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Will the Martian Space Vehicle Return to Earth? In a space exploration mission, you are preparing for a return from Mars. You are designated designer of the route from Martian launch to Martian orbit to Earth targeting and capture. In this exercise, you will design that mission and use it to look at:: Model a Martian launch. Use STK/Astrogator to target various stages of space flight. Use SOCRATES to identify satellites that are at risk of collision. Usethe Vector Geometry Tool (VGT) to construct various components from which you can create customized planes and angles.

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  • Will the Martian Space Vehicle Return to Earth?

    In a space exploration mission, you are preparing for a return from Mars. You are designated designer of the route from Martian launch to Martian orbit to Earth targeting and capture. In this exercise, you will design that mission and use it to look at::

    Model a Martian launch. Use STK/Astrogator to target various stages of space flight. Use SOCRATES to identify satellites that are at risk of collision. Usethe Vector Geometry Tool (VGT) to construct various components from which you

    can create customized planes and angles.

  • Will the Martian Space Vehicle Return to Earth?

    Problem StatementIn preparation for the manned missions to Mars, the United States is planning a Martian mission that will fly to Mars, land, and then return the sample to the international space station in Earth orbit. After a successful landing on the surface of Mars, the space vehicle is now ready to return. Before doing so, you must model the Martian launch, orbit and return to Earth, ending in a phasing orbit relative to the station.

    BREAK IT DOWN

    The mission plan is to wait to launch when the Mars velocity vector is roughly aligned with the launch orbit plane to ensure the spacecraft is targeted in the right direction.

    The Mars mission will launch from the surface of Mars at the location of the original Martian landing--Martian latitude 67 degrees, longitude 80 degrees and altitude 0 degrees around 21 Jun 2020 at 12:00:00 UTC.

    The burnout will be at the fixed velocity of 3.299 km/sec. In order to assist the targeting of the outgoing asymptotes, the launch

    should take place roughly when Mars heliocentric velocity vector lies in the plane of the initial satellite orbit.

    Using the Jaqar Swing-by Calculator (http://www.jaqar.com/swingby.html), you estimated values that will help you model the proper angles and energy.

    A mid-course maneuver will correct the trajectory so it passes Earth at the correct distance.

    Aerobraking is used to capture into an earth orbit. A phasing orbit relative to the station is targeted.

    SOLUTIONBuild a STK Scenario that uses STK/Astroator to plan a mission that will launch a spacecraft from the surface of Mars and bring it back to Earth.

    Model the World!To speed things up and allow you to focus on the portion of this exercise that teaches you to design orbit maneuvers and spacecraft trajectories in STK/Astrogator, a partially developed scenario has been provided for you. Lets open PAGE 2

    that now.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    1. Launch STK ( ).2. Click the Open a Scenario button when the Welcome to STK window

    appears.3. Browse to C:\Training\STK\SpaceExploration.4. Select MarsReturn.vdf. 5. Click Open.6. Save the new scenario in your student area (C:\My Documents\STK 9).

    In doing so, create a unique folder and rename the new folder and the scenario file (*.sc) MarsReturn.

    When you open the scenario, you will find the following objects:

    The scenario also has the following three views already set up:

    Model a SpacecraftThe first thing we need to do is model the spacecraft that will be making the trip back from Mars.

    1. Open the Insert STK Object Tool ( ) if it is not already.2. Use the Insert Default ( ) method to insert an satellite ( ) object named

    SampleReturn.

    TABLE 1.

    OBJECT DESCRIPTIONEarth Models various planets for geometries and targeting.Mars

    Sun

    SpaceStation Satellite representing a nominal space station orbit.

    TABLE 2.

    OBJECT DESCRIPTION3D Graphics - Mars View of the Martian surface.3D Graphics - Sun View of the solar surface.3D Graphics - Earth Traditional Earth view.Page 3

  • Will the Martian Space Vehicle Return to Earth?

    OBJECT GRAPHICSBefore you start configuring your spacecraft, lets make some adjustments to its display in the visualization windows.

    1. Open SampleReturns ( ) properties ( ). 2. Select the 3D Graphics - Pass page.3. Change the Lead Type for the Orbit Track to All.4. Click Apply.5. Select the 3D Graphics - Model page.6. Move the slider for Marker, Label; Marker; and Point all the way to the right.

    You will now see these things at a far distance.7. Click Apply.

    SELECT A PROPAGATOR

    1. Select the Basic - Orbit page.2. Change the Propagator selected to an Astrogator propagator.3. Click Apply.

    What Is Astrogator?STK/Astrogator is an interactive orbit maneuver and space mission planning tool for use by spacecraft operations and mission analysis staff that offers wide flexibility through the use of customized thrust models, finite and impulsive maneuvers, and the ability to solve for solutions with a differential corrector targeter. You can use Astrogator for a variety of space mission analyses, such as:

    Formation flying, rendezvous planning, constellation design, space-based intercept.

    Interplanetary, lunar, and libration point trajectories. GEO, LEO, HEO, Sun-Sync orbit maintenance requirements. Automated planning of event-driven maneuvers. Monte Carlo and other script driven analyses. Incorporating fully customizeable force, engine, and atmospheric models. High, low, and variable-thrust trajectories. PAGE 4

  • Mission Control Sequence

    Mission Control Sequence (MCS) controls

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    MISSION CONTROL SEQUENCEOne of the first things that you will notice on the Astrogator propagator is the Mission Control Sequence (MCS). The MCS is the core of your space mission scenario. The MCS functions as a graphical programming language, utilizing mission segments that dictate how Astrogator will build the trajectory of the spacecraft.

    FIGURE 1.

    By adding, removing, rearranging, and editing MCS Segments, you can define a mission of any desired level of complexity. The MCS is represented schematically by a tree structure appearing in the left pane of the Orbit page of the satellite's basic properties.

