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1. 17 ORBIT SOLVER ETERNI O LT 17 BI ELLIPTIC TRANSFER 18 REE BIA GIBT PR RE 19 ASTER Labs Inc 2 Orbitus D User Manual Version 1 2 Overview Orbitus D is a graphical user interface GUI written in MATLAB accomplished at displaying satellite orbits orbit transfers rendezvous as well as generating usable data associated with these trajectories and maneuvers This software is a perfect tool for engineering physics and astronomy students and professors of orbital mechanics It is also an excellent tool for use in industry for quick visualizations and analysis of satellite orbits The user interface is intuitive and powerful It takes only seconds to generate a satellite ground track or trajectory with the stunning graphics usually reserved for expensive commercial tools System Requirements Orbitus D is designed to work within MATLAB version 7 5 R2007b and higher MATLAB versions earlier than 2007b are not supported due to changes in fig files and pre parsed pseudocode or p code encryption that MATLAB has changed over the years However if you have a strong need of using versions earlier than MATLAB version 7 5 for your application please contact our support group for further assistance support asterlabs com Orbitus D will work on any platform including Mac OS Windows or Linux which supports the MATLAB versi2. 695 500 same sun2 jpg Venus 6 051 8 same venus2 jpg Earth 6378 137 6356 752 earth1 jpg Moon 1738 same moon2 jpg Mars 3396 19 3376 2 mars3 jpg Jupiter 71 492 66 854 jupiterlb jpg When the Earth and Moon option is input the Earth is placed at the center of the axes and the Moon s center of mass is placed at 384 400 km along the x axis The function outputs handles to each central body surface object allowing the user to move and rotate each body Earth s Moon Mars Jupiter datevec_dt Calculates a new date time vector from an original date time vector and a time step in either days or seconds eccentric2true Calculates the true anomaly from eccentric anomaly This works for all orbit types elliptic parabolic and hyperbolic This function can handle a single eccentric anomaly or a vector of many values The header for this function is shown in Figure 8 eci2LatgcLon Calculates geocentric latitude and longitude given a position in the Earth Centered Inertial ECI or GCRF frame and UTC date time A simple approximation using Greenwich Mean Sidereal Time is used to transform the given ECI position to ECEF Earth Centered Earth Fixed For more precise computations the geodetic latitude should be computed using the function eci2LatgdLon which also calculates ellipsoidal height Additionally more accurate ECI ECEF transformations can be computed using the IAU 2006 2000A method see IERS Conventions 2010 4 ASTER Labs
3. D User Manual Version 1 2 There are five modules to choose from Orbit Manipulator Allows the user to modify and visualize various orbits Orbit Solver Converts between Keplerian and Position amp Velocity type orbit elements Orbit Transfers Computes Hohmann and Bi elliptic orbit transfers Relative Motion Computes information of the relative motion between a primary and secondary spacecraft in near proximity to the primary vehicle Rendezvous Given rendezvous duration computes energy and path required to rendezvous with another orbit On the Main Menu an Info button is provided in the lower left corner Clicking this button labeled i opens the About page This page provides the Software version number as well as Special Thanks References and the Terms of Use The Terms Use in PDF format 15 also included in the downloaded zipped folder Additionally you can check for software updates from this page Each module of the software has three yellow blue and red buttons located in the lower right corner of each GUI window The yellow button with a question mark is an nfo button Clicking this button brings up a new window with information on the type of problem that is to be solved or plotted as well as definitions of some relevant key terms The blue button with a home symbol in it will take the user back to the Main Menu of Orbitus D The red button with QUIT inside it will that s right you guessed it
