spain and Portugal, who will take over the provision of satellite tracking services to a wide variety of commercial customers. The three stations involved in the transfer are all equipped ...
Wed, 15 Nov 2017 19:33:00 +0100
Boeing [NYSE:BA] won large commitments across its twin- and single-aisle commercial airplane families, debuted key capabilities including the CST-100 Starliner docking and KC-46 refueling simulators, and announced services agreements at the 2017 Dubai Airshow. "This has been a very successful show for Boeing. Our regional customers have maintained their trust in our products and technology, and our partnerships in the Middle East region continue to grow," said Bernard Dunn, President, Boeing ...
Wed, 15 Nov 2017 12:00:00 +0100
A temperate Earth-sized planet has been discovered only 11 light-years from the Solar System by a team using ESO's unique planet-hunting HARPS instrument. The new world has the designation Ross 128 b and is now the second-closest temperate planet to be detected after Proxima b. It is also the closest planet to be discovered orbiting an inactive red dwarf star, which may increase the likelihood that this planet could potentially sustain life. Ross 128 b will be a prime target for ESO's Extremely ...
Wed, 15 Nov 2017 11:29:00 +0100
Thales Alenia Space, a joint venture between Thales (67%) and Leonardo (33%), has been chosen by the Italian space agency ASI to develop an instrument called RIME (Radar sounder for Icy Moons Exploration) for the JUICE (JUpiter Icy moons Explorer) mission, part of the European Space Agency's "2015-25 Cosmic Vision" program. Scheduled for launch in 2022 with an expected arrival in 2029, the JUICE mission is designed to study the Jovian system and more specifically its icy moons, Ganymede, Call...
Wed, 15 Nov 2017 00:00:00 +0100
The Ariane 5 for Arianespace's December 12 year-ending flight for 2017 has completed its initial build-up at the Spaceport in French Guiana - where preparations also are moving ahead with four satellite passengers that will further expand Europe's Galileo global navigation system once in their final orbit. During activity in the Spaceport's Launcher Integration Building, this heavy-lift vehicle for Arianespace Flight VA240 underwent the assembly process that began by mating its two solid prop...
Tue, 14 Nov 2017 19:47:00 +0100
The Defense Advanced Research Projects Agency (DARPA) has awarded BAE Systems a contract worth up to $12.8 million to develop an innovative space evaluation and analysis testbed to support the development, integration, evaluation and analysis of advanced space enterprise command and control (C2) tools and capability technologies. The U.S. military must be able to quickly establish situational awareness and execute operations in space. Within the space domain, many thousands of objects that ar...
Tue, 14 Nov 2017 13:45:00 +0100
Orbital ATK (NYSE: OA), a global leader in aerospace and defense technologies, today announced that the "S.S. Gene Cernan" CygnusTM spacecraft successfully completed its rendezvous and berthing maneuvers with the International Space Station earlier this morning. This marks the company's eighth successful berthing with the orbiting laboratory. Cygnus launched into orbit aboard an Orbital ATK Antares(tm) rocket at NASA's Wallops Flight Facility on November 12. The spacecraft then executed a ser...
Mon, 13 Nov 2017 17:45:00 +0100
Thales Alenia Space has signed a contract with ArianeGroup, prime contractor and design authority of Ariane 6, to design, develop, qualify and manufacture the telemetry transmitter of the new European launcher. The telemetry transmitter is responsible for transmitting to the ground the data generated by the launcher throughout the whole launch mission. It is the first contract of the company in Spain in the launchers segment. After three decades of activity in the space sector participating i...
Mon, 13 Nov 2017 17:00:00 +0100
What seemed at first like a rare instance of a huge, ancient galaxy revealed itself to be an even rarer pair of extremely massive galaxies, seen on the brink of merging when the Universe was only a billion years old. This outstanding source was first identified by ESA's Herschel space observatory, and later exposed in greater detail with the ground-based Atacama Large Millimeter/submillimeter Array (ALMA) in Chile. The earliest galaxies in the 13.8 billion-year history of our cosmos starte...
Mon, 13 Nov 2017 16:00:00 +0100
Gas giant Jupiter, organic molecules in star-forming clouds and baby galaxies in the distant Universe are among the first targets for which data will be immediately available from the James Webb Space Telescope once it begins casting its powerful gaze on the Universe in 2019. Thirteen "early release" programmes were chosen from more than 100 proposals after a competitive peer-review selection process within the astronomical community. The programmes have been allocated nearly 500 hours of obs...
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    Personal information
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    Candidate Profile
     Date Submitted:20-03-2014
     Last Modified:26-03-2014 (02:49)
    Job information
     Current job:Senior Research Engineer
     Employment Term:Permanent
     Job location:Anywhere
     Date available:within 2 months
     Industry:,
     KeywordsAstrodynamics, Optimal Control, Trajectory Optimization, Nonlinear Dynamical Systems, Vibrations
    CV