    MCS CONTROLSThe Astrogator propagator includes a full set of controls that can be used for inserting, deleting, copying, and editing segments.

    FIGURE 2.

    Model the Martian LaunchOur first goal is to launch from Mars by leaving the surface and then coasting in a Martian orbit before maneuvering and reaching an escape orbit. Well model each piece--launch and propagate, then maneuver and propagate. That being the case, we dont need the default initial state segment.

    1. Select the default Initial State segment ( ) in the MCS tree.2. Click the ( ) button.Page 5

    3. When the delete warning appears, click OK.

  • Will the Martian Space Vehicle Return to Earth?

    4. Select the Propagate segment ( ).5. Click the ( ) button.6. When the delete warning appears, click OK.

    ADD A LAUNCH SEGMENTThe first steps for leaving Mars is to target the launch from the surface and get the spacecraft heading in the right direction. The mission plan is to wait to launch when the Mars velocity vector is roughly aligned with the launch orbit plane to ensure the spacecraft travels towards Earth.

    1. Right-click the Return segment ( ) in the MCS tree.2. Select Insert Segment ( ).3. When the segment selection dialog appears, select Launch ( ).4. Click OK.5. Press F2.6. Rename the new segment MarsLaunch.

    LAUNCH PARAMETERSAccording to what you know, the Mars mission will launch from the surface of Mars (zero altitude) at Martian coordinates 67 degrees latitude by 80 degrees longitude around June 21, 2020 at 12:00:00. You need to set up the launch so that it leaves Mars at the correct time from the correct location. Lets do that now

    1. Select MarsLaunch ( ) in the MCS tree. When you select a segment in the MCS tree, its properties display in the panel to the right.

    2. Set the following Launch parameters:

    TABLE 3. MarsLaunch Launch parameters

    OPTION VALUECentral Body MarsLaunch GeodeticEpoch 21 Jun 2020 12:00:00 UTCGLatitude 67 degLongitude 80 degAltitude 0 kmPAGE 6

  • MarsLaunch properties

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    BURNOUT VELOCITYThe default values for the Astrogator launch segment yield a circular orbit at 300 km altitude for Earth. In order to enter a 300 km circular orbit around Mars, the burnout velocity should be changed to 3.299 km/sec. Let's let Astrogator know that too.

    1. Click the Burnout Velocity button.2. Set the following Burnout parameters:

    3. Leave all other default values, and click OK.

    FIGURE 3.

    Model the Coast to the Martian Orbit

    TABLE 4. MarsLaunch Burnout parameters

    OPTION VALUEBurnout Options Use Fixed VelocityFixed Velocity 3.299 km/secPage 7

    The first segment in the target sequence models the launch from the surface of Mars. You want the spacecraft to coast to the maneuver location. At the

  • Will the Martian Space Vehicle Return to Earth?

    maneuver location the engine will fire and put the spacecraft on a path back to Earth. You need to add a propagate segment that models the spacecraft coasting in Martian orbit. This will take the spacecraft from the burnout state to the proper maneuver time. In order to do this, we need to create a custom propagator to use in modeling the propagate segment. Lets do that now.

    The Component BrowserThe Astrogator Component Browser is a powerful tool that enables you to redefine components of your space mission analysis and create new ones. The components are organized into groups listed in a tree structure.

    1. Select the Component Browser ( ) option from SampleReturns menu.

    2. Select the Astrogator Components in the Show menu.3. Take a look at the components in the Component Browser.

    The components are organized into groups listed in a tree structure in the left pane of the component browser. Individual components in a given group or subgroup are displayed in the right pane when you click the corresponding folder or subfolder in the left pane.

    CUSTOMIZE COMPONENTSIn order to correctly propagate a satellite around Mars, youll need to create a customized propagator. We can do that using the Component Browser.When you select Propagators in the tree, all available components will display in the table on the right.

    4. Expand the Propagators in the Component Tree.5. Select Previous Versions.6. Select Earth Full RKF.

    The Componet Browser can also be found from the Utilities menu in the STK Workspace.PAGE 8

  • Propagator components

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    FIGURE 4.

    7. Click the Duplicate button.8. Name the new propagator Mars Full RKF.9. Click OK.

    EDIT THE PROPAGATORIn order to correctly propagate a satellite around Mars, we need to create a Mars-specific propagator that uses a Mars gravity field, the Sun as a third body perturbation, and solar radiation pressure as another perturbation. Lets do that now.

    1. Scroll down the components list to locate the new propagator (Mars Full RKF) in the components list. It should be green.

    2. Double-click Mars Full RKF ( ) in the components list.3. When the Propagator definition window opens, ensure that the Propagator

    Function tab is selected.4. Change the Central Body to Mars. When you change the central body, the

    Gravitational Force is automatically updated with respect to the selected

    Components with Orange and Yellow icons cannot be edited. You must duplicate the yellow component before you can customize it. Components with green icons are customized by a user and can be edited or removed. Page 9

    body.

  • Mars propagator definition

    Will the Martian Space Vehicle Return to Earth?

    5. Select Moon in the list of propagator functions. A Mars propagator does not need to consider the Moon.

    6. Click the Remove button.

    FIGURE 5.

    7. Click OK.8. Click OK to close the Components Browser.

    Propagate Segment PropertiesNow, you can use the new propagator in the propagate segment to model the spacecrafts coast into the Martian orbit.

    1. Right-click the Return segment ( ) in the MCS tree.2. Select Insert Segment ( ).3. When the segment selection dialog appears, select Propagate ( ).4. Click OK.5. Open the Propagate Segments properties ( ).6. Enter the following:

    TABLE 5. Mars coast segment properties

    OPTION VALUEName MarsCoastPAGE 10

    Color Select a color that isnt being used by any segment.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    7. Click OK.8. Select MarsCoast ( ) in the MCS tree.