4. in order to get valid solutions Once the Calculate amp Plot button is pressed two plots are generated to the right hand side as shown in Figure 7 and the required delta v is displayed in the output box The plot on top is the path of the chase satellite during the maneuver in the Clohessy Wiltshire Hill frame The plot on the bottom consists of the target orbit original chase orbit and the path of the chase spacecraft during the rendezvous maneuver all plotted in the ECI frame Additionally there is a slide bar in the GUI window that controls the time after the initial burn As time since the initial burn the Time After Burn slide bar is adjusted the target and chase spacecraft update their locations on both plots All orbit position and velocity data can also be exported for further research e 9 ASTER Labs Inc 12 Orbitus D User Manual Version 1 2 User Functions Orbitus D functions are available for the user to utilize as desired These functions are stored in the UserFunctions subfolder Each encrypted function each p file has an accompanying m file containing a detailed header of important information on how to use the function This information can be accessed by either opening the m file or typing gt gt help function name atthe command line of MATLAB A list of available functions is given below An example function header is provided in Figure 8 for the function eccentric2true true anom e
5. the required incremental velocity or delta v information is displayed in the GUI window and the position and velocity data as well as the delta v data can be exported Additionally the user has the option of using either Earth or the Sun as the orbit s central body 4 ASTER Labs Inc 10 Orbitus D User Manual Version 1 2 RELATIVE MOTION Relative Motion Primary SC Clohessy Wiltshire Hill Frame m Input Primary and Secondary Spacecraft Parameters Primary Spacecraft Orbit Secondary Spacecraft Orbital Elements He Relative Position and Velocity CW frame Semimajor 8000 km Rx d km Eccentricity 0 Ry 0 Inclination 12 deg Rz 0 00001 km RAAN 0 deg Vx 0 Mu pad 1000 p es Arg of Peri 0 d w 0 kms 0 000 100 of Peri leg 1000 100 Y m X m True Anomaly 20 deg Vz 00001 km s m Input Propagation Time Output and Time Control 5 Hours Maximum SC Separation 1143 04 meters Current SC Separation k Calculate amp Plot J 425 803 meters Time After Burn 5070 sec 25 ASTER LAGS 2 a Figure 6 Relative Motion module To utilize the Relative Motion module the user must specify three things the primary spacecraft orbit the secondary spacecraft relative position and velocity and the amount of time desired to propagate the scenario into the future The primary spacecraft orbit can be defined by orbital elements or a position and velocity
6. vector in the ECI frame The secondary spacecraft must be given a relative position and velocity vector in the Clohessy Wiltshire Hill frame Once the Calculate amp Plot button is pressed two plots are generated to the right hand side as shown in Figure 6 The plot on top displays the secondary spacecraft s path with respect to the primary spacecraft over the designated amount of time This is in the Clohessy Wiltshire Hill frame The plot on the bottom displays the two spacecraft s orbits in the ECI frame It should be noted that the Clohessy Wiltshire Hill equations are being used for these calculations This means that the eccentricity of the primary spacecraft orbit needs to be zero or close to zero in order to get valid solutions Also the initial relative position cannot be zero in magnitude An easy fix is to make the initial position very small a few mm or cm if required Additionally the maximum spacecraft separation distance and the current separation distance are displayed in the output box of the GUI window A time slide bar controls the time since the initial conditions were valid As the time is adjusted the value in the Current SC Separation field is updated as are the spacecraft positions in the plots Orbit position and velocity data can also be exported for further investigation e 9 ASTER Labs Inc 11 Orbitus D User Manual Version 1 2 RENDEZVOUS Two Impulse Rendevous Target Clohessy Wiltshire Hill F
7. Inc 14 Orbitus D User Manual Version 1 2 eci2LatgdLon Calculates geodetic latitude and longitude given a position in the Earth Centered Inertial ECI or GCRF frame and UTC date time using an iterative method A simple approximation using Greenwich Mean Sidereal Time is used to transform the given ECI position to ECEF Earth Centered Earth Fixed Tolerance 1e 8 Constants WGS84 Semi major Axis of Earth 6378 137 km Semi minor Axis of Earth 6356 75231425 km GMST Calc Calculates the Greenwich Mean Sidereal Time degrees east of vernal equinox hohmann transfer Computes burn magnitudes and transfer ellipse parameters for a Hohmann transfer jd2utc mjd Converts a Julian date into a calendar date time vector and modified Julian date Julian Day Calculates the Julian day given a date time vector Julian date is defined as the number of days since noon on January 1st 4713 BC kepler Calculates position and velocity vectors after an elapsed time given the initial position and velocity vectors This uses the universal formulation of Kepler s equation The inputs may be specified in SI units or canonical units LeapYear Check Determines if the year given is a leap year 1 e February has 29 days Near term leap years should be 1980 1984 1988 1992 1996 2000 2004 2008 2012 and 2016 mean2eccentric Calculates the eccentric anomaly from the mean anomaly using Newton s method The tolerance is set to le 8 OrbE2