    EDUCATION
    University of Southern California – Los Angeles, CA 90089-1453, USA
    ▪ Ph.D. in Aerospace Engineering (December 2012)
    ◦ Supervisor: Prof. Firdaus E. Udwadia
    ◦ Dissertation: New Approaches to Satellite Formation-Keeping and the Inverse Problem of the Calculus of Variations
    Yonsei University – Seoul 120-749, Republic of Korea
    ▪ M.S. in Astronomy  and Space Science (February 2008)
    ◦ Supervisor: Prof. Sang -Young Park
    ◦ Thesis: Analytic Solutions to Fuel-Optimal Reconfiguration of Satellite Formation Flying
    ▪ B.S. in Astronomy and Space Science (major) and Physics (minor) (February  2006)

    WORK EXPERIENCE
    Samsung Techwin Co., Ltd., Power Systems Division,  Control Group           (March 2013 – )
    –  Gyeonggi-do 463-400, Republic of Korea
    ▪  Works  as  a  senior  research  engineer.  Develops  control  algorithms  for  propulsion  control  and monitoring systems of MUAVs (Medium-altitude Unmanned Aerial Vehicles) together with Korean  Agency  for  Defense  Development.  Main  work  includes  1)  analysis  of  the  control  requirements,  2)  design  of  controllers  using  Matlab/Simulink,  and  3)  verification  of  the designed controllers via software testing and HILS (Hardware-In-the-Loop Simulations).

    JOURNAL PUBLICATIONS
    ▪  Udwadia, F. E., Wanichanon, T., and  Cho, H., “Methodology for Satellite Formation-Keeping in the  Presence  of  System  Uncertainties,”  Journal  of  Guidance,  Control,  and  Dynamics.
    (Accepted for publication)
    ▪  Udwadia,  F.  E.  and  Cho,  H.,  “First  Integrals  and  Solutions  of  Duffing-Van  der  Pol  Type Equations,” Journal of Applied Mechanics, Vol. 81, No. 3, 2014, pp. 034501-1 – 034501-4.
    DOI: 10.1115/1.4024673
    ▪  Cho,  H.  and  Udwadia,  F.  E. ,  “Explicit  Control  Force  and  Torque  Determination  for  Satellite Formation-Keeping  with  Attitude  Requirements,”  Journal  of  Guidance,  Control,  and Dynamics, Vol. 36, No.2, 2013, pp. 589-605.
    DOI: 10.2514/1.55873
    ▪  Udwadia,  F.  E.  and  Cho,  H.,  “Lagrangians  for  Damped  Linear  Multi-Degree-of-Freedom Systems,” Journal of Applied Mechanics, Vol. 80, No.4, 2013, pp. 041023-1 – 041023-10.
    DOI: 10.1115/1.4023019
    ▪  Cho, H., Park, S. –Y., Yoo, S. –M., and Choi, K. –H., “Analytical Solution to Optimal Relocation of  Satellite  Formation  Flying  in  Arbitrary  Elliptic  Orbits,”  Aerospace  Science  and Technology, Vol. 25, No.1, 2013, pp. 161-176.
    DOI: 10.1016/j.ast.2012.01.005
    ▪  Cho,  H.,  Park,  S.  –Y.,  Park,  H.  –E,  and  Choi,  K.  –H.,  “Analytic  Solution  to  Optimal Reconfigurations  of  Satellite  Formation  Flying  in  Circular  Orbit  under  J2  Perturbation,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 48, No. 3, 2012, pp.  2180-2197.
    DOI: 10.1109/TAES.2012.6237587
    ▪  Udwadia,  F. E.,  Leitmann,  G.,  and  Cho,  H.,  “Some  Further  Remarks  on  Hamilton’s  Principle,” Journal of Applied Mechanics, Vol. 78, No. 1, 2011, pp. 011014-1 – 011014-4.
    DOI: 10.1115/1.4002435
    ▪  Cho,  H.  and  Udwadia,  F.  E.,  “Explicit  Solution  to  the  Full  Nonlinear  Problem  for  Satellite Formation-Keeping,” Acta Astronautica, Vol. 67, No. 3-4, 2010, pp. 369-387.
    DOI: 10.1016/j.actaastro.2010.02.010
    ▪  Cho, H.  and Yu, A., “New Approach to Satellite Formation-Keeping: Exact Solution to the Full Nonlinear Problem,” Journal of Aerospace Engineering, Vol. 22, No. 4, 2009, pp. 445-455.
    DOI: 10.1061/(ASCE)AS.1943-5525.0000013
    ▪  Cho, H.  –C.  and  Park, S.  –Y.,  “Analytic Solution for Fuel-Optimal Reconfiguration in Relative Motion,”  Journal of Optimization Theory and Applications, Vol. 141, No. 3, 2009, pp. 495-512.
    DOI: 10.1007/s10957-008-9482-3
    ▪  Cho, H., Park, S.  –Y., and Choi, K. –H., “Application of Analytic Solution in Relative Motion to Spacecraft Formation Flying in Elliptic Orbit,”  Journal of Astronomy and Space Sciences, Vol. 25, No. 3, 2008, pp. 255-266.
    DOI: 10.5140/JASS.2008.25.3.255