    Here well take an initial guess at the Trip value, which, in this instance, represents the length of time that the spacecraft will have to propagate to reach the next segment. Later, well target that value and let Astrogator adjust it for us.

    9. Click the button to change the Propagator.10. Expand the Previous Versions directory.11. Set the Propagator to Mars Full RKF.12. Click OK.13. Set the Trip to one (1) hr.

    Add a Maneuver SegmentThus far, you have modeled the launch from the surface and the coast into the Martian orbit. The next step is to add the maneuver that will help you reach the escape orbit.

    1. Use the same process to add a Maneuver segment ( ) after the MarsCoast Propagate segment ( ).

    2. Change the name of the Maneuver segment ( ) to EscapeMnvr.

    There is no need to change the color of the maneuver. You will not be able to see it in the visualization windows.

    THRUST VECTORThe term thrust vector is used to describe the direction of acceleration applied to the satellite. This direction is opposite to the exhaust of an engine. For example, for a single chemical rocket engine mounted to a satellite, the thrust vector is opposite to the direction of the flames.

    If multiple engines are being used together in a thruster set, the thrust vector is along the direction of the overall effective acceleration. This is determined by calculating the acceleration vector of each individual thruster, with both the direction and magnitude. The thrust vector is then calculated along the direction of the vector to be the sum of all the acting acceleration vectors.Page 11

  • Will the Martian Space Vehicle Return to Earth?

    ATTITUDE PARAMETERSYou know you need to leave Martian gravity. Burning in the velocity direction with respect to Mars is the most efficient way to attempt to leave Martian gravity using an impulsive maneuver with one burn. Well add a Delta-V maneuver that is along the direction of the spacecraft velocity with respect to Mars, which is the X direction of the VNC (Mars) frame.

    Here, again, well take an initial guess at the X velocity value needed to get us out of Martian gravity. Later, well target this value and let Astrogator adjust it for us.

    1. Select EscapeMnvr ( ) in the MCS tree.2. Ensure that the Attitude tab is selected.3. Set the following:

    Add a Second Propagate SegmentNow, you need to add a second propagate segment that will take the spacecraft roughly to the Mars sphere of influence (SOI) boundary which is where the midcourse maneuver should occur.

    1. Use the same process to add a second Propagate segment ( ) after the Maneuver ( ).

    2. Double-click the new Propagate segment ( ).3. Enter the following:

    TABLE 6. Escape maneuver attitude definition

    OPTION VALUEAltitude Control Thrust VectorThrust Axes VNC (Mars)X(Velocity) 3 km/sec

    TABLE 7. Leave Mars SOI segment properties

    OPTION VALUEName LeaveMarsSOIColor Select a color that isnt being used by any segment.PAGE 12

    4. Click OK.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    DEFINE THE PROPERTIES OF THE SECOND PROPAGATORWell use our customized Mars propagator, and a fifteen (15) day trip, as that is a good estimate of the time that it will take to travel from launch to the Mars SOI boundary. Later, well target this value, and let Astrogator adjust it.

    1. Select LeaveMarsSOI ( ) in the MCS tree.2. Change the Propagator to Mars Full RKF.3. Click the Insert... button.4. Select the R Magnitude item ( ).5. Click OK to add the new Stopping Condition to the table.6. Set the following:

    7. Select the Duration stopping condition in the table.8. Click the Remove button.

    Change Your PerspectiveYou can take a look at your mission so far. Lets do that.

    1. Click Run ( ).2. Bring the 3D Graphics - Mars window to the front.3. Mouse around until you can clearly see the various segments that make up

    the portion of the orbit where the spacecraft is leaving Mars.

    TABLE 8. Leave Mars SOI stopping conditions

    OPTION VALUETrip 580,000 kmCoord System Mars J2000Page 13

  • 3D View: Martian launch sequence

    Will the Martian Space Vehicle Return to Earth?

    FIGURE 6.

    The color of each segment in the orbit coincides with the color of the segment in the MCS tree.

    Create a Target SequenceOur first goal is to launch from Mars by leaving the surface and then coasting in a Martian orbit before maneuvering and reaching an escape orbit. Youve already modeled each segment--launch and propagate, then maneuver and propagate. Lets put them inside a target sequence that will target specific goals, and let Astrogator solve for the control values to achieve those goals.

    In order to assist the targeting of the outgoing asymptotes, the launch should take place roughly when Mars heliocentric velocity vector lies in the plane of the initial satellite orbit. We'll use Vector Geometry Tool to create three different geometric elements that will help us model this relationship.

    Vector Geometry ToolThe Vector Geometry Tool (VGT) enables you to define elements used in constructing coordinate systems, vectors, axes, and points, as well as angles and planes. These structures and elements are then added to the standard PAGE 14

    structure and elements available to display in the 3D Graphics and 3D Attitude Graphics, and to use as Astrogator calculation objects.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    CREATE THE ORBIT NORMAL VECTORFirst, well create the spacecrafts orbit normal vector from the satellite.

    1. Select SampleReturn ( ) in the STK Object Browser.2. Open on the Vector Geometry Tool ( ).3. Ensure that SampleReturn ( ) is selected in the tree.4. Click the Create New Vector... ( ) button.5. Set the following definition values:

    6. Leave all other default values.7. Click OK to add the new vector.

    CREATE THE ORBITAL PLANEThe second element that we need to create is the spacecrafts orbit plane with respect to Mars. The orbital plane is defined as the plane perpendicular to normal to the satellites orbital angular momentum; therefore, you will use the Normal type for the plane that you create. We need to

    1. Ensure that SampleReturn ( ) is selected in the tree.2. Click the Create New Plane... ( ) button.3. Set the following parameters:

    TABLE 9. Mars orbit normal vector definition

    OPTION VALUEName Orbit Normal (Mars)Description Spacecraft orbit normal vector.Type Orbit NormalCentral Body Mars

    TABLE 10. Mars orbit plane definition

    OPTION VALUEName Orbit Plane (Mars)Description Satellite orbit plane about Mars.Type NormalPage 15

  • Will the Martian Space Vehicle Return to Earth?