8. Orbitus Orbit Mechanics and Manipulation Tool User Manual Version 1 2 Ben K Bradley and Suneel I Sheikh 3 May 2013 e 9 ASTER LABS w 2009 2013 ASTER Labs Inc All rights reserved www asterlabs com Orbitus D User Manual Version 1 2 Contents A E AS E EE EE A EAE EEA EE AE EEE 3 SYSTEM REQUIREMENTS ecco roseo e eene eo na aeneo nee anoo 3 INSTALLATION TC I 4 IMPORTANT NOTES reo eet ra cnp aoo ro oescdcnsaswdcacescocadeceasccsasscccescesecedseeceessceceiescesecescesdacsevecdssssece 4 WHAT S NEW IN VERSION 1 412 iiie soceses esses suect ns o PER RE REPE Repo E EE EE S eERP e sss Roo Se SERRE EE ey P TeeeepS 5 SOFTWARE MODUL ES eee ee ee eene eere soe esaet eese ess eee sesto essa ee sete sese ee sese ses esee sese sese esee ee sese esee eoa 6 Nr s LEE EET 6 ORBIT MANIPULATOR 2 0 cece cc ceccececccsscccccceccecccsscececeusccccccsscececsessceceauececceuaeeeceususecceauseesecaaeceeeeenteceeane 8 ORBIT SOLVER e 9 ORBIT MES NOE m 10 RELA NBN VIOLET 11 RE NDE Z VOUS TP 12 USER FUNG TIONS 13 EXAMPEES 2 eoi ieeveecveeevenbeerebesdveveenzs PUR TE
9. STER Labs Inc 18 Orbitus D User Manual Version 1 2 RENDEVOUS 1 From the main menu click on Rendezvous 2 Select Orbital Elements for both the target and chase spacecraft orbit 3 Enter in the following values for both sets of orbital elements Target Chase Semi major 10000 10500 Eccentricity 0 0 04 Inclination 23 22 RAAN 10 15 Arg of Periapsis 0 0 True Anomaly 0 0 4 In the Input Time Until Rendezvous box enter 2 hours 5 Click on Calculate amp Plot new window with the trajectories plotted should appear to the right 7 The slide bar in the Output and Time Control box 15 now active This controls the time since the initial burn Altering the time will adjust the locations of the spacecraft in the plots accordingly 9 ASTER Labs Inc 19 Orbitus D User Manual Version 1 2 References 1 2 3 4 5 6 7 8 9 10 9 Bates R R Mueller D D and White J E Fundamentals of Astrodynamics Dover Publications 1971 Battin R H An Introduction to the Mathematics and Methods of Astrodynamics American Institute of Aeronautics and Astronautics 1999 Chobotov V A Ed Orbital Mechanics American Institute of Aeronautics and Astronautics 1991 Curtis H Orbital Mechanics For Engineering Students Butterworth Heinemann 2005 Danby J M A Fundamentals of Celestial Mechanics Willmann Bell 1992 Escobal P R Methods of Orbit Determination Krieg
10. ccentric2true E e Calculates the true anomaly from eccentric anomaly This works for all orbit types elliptic parabolic hyperbolic Author Ben K Bradley Last Revision Date 26 October 2010 Copyright 2008 2010 by ASTER Labs Inc All rights reserved INPUT Description nits ti Eccentric Anomaly single value or vector rad eccentricity of orbit OUTPUT true anom True Anomaly same size as input E 0 2pi rad Coupling none References 1 Vallado D A Fundamentals of Astrodynamics and Applications Third Edition Microcosm Press 2007 2 Curtis H D Orbital Mechanics for Engineering Students Elsevier Ltd 2005 oe oe oe oe oo Figure 8 Example header for sample function eccentric2true e 9 4 e ASTER Labs Inc 13 Orbitus D User Manual Version 1 2 CentralBody Plot Plots the desired central body in a new figure window or an existing one if given the axes handle Central body options are the Sun Venus Earth Moon Earth and Moon Mars and Jupiter Additionally units can be set to SI or canonical Each body has a semi major axis semi minor axis and picture file associated with it These items are given in the table below Semi major Radius Semi minor Radius Body km km Image File Sun
11. er Publishing 1965 Montenbruck O and Gill E Satellite Orbits Models Methods Applications Springer Verlag Berlin 2000 Moulton F R An Introduction To Celestial Mechanics Dover Publications 1970 Prussing J E and Conway B A Orbital Mechanics Oxford University Press 1993 Vallado D A Fundamentals of Astrodynamics and Applications Microcosm Press 2007 ASTER Labs Inc 20 Orbitus D User Manual Version 1 2 Enjoy We hope you find our Orbitus D software useful We would happily take suggestions or noted corrections Please submit these directly to us via email at support asterlabs com Development Group Orbitus D is developed by ASTER Labs Inc Our development team includes Ben K Bradley and Suneel I Sheikh 9 ASTER Labs Inc 21