    CONFERENCE PRESENTATIONS
    ▪  Cho,  H.,  and  Udwadia,  F.  E.,  (ASME  2012  International  Mechanical  Engineering  Congress  & Exposition,  IMECE  2012,  Houston,  Texas,  November  2012)  Inverse  Problem  for Lagrangian Dynamics for Multi-Degree-of-Freedom Systems with Linear Damping.
    ▪  Udwadia,  F.  E.,  and  Cho,  H.  (The  13 th ASCE  Earth  and  Space  2012  Conference,  Pasadena, California, April 2012) New Solutions to the Exact Formation-keeping Control of Satellites with Attitude Constraints.
    ▪  Cho,  H.,  and  Udwadia,  F.  E.,  (AIAA  SPACE  2011  Conference  &  Exposition,  Long  Beach, California,  September  2011)  New  Approach  to  Formation-Keeping  Problem  of  Multiple Satellites with Attitude Requirements.
    ▪  Wanichanon,  T.,  Cho,  H.,  and  Udwadia,  F.  E., (AIAA  SPACE  2011  Conference  &  Exposition, Long  Beach,  California,  September  2011)  Satellite  Formation-Keeping  Using  the Fundamental Equation in the Presence of Uncertainties in the System.
    ▪  Cho,  H.,  and  Udwadia,  F.  E.,  (Engineering  Mechanics  Institute  (EMI)  2010  Conference,  Los Angeles,  California,  August  2010)  Explicit  Solution  to  Satellite  Formation-Keeping Problem with Attitude Constraints.
    ▪  Cho,  H.,  and  Park,  S.  –Y.,  (The  16th Mediterranean  Conference  on  Control  and  Automation, Corsica,  France,  June  2008)  Simple  Analytic  Solution  to  the  Optimal  Reconfigurations  in General Relative Motions.
    ▪  Cho, H.,  Park,  S.  –Y.,  and  Choi,  K.  –H.,  (The  Annual  Spring  Conference  of  the  Korean  Space Science  Society,  Cheongju,  Rep.  of  Korea,  April  2008)  Simple  Analytic  Solutions  for Optimal Reconfigurations in General Relative Motion.
    ▪  Cho,  H.,  Park,  S.  –Y.,  and  Choi,  K.  –H.,  (The  Annual  Fall  Conference  of  the  Korean  Space Science  Society,  Daegu,  Rep.  of  Korea,  October  2007)  An  Analytic  Solution  to  FuelOptimal  Reconfiguration  of  Satellite  Formation  Flying  in  the  Presence  of  J2  Geopotential Disturbance.
    ▪  Cho, H. –C., Yoo, S. –M., Park, S. –Y., and Choi, K. –H., (The Annual Spring Conference of the Korean  Space  Science  Society,  Busan,  Rep.  of  Korea,  April  2007)  Applications  of Analytical Solutions into Reorienting, Resizing, and Retargeting of Formation Flying.
    ▪  Yoo, S. –M., Cho, H. –C., Park, S. –Y., and Choi, K. –H., (The Annual Spring Conference of the Korean Space Science Society, Busan, Rep. of Korea, April 2007) Numerical Validation of Analytical  Solution to  Optimal  Reconfiguration  of  Satellite  Formation  Flying  in  Arbitrary Elliptical Orbits.
    ▪  Cho,  H.  –C.,  Park,  S.  –Y.,  Yoo,  S.  –M.,  and  Choi,  K.  –H.,  (The  17th AAS/AIAA  Space  Flight Mechanics Meeting, Sedona, AZ, January 2007) Analytical Solution to Optimal Relocation of Satellite Formation Flying in  Arbitrary Elliptical Orbits.