    Define the Normal Vector

    1. Click the Select... button under Normal Vector.2. Expand the tree as follows:

    ... SampleReturn... Orbit Normal (Mars)

    3. Select the Orbit Normal (Mars) vector that you just created.4. Click OK.

    Define the Reference Vector

    1. Click the Select... button under Reference Vector.2. Expand the tree as follows:

    ... Mars... J2000

    ... X3. Select the Mars J2000 X vector. 4. Click OK.

    Define the Reference Point

    1. Click the Select... button under Reference Point.2. Expand the tree as follows:

    ... Mars... Center

    3. Select the Mars Center point.

    4. Click OK.5. Click OK to add the new plane.

    CREATE THE ANGLE BETWEEN

    You can select Mars Center from either instance of Mars in the elements tree.PAGE 16

    Finally, create the angle between the velocity vector and the orbital plane.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    1. Click the Create New Angle... ( ) button.2. Set the following definition criteria:

    The To Plane type is defined as the angle from a vector (reference vector) to a plane (reference plane).

    Select the Reference Vector

    1. Click the Select... button under Reference Vector.2. Expand the tree as follows:

    ... Mars... Velocity

    3. Select the Mars Velocity vector. 4. Click OK.

    Select the Reference Plane

    1. Click the Select... button under Reference Plane.2. Expand the tree as follows:

    ... SampleReturn... Orbit Plane (Mars)

    3. Select the Mars Orbit Plane. 4. Click OK.5. When you return to the Angle properties, enable the Signed Positive Toward

    Plane Normal option.6. Click OK.7. Close the Vector Geometry Tool ( ).

    TABLE 11. Mars orbit plane angle definition

    OPTION VALUEName Orbit Plane Angle (Mars)

    DescriptionAngle between the Mars velocity vector and the spacecrafts orbital plane.

    Type To PlanePage 17

    You have created the necessary targeting geometries for your mission. Now, we can apply them to the segments in the target sequence.

  • Will the Martian Space Vehicle Return to Earth?

    Target Sequence ProfilesThe default Target Sequence profile is Differential Corrector which is what well be using here. The Differential Corrector search profile targets specific values defined as independent variables. The target sequence will change the value of independent variables as needed to achieve the goal defined by the dependent variables, utilizing a differential correction algorithm. You can find more in depth information about the differential correction algorithm in the Astrogator help system.

    1. Right-click the Return segment ( ) in the MCS tree.2. Select Insert Segment ( ).3. When the segment selection dialog appears, select Target Sequence ( ).4. Click OK.5. When you return to Astrogator, the new target sequence will be listed in the

    MCS tree.6. Click on the name of the Target Sequence ( ) to make it editable.7. Change the name to MartianLaunch.

    ADD THE SEGMENTS TO THE TARGET SEQUENCE

    1. Expand ( ) the MartianLaunch target sequence ( ).2. When you expand MartianLaunch ( ) you will see a Return segment ( ).3. Drag the MarsLaunch segment ( ) and drop it inside the target

    sequence ( ) before the Return segment ( ).4. Use the same process to add the remaining segments to the target

    sequence.5. Ensure that they are arranged in the following order:

    ... MarsLaunch... MarsCoast

    ... EscapeMnvr... LeaveMarsSOI

    Linking Independent VariablesAny element of a nested MCS segment or linked component that is available for selection as an independent variable will be identified by a target icon ( ) PAGE 18

    appearing beside it. To select a given element as an independent variable, simply click the associated target icon. Your selection will be confirmed by the

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    appearance of a check mark over the icon ( ). Linking independent variables allows the selected value to be changed by a search profile to achieve targeting goals.

    LAUNCH VARIABLESWell set the independent variables for the launch segments so that we can use them in the search profile. Allowing Astrogator to adjust these values for us will help ensure that the spacecraft is headed in the correct direction.

    1. Select MarsLaunch ( ) in the MCS tree to display its properties.2. Click the target icon ( ) beside the Launch Epoch to mark it as an

    independent variable.

    ResultsBeneath the MCS tree is a Results... button, which allows you to specify calculation objects to be reported and targeted for each segment. Clicking this button will open the User-Selected Results window, in which you can select calculation objects to include in the summary report for the currently selected segment, and to target when defining a search profile for the target sequence.

    TARGET THE LAUNCHYou want to target the launch so the spacecrafts orbital plane is aligned with Mars velocity vector. You will add that angle now.

    1. Select MarsLaunch ( ).2. Click the Results... button below the MCS tree.3. Expand the component tree as follows:

    ... Vector... Angle

    4. Double-click the Angle component ( ). When you double-click a component in the tree, Astrogator will display information about that component on the right hand side of the panel.

    5. Change the name to Orbit Plane Angle (Mars).6. Double-click the Angle value under Component Details.7. When the reference selection dialog appears, expand the tree as follows:Page 19

    ... SampleReturn... Orbit Plane Angle (Mars)

  • User selected results window

    Will the Martian Space Vehicle Return to Earth?

    8. Select Orbit Plane Angle (Mars) ( ).9. Click OK.10. Click OK to dismiss the Results window for MarsLaunch ( ).

    FIGURE 7.