12. er needs to know in order to use the function correctly and effectively This information can be accessed by either opening the m file or typing gt gt help function name at the command line of MATLAB where function name is the actual name of the script A description of each available function is provided in the User Functions section of this manual The MATLAB Image Processing Toolbox is no longer needed to display the high quality central body maps The standard MATLAB toolboxes now provide this capability The user accessible function CentralBody Plot now allows the user to plot the Sun Earth Moon Venus Mars or Jupiter as a central body with a high quality map of that body See the User Functions section of this manual for more information A number of functions have had their processing sped up through increased vectorization of the code Orbitus D User Manual Version 1 2 Software Modules MAIN MENU Orbitus Orbit Manipulator Orbit Solver Orbit Transfers Relative Motion Rendezvous Figure 1 Main Menu module of Orbitus D Figure 1 shows the Main Menu which is the first screen that the user views after starting Orbitus D The Main Menu allows the user to select the type of orbital mechanics problem that they would like to visualize and solve Once a problem type is selected the Main Menu disappears and a window corresponding to the user selection appears ASTER Labs Inc 6 Orbitus
13. he software d three dimensional plots can be rotated and zoomed e If user interface windows appear bigger than your screen you may need to change the resolution of your monitor f Information about your Orbitus D license and version can be viewed by entering the following at the MATLAB command line gt gt About OrbitusED Known Issue The MATLAB function of gui mainfocn can occasionally produce an error to the command window when switching between Orbitus D modules This is known only to happen in MATLAB version 7 5 R2007b and earlier However this GUI error does not affect the Orbitus D module function or computations h We would happily take suggestions or noted corrections Please submit these directly to our support group via email at support asterlabs com ASTER Labs Inc 4 Orbitus D User Manual Version 1 2 What s New in Version 1 2 There are some great new features that have been added to Orbitus D for this new release including the ability for the user to make use of the built in functions of Orbitus D for their own endeavors A summary of the updates is provided below 9 ASTER Labs Inc All the MATLAB functions of Orbitus are now available for the user to utilize on their own and interface them with their own code A new subfolder called UserFunctions contains these usable functions Each function has an accompanying m file that contains everything the us
14. ian orbital elements and a position and velocity vector in the ECI frame Additionally the Sun can be selected as the central body In this case position and velocity would be in the Heliocentric Coordinate frame Once an orbit is plotted the user can export the position and velocity tabulated data within the orbit to either a text file or Microsoft Office Excel file This gives the user the opportunity to examine certain properties of the orbit in further detail in any manner they desire Figure 4 Elliptical orbit created by Orbit Solver module e 9 ASTER Labs Inc Orbitus D User Manual Version 1 2 ORBIT TRANSFERS Figure 5 Left Hohmann transfer Right Bi elliptic transfer Created by the two Orbit Transfer modules Orbital maneuvers can transfer a spacecraft from one orbit to another Using the Orbit Transfers module of the Orbitus D software allows the user to calculate and plot Hohmann transfers and bi elliptic transfers For Hohmann transfers the user only needs to specify the initial and final orbit elements of the transfer Bi elliptic transfers require the user to also include either a maximum intermediate radius or duration of the transfer An example of an intermediate radius is illustrated using a green trace in the right hand plot of Figure 5 The orbits may be specified by orbital elements position and velocity vectors or simply combinations of eccentricity and periapsis or apoapsis Once plotted