    INVITED TALK
    ▪  Cho,  H.,  and  Udwadia,  F.  E.,  (The  12th ASCE  Earth  and  Space  2010  Conference,  Honolulu, Hawaii,  March  2010)  Explicit  Analytic  Solution  to  the  Satellite  Formation-Keeping Problem.

    COMPUTER SKILLS
    Matlab/Simulink, C/C++, Fortran, LabVIEW, Maple, Mathematica, SolidWorks, Solid Edge, PLC

    FELLOWSHIPS
    ▪ Brain Korea 21 Fellowship, Korean Science and Engineering Foundation, 2006  – 2008
    ▪ National Research Lab Fellowship, Korean Science and Engineering Foundation, 2006 – 2008
    ▪ Academic Excellence Scholarship, Yonsei University, 2005
    ▪ Academic Excellence Scholarship, Yonsei University, 2004

    EXTERNAL REVIEWER  FOR:
    ▪ Journal of Aerospace Engineering (8 papers)
    ▪ Applied Mathematics and Computation (5 papers)
    ▪ Journal of Optimization Theory and Applications (2 papers)
    ▪ ASME Applied Mechanics Reviews (1 paper)
    ▪ Journal of Sound and Vibration (1 paper)

    RESEARCH INTERESTS
    Astrodynamics,  Optimal  Control,  Trajectory  Optimization,  Satellite  Formation  Flying,  Nonlinear Dynamical Systems, Multi-body Dynamics and Control, Linear, Nonlinear, and Random Vibrations, Numerical Integration of Ordinary/Partial Differential Equations

    TEACHING EXPERIENCES
    ▪  Teaching Assistant  for the junior-level  Computer-Aided  Analyses  for Aero-Mechanical Design.
    (Instructor:  Dr.  Yann  Staelens):  Duties  included  grading ,  hands-on  training  of  SolidWorks  and Solid Edge, and holding office hours                                
    (Spring 2011, Spring 2012)
    ▪ Teaching Assistant  for the junior-level Dynamics. (Instructor: Prof. Roger G. Ghanem, Dr. David C. Wilcox): Duties included lectures and holding office hours
    (Spring 2010, Fall 2010, Fall 2011)
    ▪  Teaching  Assistant  for  the  graduate-level  Linear  Control  Systems  II.  (Instructor:  Prof.  Henryk Flashner): Duties included grading, lectures, and holding office hours                      
    (Fall 2009, Fall 2010)
    ▪  Teaching  Assistant  for  the  graduate-level  Engineering  Analytical  Methods.  (Instructor:  Prof. Satwindar S. Sadhal): Duties included grading and holding office hours            
    (Spring 2010)
    ▪  Teaching  Assistant  for  the  graduate-level  Engineering  Analysis.  (Instructor:  Prof.  Charlie Campbell): Duties included grading and holding office hours                       
    (Fall 2009)
    ▪ Teaching Assistant  for the senior-level  Control Systems Laboratory. (Instructor: Dr. Jerry Chen): Duties included grading and holding office hours                                
    (Spring 2009)
    ▪  Teaching  Assistant  for  the  senior-level  Space  Flight  Dynamics.  (Instructor:  Prof.  Sang-Young Park) Duties included grading, lectures, and hands-on training of STK (Satellite Tool Kit®)
    (Spring 2006)