    Search ProfilesSearch profiles define goals and modify variables to achieve them. There are two types of search profiles you can use in a target sequence--differential correctors and plugins. The differential corrector profile targets specific values - defined as independent variables. The target sequence will change the value of independent variables as needed to achieve the goal defined by the dependent variables, utilizing a differential correction algorithm.

    Dependent variables are defined in terms of Astrogator's extensive repertoire of calculation objects. The selections that appear here were selected in the User-Selected Results window for that segment accessed via the Results... button. Calculation objects are selected for dependent variable definition in the User-PAGE 20

    Selected Results window, but the manner in which they will be used is specified here in the setup of the differential corrector.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    ORBIT PLANE MATCHING DIFFERENTIAL CORRECTORThe first differential corrector profile will change the launch epoch to align the orbit plane with Mars velocity vector. This differential corrector profile will use estimated values. This type of rough guess will at least head us in the right direction.

    1. Select the MartianLaunch ( ) target sequence. 2. Double-click the Name value for the Differential Corrector in the Profiles table

    to make it editable.3. Rename it Orbit Plane Matching.4. Click the Properties... button.5. Ensure that the Variables tab is selected.6. Set the following:

    7. Ensure that the Desired Value for the Orbit Plane Angle (Mars) constraint is set to zero (0) degrees.

    8. Click OK.

    Run the Active ProfileYou can configure a Target Sequence to execute in many different ways depending on the solution you are trying to achieve.

    Should converge in about 6 iterations

    1. When you return to Astrogator, change the Action for the target sequence to Run active profiles.

    2. Click Run ( ). When the run finishes, a targeting status grid will appear.

    TABLE 12. Orbit plane matching properties

    OPTION VALUELaunch Epoch OnPerturbation 5 minMax Step 1 hrOrbit Plane Angle (Mars) On

    If the differential corrector doesnt converge in one run, click the green arrow to run it againPage 21

  • 3D View: Martian launch orbit plane matching

    Orbit plane matching adjusted values

    Will the Martian Space Vehicle Return to Earth?

    FIGURE 8.

    Did the profile converge? If so, what is the new launch date and time?

    3. When you finish, close the targeted status grid.4. Bring the 3D Graphics - Mars window to the front.

    FIGURE 9.

    Are all six (6) iterations visually represented?

    INITIAL & FINAL DATE AND TIMEThe Initial and Final fields beneath the segment parameters area are apparent for every segment in the MCS and serve the same purpose for each; the Initial field displays the scenario time and date at the beginning of the currently selected segment, while the Final field displays the scenario time and date at the end of that segment. If a segment has not yet been run, these fields will be marked Not Set for that segment - since these values are not determined until PAGE 22

    the segment is run.

  • 3D View: Sample return at mars coast

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    The targeter will alter the launch epoch in order to force the angle to zero. The initial and new values will display below the Profiles panel.

    What is the difference in the initial and final values?

    LET ASTROGATOR CHANGE YOUR PERSPECTIVEOnce Astrogator updates the Initial and Final values for each segment, you can select any segment in the MCS tree and update the view in the visualization window such that the SampleReturn spacecraft will be at that position in time.

    1. Select any segment in the MCS tree.2. Click on the unit selector ( ) beside the Initial time.3. Select Set Animation Time.4. Bring the 3D Graphics - Mars window to the front.

    FIGURE 10.

    In the picture above, we selected the EscapeMnvr segment and updated the animation to the Initial time, so Astrogator positioned the spacecraft at the beginning of the maneuver. Although the maneuver doesnt have a visible portion of the orbit, you can see where the spacecraft will be when it occurs. If we had done the same thing using the Final time, Astrogator would have positioned me at the end of the segment.Page 23

  • Will the Martian Space Vehicle Return to Earth?

    Asymptote Targeting ProfileLets create a second differential corrector. Using this profile, well target the outgoing asymptote properties and the energy of the transfer orbit to see if we can obtain more accurate results.

    PROPAGATE VARIABLESFirst, well define the independent variables for the propagate segment. When we created the propagate segment, we guessed at the approximate coast time before performing the escape maneuver. Well mark that as an independent variable and let Astrogator adjust the amount of time that the spacecraft should coast.

    1. Bring Astrogator to the front.2. Select MarsCoast ( ) in the MCS tree.3. Click the beside Trip to mark it as an independent variable ( ).

    MANEUVER VARIABLESEarlier you took an initial guess at the X velocity value needed to get out of Martian gravity in the maneuver segment (EscapeMnvr). Now, we can mark that as an independent variable so that Astrogator can adjust it if necessary.

    1. Select EscapeMnvr ( ) in the MCS tree to display its properties.2. Click the target icon ( ) beside the X(Velocity) value to mark it as an

    independent variable ( ).

    Maneuver Targeting ComponentsThe second Differential Corrector profile targets the outgoing asymptote properties and the energy of the transfer orbit to chane the launch epoch, coast duration and burn magnitude to match the outgoing asymptote and energy. First, the proper components need to be added so that they can be selected in the new Differential Corrector profile.

    1. Select EscapeMnvr ( ) in the MCS tree.2. Click the Results... button.PAGE 24

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    ADD C3 ENERGY

    1. When the User-Selected Results dialog appears, expand the tree as follows:... Target Vector

    ... C3 Energy2. Double-click the C3 Energy component ( ).3. Select C3 Energy in the topmost table.4. Double-click the Value for Central Body in the Components Details area.5. When the component selection dialog appears, select Mars ( ).6. Click OK.

    ADD OUTGOING ASYMPTOTE PARAMETERSThe outing asymptote parameters will also need to be available to Astrogator for targeting purposes.