15. nd the equatorial plane Utilizing these options can aide in the understanding of the orbital elements effect on the orbit Additionally the Groundtrack input box in the lower left allows the user to define the date and time at which the orbital elements were observed A groundtrack trace is plotted to the lower right in a two dimensional map display When the groundtrack is turned on any changes to the orbital elements will also update the groundtrack display The slidebar beneath the groundtrack controls the current time in UTC thus controlling the current position of the satellite in its orbit vi ASTER Labs Inc Orbitus D User Manual ORBIT SOLVER Select Units and Central Body Units SI km s Hd Body Earth E Input Orbit Parameters Select conversion direction Orbital Elements Position Velocity Semim 10200 km Eccentricity 0 13 Inclination 28 deg RAAN deg Arg of Peri 75 deg True Anomaly 35 deg Calculate amp Plot ASTER LAGS Orbit Solver Output Orbit Type Elliptical Posigrade Orbit Direction Flying away from periapsis Period 2 8478 hours 6443 91 km Rys 4962 02 km RZ 3998 03 km M xs 4 95812 km s Vys 484478 kms Viz 0 91276 km s Export Data Figure 3 Orbit Solver module Version 1 2 The Orbit Solver module gives the user the ability to plot any orbit and convert between Kepler
16. omaly This function can handle a single value for true anomaly or a vector of many values This function also works for all orbit types elliptic parabolic and hyperbolic 9 ASTER Labs Inc 16 Orbitus D User Manual Version 1 2 Examples Several tutorial examples are provided below for a select set of Orbitus D modules Users are encouraged to play with the defined input parameters to visualize and understand how an orbit or maneuver is affected Playing and learning is an important feature of Orbitus D ORBIT SOLVER 1 From the Orbitus D main menu click on Orbit Solver 2 Select 57 km s as the units and Earth as the central body from the drop down menus 3 Select Orbital Elements gt Position Velocity from the menu for the conversion method 4 Select Semi major Axis as the first orbital element 5 Enter in the following orbital elements Semi major axis 12000 Eccentricity 0 3 Inclination 35 RAAN 20 Arg of Periapsis 20 True Anomaly 60 6 Click the Calculate amp Plot button 7 You should now see a new window with the orbit plotted around the Earth There are rotate and zoom buttons at the top of this new figure window Also a description of the orbit and the position and velocity vectors in the ECI frame should be displayed in the output box in the GUI window 8 If you choose you could export the position data of one revolution of the orbit to a file by clicking on the Export Da
17. ons listed above MATLAB is a high level language and interactive development environment It is produced by The MathWorks Inc Users are referred to their website for more information http www mathworks com products matlab ASTER Labs Inc 3 Orbitus D User Manual Version 1 2 Installation 1 Download the zipped folder from the ASTER Labs web store after your purchase http www asterlabs com store 2 If not done automatically by your web browser unzip the downloaded folder 3 Put the unzipped Orbitus D folder into a directory or folder of your choice 4 Open up MATLAB and navigate to the Orbitus D folder 5 At the MATLAB command line type the following command then hit enter gt gt Install OrbitusED 6 Follow any instructions shown in the installation user interface that appears 7 Orbitus D is now installed A message should appear in the command window with a summary of the Orbitus D license information 8 This Orbitus D license is tied to the MATLAB license number that was entered when the software was purchased 9 To start Orbitus D type the following in the command window and hit enter gt gt OrbitusED Important Notes 9 a The value for the Earth s gravitational parameter being used is 398 600 4415 km s b The value for the Earth s radius being used is 6 378 137 km c External orbit perturbations are not taken into account in any part of t
18. quit the program if clicked Don t worry this button won t quit MATLAB It only closes the Orbitus D GUI window 9 ASTER Labs Inc 7 Orbitus D User Manual Version 1 2 ORBIT MANIPULATOR Orbit Manipulator r Keplerian Orbital Elements Option to Select Example n a Satelite Orbit Monve Semi major Axis lt gt 26700 km Eccentricity F MIL 0 74 Inclination 8 63 4 degrees RAAN lt gt 103 degrees Argument of Periapsis 4 gt 270 degrees Longitude of Periapsis if incl 0 C 4 degrees True Anomaly at Epoch lt gt 0 degrees V True Anomaly Slider On Off 3 o Groundtrack AWAY E M On Off ENS of Rev Year Month Day Hour Min MM aj 2 EpochDate UTC 2000 8 15 3 s2 180 120 60 0 60 120 180 T 242864 2252 Longitude Current Time Slider lt gt ASTER LAGS 15 Aug 2009 06 34 46 2 C Figure 2 Orbit Manipulator module The Orbit Manipulator module allows the user to manipulate the Keplerian orbital elements of an orbit using slide bars on the left hand side of the window As any of these orbit elements are modified the picture of the orbit on the right hand side changes in real time The image of the orbit in 3D is plotted in the Earth Centered Inertial ECI frame The Plot Settings button to the right of the 3D plot shaped like a gear allows the user to plot the apse line node line a