    RESEARCH EXPERIENCES
    University of Southern California, Los Angeles, CA 90089-1453
    ▪  New  methodology  for  satellite  formation-keeping  with  attitude  requirements  in  the  presence  of system uncertainties                                          (August 2008 – May 2012)
    The  purpose  of  this  research  is  to  analytically  develop  exact  formation-keeping  guidance schemes  that  determine  control  inputs  and  state  trajectories  in  the  presence  of  both  orbital  and attitude requirements. The obtained solution is new in that 1) it is assumed that the leader satellite’s reference  orbit  can  be  any  arbitrary  one  and  the  follower  satellites  are  required  to  point  to  an arbitrarily  chosen  specific  spot  in  space  that  may  be  time-varying,  2)  a  method  to  correct  initialcondition  misalignment  problems  due  to  sensor  measurement  noise  is  developed  so  that  both  the orbital  and  attitude  control  requirements  are  asymptotically  satisfied  at  any  desired  rate  of convergence,  and  3)  the  effect  of  model  uncertainties  is  also  considered  by  augmenting  an additional additive controller  based on a generalization of the notion  of sliding surface control.  It should  be  stressed  that  nonlinear  relative  dynamics  is  considered  in  its  entirety  without  any linearizations/approximations  and  the  solution  is  obtained  in  an  explicit  form,  which  shows  the possibility of precisely controlling nonlinear multi-body systems.
    ▪ New approaches to the inverse problem of the calculus of variations                                         (August 2010 – December 2012)
    To develop the equations of motion for a mechanical system, it is usual to define a Lagrangian function first and then obtain the equations of motion by applying the Lagrange equation when the forces are derivable from  a potential function. However, it is interesting  and useful  to  investigate the types of forces that can be engendered when substituting the forces into the Lagrange equation guarantees the proper equations of motion even when the forces do not arise from a potential, that is,  when  they  are  nonconservative.  In  this  inverse  problem   of  the  calculus  of  variations,  by extending  the  existing  Bolza’s  approach,  a  more  general  and  systematic  way  of  handling  the problem  is  found  for  single-degree-of-freedom  (SDOF)  systems.  Then,  new  results  for  linearly damped  multi-degree-of-freedom  (MDOF)  systems  are  obtained  using  extensions  of  results  for SDOF  systems.  Conservation  laws  for  these  damped  MDOF  systems  are  also  found  using  the Lagrangians  obtained,  and  the  first  integrals  and  the  analytical  solutions  of  some  nonlinear oscillators (ex. Duffing-van der Pol oscillator) are newly proposed. These new findings can be used for development of  approximate solutions of nonlinear differential equations or various numerical techniques.
    Yonsei University, Seoul 120-749, Republic of Korea
    ▪ Analytical analysis of fuel-optimal reconfiguration of formation flying   (Sponsor: Korean Science and Engineering Foundation)                        (March 2006 – July 2008)
    The problem of relative motion, formation flying, and rendezvous has been studied.  The  most significant advantage of the research has been the development of completely analytical  results, by use  of  the  Fourier  series  and  the  Pontryagin’s  minimum  principle.  The  major  contributions  have been  the  solutions  to  the  fuel-optimal  rendezvous  problem  for  satellite.  The  results  are  also  valid when the orbits of the satellites are non-circular with arbitrary eccentricity. The  J2-perturbed case has been  also considered.  These findings allow  us to  predict the form  of the optimal solutions in advance  without having  to  solve  the  problem  and  significantly  reduce  the  amount  of  calculations required.


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