    1. Double-click the Outgoing Asymptote Dec component ( ) under Target Vector ( ).

    2. Select Outgoing Asymptote Dec in the topmost table.3. Double-click the Value for Coord System in the Components Details area.4. When the reference selection dialog appears, expand the tree as follows:

    ... Mars... J2000

    5. Select J2000 ( ).6. Click OK.7. Double-click the Outgoing Asymptote RA component ( ).8. Repeat steps 2-6 to change the coordinate system for Outgoing Asymptote

    RA.9. Click OK.10. Click OK to dismiss the User-Selected Results dialog.

    Asymptote Targeting ProfileWell target the outgoing asymptote properties and the energy of the transfer orbit using the values from the Jaqar Swing-by Calculator.

    1. Select the MartianLaunch ( ) target sequence. Page 25

    2. Click the New... button in the profiles table.

  • Will the Martian Space Vehicle Return to Earth?

    3. Select Differential Corrector ( ).4. Click OK to add the new profile to the target sequence.5. Rename the profile Asymptote Targeting.

    CONTROL PARAMETERSThe Control Parameters are independent variables that you marked for inclusion while setting up the target sequence. Well set the values for the control parameters and equality constraints using values obtained using and external Lambert problem solver.

    1. Select the Targeting profile.2. Click the Properties... button.3. Ensure that the Variables tab is selected.4. Enable the following:

    EQUALITY CONSTRAINTSEquality constraints in the search profile outline dependant variables to be considered in your analysis. Here well set the desired value based on the results from the Jaqar Swing-by Calculator, and again, well let Astrogator adjust those values as necessary.

    1. Select the C3 Energy Equality Constraint.2. Set the following:

    TABLE 13. Asymptote targeting control parameters

    CONTROL PARAMETER STATE PERTURBATION MAX STEPLaunch Epoch On 15 min 1 hrStopping Condition Duration Trip On 60 sec 500 secImpulsive Mnvr Cartesian X On 0.0001 (Default) 0.1 (Default)

    TABLE 14. Asymptote targeting equality constraints

    EQUALITY CONSTRAINT STATE DESIRED VALUEC3 Energy On 14.3572 km^2/sec^2Outgoing Asymptote Dec On 3.30596 degOutgoing Asymptote RA On -131.622 degPAGE 26

    3. Click OK.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    RUN THE ACTIVE PROFILE

    3D View: Martian launch sequence

    Now, you can run the selected profile and see what Astrogator comes up with. Then well apply those changes. Doing this will apply the values of search profiles' controls and the changes specified by the segment configuration profiles to the segments within the target sequence.

    1. Ensure that the Action is set to Run active profiles.2. Click Run ( ).

    Did the profile converge? If so, did you achieve the desired values?

    3. Once converged, click the Apply Changes button.4. Change the Action to Run nominal sequence.

    CHANGE YOUR PERSPECTIVE

    1. Bring the 3D Graphics - Mars window to the front.2. Mouse around until you get a good look at the various iterations of

    SampleReturns orbit.

    FIGURE 11.Page 27

    3. When you finish, close the status grid.4. Save ( ) the scenario ( ).

  • Will the Martian Space Vehicle Return to Earth?

    Are We Headed In the Right Direction?

    3D View:

    Lets quickly test the Lambert solver, by propagating out one year in heliocentric space and seeing if were going in the right direction using the values that the Jaqar Swing-By Calculator gave us.

    1. Add a Propagate segment ( ) after the MartianLaunch target sequence ( ).2. Select Propagate ( ) in the MCS tree.3. Change the color of the segment so that you can clearly identify it in the

    visualization windows.4. Change the Propagator to Heliocentric ( ).5. Click the Advanced... button.6. Change the Maximum Propagation Time to one (1) yr (year).7. Click OK.8. Change the Trip value under Stopping Conditions to one (1) yr (year).9. Click Run ( ).

    CHANGE YOUR PERSPECTIVE

    1. Bring the 3D Graphics - Sun window to the front.2. Mouse around until you can clearly see where the spacecraft would be

    headed.

    FIGURE 12.PAGE 28

    Is the spacecraft headed in the right direction? Would you arrive at Earth?

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    The satellite is now headed roughly back toward Earth, but not quite. A midcourse maneuver will assure the desired Earth arrival in the orbit.

    3. When you finish, delete ( ) the newly added Propagate segment ( ).

    Earth ArrivalNow, lets create the midcourse maneuver that will assure an Earth arrival. The first target sequence launched you from the surface of Mars and took you to the Mars SOI boundary. The one we create here will target a maneuver that sets the spacecraft into a path which results in the desired orbit around Earth.

    1. Add a new Target Sequence ( ) below the MartianLaunch ( ) sequence.2. Change the name to EarthArrival.

    MODEL THE MID-COURSE MANEUVERThe first target sequence left you at Mars SOI on a path towards Earth, but as we just demonstrated that path isnt quite accurate enough. We can add a midcourse maneuver here that will get us at the correct perigee altitude for aerobraking and put us in the same orbital plane as the ISS, which is where we want to be. A midcourse maneuver will assure an arrival in the desired orbit geometry around the Earth.

    1. Add a Maneuver segment ( ) to the EarthArrival ( ) sequence.2. Double-click the new Maneuver segment ( ).3. Change the name of the Maneuver segment ( ) to MidCrsMnvr.

    There is no need to adjust the color. The maneuver segment will not be distinguishable in the visualization windows.

    4. Select MidCrsMnvr ( ) in the MCS tree.5. Set the following:

    TABLE 15. Mid course maneuver stopping conditions

    OPTION VALUEAltitude Control Thrust VectorThrust Axes VNC (Sun)X (Velocity)Page 29

    Independent variable ( )

  • Will the Martian Space Vehicle Return to Earth?

    Well use the velocity relative to the sun to define the thrust axes because were now in heliocentric space. Astrogator will adjust all three components of the maneuver to achieve the correct perigee altitude and orbital plane.