19. rame r Input Target and Chase Orbit Parameters Target Orbit Chase Orbit Orbital Elements ie Orbital Elements Semimajor 10000 km Semimajor 10500 km Eccentricity 0 Eccentricity 0 01 Inclination 23 deg Inclination 22 deg e poe ene 10 ra 15 ro i ve ase RENE deg BN MEE p 0 Arg of Peri 0 deg Arg of Peri 0 km True Anomaly 0 True Anomaly 0 deg Input Time Until Rendezvous Output and Time Control E Hours Total Delta V Required 0 420377 km s C Ames e Calculate amp Plot K Current Target SC Location Time After Burn X A 3660 sec Export Data C e 9 mores uem 2 a Figure 7 Rendezvous module The Rendezvous module facilitates the visualization of complex rendezvous of two spacecraft To implement a rendezvous the user must input the target spacecraft orbit chase spacecraft orbit and the desired duration of the rendezvous maneuver The target spacecraft orbit can be specified by orbital elements or a position and velocity vector in the ECI frame The chase spacecraft orbit can be specified by orbital elements a position and velocity vector in the ECI frame or relative position and velocity vectors in the Clohessy Wiltshire Hill frame It should be noted that the Clohessy Wiltshire Hill equations are being used for these calculations This means that the eccentricities of both orbits need to be zero or close to it
20. rv Orbital elements are used to calculate position and velocity vectors in the Geocentric Equatorial Coordinate System GECS or ECI Works for elliptic parabolic and hyperbolic trajectories This has been vectorized to compute many positions simultaneously The input for true anomaly may be a single value or a column vector of many values Additionally the desired value for the gravitational parameter may be input OR a character may be given to specify use of a stored value For Earth use E 398600 4415 km s For Sun use S 1 32712428e11 km s If canonical units are desired use c and the gravitational parameter will be set to 1 9 ASTER Labs Inc 15 Orbitus D User Manual Version 1 2 rv2OrbE Computes the Keplerian classical orbital elements including special cases given a position and velocity in the ECI Earth Centered Inertial frame Works for elliptic parabolic and hyperbolic trajectories The desired value for the gravitational parameter may be input OR a character may be given to specify use of a stored value For Earth use E 398600 4415 km s For Sun use 5 1 32712428e11 5 If canonical units are desired use c and the gravitational parameter will be set to 1 time of flight Calculates the time of flight from periapsis to the desired eccentric anomaly A single eccentric anomaly or vector of many values may be input true2eccentric Calculates the eccentric anomaly from true an
21. ta button in the GUI window 9 Now let s try plotting a hyperbolic trajectory quickly 10 Change the Semi major Axis value to 40000 11 Change the Eccentricity to 1 4 12 Click on Calculate amp Plot 13 Great You ve just plotted a hyperbolic trajectory in no time at all 14 Return to the main menu by clicking the blue button in the lower right of the GUI 9 ASTER Labs Inc 17 Orbitus D User Manual Version 1 2 BI ELLIPTIC TRANSFER 1 2 3 4 5 6 7 8 9 From the main menu click on Orbit Transfers In the new window click on Bi Elliptic Select S7 km s as the units and Earth as the central body Select Eccentricity and Periapsis in the drop down menu of the nput Initial Orbit box Input the following values for the initial orbit Eccentricity 0 1 Periapsis 9000 Select Periapsis and Apoapsis from the drop down menu of the Input Final Orbit box Input the following values for the final orbit Periapsis 15000 Apoapsis 20000 Select Max Intermediate Radius from the drop down menu of the Input Restriction on Transfer box Enter a value of 35000 for the Max Intermediate Radius 10 Click on the Calculate amp Plot button 11 You should see a new window with the initial orbit final orbit and transfer trajectories plotted around Earth The transfer time intermediate radius and delta v required for the transfer 15 also displayed in the GUI window A
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