    PROPAGATE TO EARTH SOINow, well add the first of two propagate segments after the maneuver. The first propagate segment takes the satellite close to Earths SOI.

    1. Add a Propagate segment ( ) after the maneuver.2. Double-click the new Propagate segment ( ).3. Set the following:

    4. Change the Propagator to Heliocentric.5. Click the Advanced... button.6. Change the Maximum Propagation Time to one (1) yr.7. Click OK.

    STOPPING CONDITIONS

    1. Click the Insert... button.2. Select the R Magnitude item ( ).3. Click OK to add the new Stopping Condition to the table.4. Change the Trip value for R Magnitude to two million (2e+006) km.5. Select the Duration stopping condition in the table.6. Click the Remove button.

    Y (Normal) Independent variable ( )Z (Co-normal) Independent variable ( )

    TABLE 16. To Earth SOI segment properties

    OPTION VALUEName ToEarthSOIColor Any color not currently being used.

    TABLE 15. Mid course maneuver stopping conditions

    OPTION VALUEPAGE 30

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    PROPAGATE TO EARTH PERIAPSISNow, add the second propagate segment. The second propagate goes to Earth periapsis. This periapsis will be targeted to 150 km altitude and in the same plane as the space station.

    1. Add a second Propagate segment ( ) after ToEarthSOI ( ).2. Double-click the new Propagate segment ( ).3. Set the following:

    4. Click OK.

    STOPPING CONDITIONS

    1. Click the Insert... button.2. Select the Periapsis item ( ).3. Click OK to add the new Stopping Condition to the table.4. Select the Duration stopping condition in the table.5. Click the Remove button.

    TARGET THE B-PLANE Now we have an arrival trajectory, which is close, but we want to return to Earth. The best way to do that is to target the B-plane. The B-plane is a planar coordinate system that allows targeting during a gravity assist or for planetary orbit insertion. It can be thought of as a target attached to the assisting body. If you have a trajectory that is close to the encounter planet, the B-plane gives you targets that behave very linearly, which is important with the differential corrector targeting scheme in Astrogator. However, had we targeted the B-plane before we had proper initial conditions (i.e. we were pointing in some random direction this would not have worked since we may never have crossed the plane. We first had to target to get close to Earth, and only then were we close enough to Earth with our trajectory to use B-plane targeting.

    TABLE 17. To perigee segment properties

    OPTION VALUEName ToPerigeeColor Any color not currently being used.Page 31

  • Will the Martian Space Vehicle Return to Earth?

    FIGURE 13.

    The B-plane is defined as the plane that contains the focus of an idealized two-body trajectory (assumed to be a hyperbola) that is perpendicular to the incoming asymptote of that hyperbola. The incoming and outgoing asymptotes, and, the focus are contained in the trajectory plane, which is perpendicular to the B-plane. The intersection of the B-plane and the trajectory plane defines a line in space. The B-vector is defined to lie alone this line, starting on the focus and ending at the spot where the incoming asymptote pierces the B-plane. The vectors and lie in the B-plane and are used as axes.

    USER SELECTED RESULTS

    1. Select the ToPerigee propagate segment ( ).2. Click the Results... button.3. Expand the component tree as follows:

    ... MultiBody

    ... BDotR

    ... BDotT4. Double-click the BDotR component ( ) to add it to the list.5. Select BDotR in the topmost table.6. Double-click the Value for Reference Vector in the Components Details area.7. When the reference selection dialog appears, expand the tree as follows:PAGE 32

    ... Earth

    ... Orbit Normal

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    8. Select Orbit Normal ( ).9. Click OK.10. Double-click the Value for Target Body in the Components Details area.11. Select Earth ( ).12. Click OK.13. Double-click the BDotT component ( ) to add it to the list.14. Repeat steps 4-11 for BDotT.15. Click OK.

    Earth Arrival Differential CorrectorsUsing an initial rough estimate of the geometry of the orbit were trying to enter, well target the B-Plane.

    1. Select EarthArrival ( ) in the MCS tree.2. Select the Differential Corrector.3. Rename it BPlane.4. Click the Properties... button.5. Enable the maneuvers as active controls:

    6. Enable the equality constraints as active controls:

    7. Click OK.

    TABLE 18. B-plane targeting control parameters

    CONTROL PARAMETERS STATEImpulsive Mnvr.Cartesian X OnImpulsive Mnvr.Cartesian Y OnImpulsive Mnvr.Cartesian Z On

    TABLE 19. B-plane targeting equality constraints

    EQUALITY CONSTRAINTS STATE DESIRED VALUEBDotR On 10,000 kmBDotT On 20,000 kmPage 33

  • 3D View: B-plane targeting

    Will the Martian Space Vehicle Return to Earth?

    RUN THE ACTIVE PROFILENow, you can run the selected BPlane profile and let Astrogator adjust the BDot values. Then well apply those changes. Doing this will apply the values of search profiles' controls and the changes specified by the segment configuration profiles to the segments within the target sequence.

    1. Ensure that the Action is set to Run active profiles.2. Click Run ( ).

    Did the profile converge? If so, did you achieve the desired values?

    3. When you finish, close the status grid.4. Bring the 3D Graphics - Sun window to the front.

    FIGURE 14.

    Did targeting the B-Plane get you closer to Earth?

    Lets see how close.

    LET ASTROGATOR CHANGE YOUR PERSPECTIVEPAGE 34

    1. Bring Astrogator to the front.2. Click on the unit selector ( ) beside the Final time.

  • 3D View (Earth): B-plane targeting

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    3. Select Set Animation Time.4. Bring the 3D Graphics - Earth window to the front.

    FIGURE 15.

    Target Keplerian ElementsWe can use another differential corrector to achieve the desired perigee altitude for aerobraking and to match the plane of the space stations orbit.

    ALTITUDE OF PERIAPSIS

    1. Select the ToPerigee propagate segment ( ).2. Click the Results... button.3. Expand the component tree as follows:

    ... Keplerian Elems

    ... Altitude of Periapsis4. Double-click the Altitude of Periapsis component ( ) to add it to the list.

    RELATIVE INCLINATIONPage 35

    1. Expand the component tree as follows:... Formation

  • Will the Martian Space Vehicle Return to Earth?

    ... RelativeValue2. Double-click the RelativeValue component ( ) to add it to the list.3. Select RelativeValue in the topmost table.4. Set the following:

    RELATIVE RAAN

    1. Expand the component tree as follows:... Formation... RelativeValue

    2. Double-click the RelativeValue component ( ) to add it to the list.3. Select RelativeValue in the topmost table.4. Set the following:

    5. Click OK.

    KEPLERIAN ELEMENTS DIFFERENTIAL CORRECTORLets create a second differential corrector to target Keplerian elements.

    1. Select EarthArrival ( ) in the MCS tree.2. Click the New... button above the profiles table.

    TABLE 20. Relative inclination values

    OPTION VALUECalcObject Keplerian Elems/InclinationComponentName RelativeInclinatinReference Selection UserSpecifiedReferenceReference Satellite/SpaceStation

    TABLE 21. Relative RAAN values

    OPTION VALUECalcObject Keplerian Elems/RAANComponentName RelativeRAANReference Selection UserSpecifiedRefreenceReference Satellite/SpaceStationPAGE 36

    3. Select Differential Corrector ( ).

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    4. Click OK to add the new profile to the target sequence.5. Rename the profile KeplerianElems.6. Click Properties...7. Enable the maneuvers as active controls:

    8. Enable the equality constraints as active controls:

    Well set the desired relative values to zero since were targeting the space station.

    9. Click OK.

    RUN THE ACTIVE PROFILENow, you can run the selected KeplerianElems profile.

    1. Ensure that the Action is set to Run active profiles.2. Click Run ( ).

    Did the profile converge? If so, did you achieve the desired values?

    3. Once converged, click the Apply Changes button.4. Change the Action to Run nominal sequence.

    TABLE 22. Keplerian element targeting control parameters

    CONTROL PARAMETERS STATE PERTURBATIONImpulsive Mnvr.Cartesian X On 0.00001 km/secImpulsive Mnvr.Cartesian Y On 0.00001 km/secImpulsive Mnvr.Cartesian Z On 0.00001 km/sec

    TABLE 23. Keplerian element targeting equality constraints

    EQUALITY CONSTRAINTS STATE DESIRED VALUEAltitude of Periapsis On 150 kmRelative Inclination On 0.0Relative RAAN On 0.0Page 37

  • 3D View: Keplerian element targeting

    Will the Martian Space Vehicle Return to Earth?

    LET ASTROGATOR CHANGE YOUR PERSPECTIVE

    1. Click on the unit selector ( ) beside the Final time.2. Select Set Animation Time.3. Bring the 3D Graphics - Earth window to the front.

    FIGURE 16.

    4. When you finish, close the status grid.5. Save ( ) the scenario ( ).

    Earth CaptureThe satellite is now arriving at Earth in the proper orbit.

    1. Add a new Target Sequence ( ) below the EarthArrival ( ) sequence.2. Change the name to EarthCapture.

    MANEUVERLets add a maneuver that will put the spacecraft in the initial capture orbit.

    1. Add a Maneuver segment ( ) to the EarthCapture ( ) sequence.PAGE 38

    2. Rename the segment CaptureMnvr.3. Change the name of the Maneuver segment ( ) to CaptureMnvr.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    4. Select CaptureMnvr ( ) in the MCS tree.5. Set the following:

    RESULTS

    1. Click the Results... button.2. Expand the component tree as follows:

    ... Keplerian Elems

    ... Eccentricity3. Double-click the Eccentricity component ( ) to add it to the list.4. Click OK.

    PROPAGATE

    1. Add a Propagate segment ( ) after the maneuver.2. Select the new Propagate segment ( ).3. Set the following:

    4. Click OK.

    STOPPING CONDITIONSNow, well add a stopping condition to

    1. Click the Insert... button.

    TABLE 24.

    OPTION VALUEAltitude Control Antivelocity Vector

    Delta V Magnitude2 km/secMark as independent variable ( )

    TABLE 25. To apoasis segment properties

    OPTION VALUEName ToApoapsisColor Any color not currently being used.Page 39

    2. Select the Apoapsis item ( ).3. Click OK to add the new Stopping Condition to the table.

  • Will the Martian Space Vehicle Return to Earth?

    4. Select the Duration stopping condition in the table.5. Click the Remove button.

    Earth Capture Differential CorrectorThe space station is in a circular orbit. The eccentricity of that orbit is zero. Although we want to match that value well target a larger value and see if we can get to an elliptical orbit. Then we can simulate aerobraking.

    1. Select EarthCapture ( ) in the MCS tree.2. Select the Differential Corrector.3. Rename it Target Capture.4. Click the Properties... button.5. Enable ImpulsiveMnvr.SphericalMagnitude.6. Enable the Eccentricity equality constraint.7. Set the Desired Value for Eccentricity to 0.6.8. Set the Tolerance value to 1e-5.9. Click OK.

    RUN!

    1. Ensure that the Action is set to Run active profiles.2. Click Run ( ).

    Did the profile converge? If so, did you achieve the desired values?

    3. Once converged, click the Apply Changes button.4. Change the Action to Run nominal sequence.5. When you finish, close the status grid.

    LET ASTROGATOR CHANGE YOUR PERSPECTIVE

    1. Click on the unit selector ( ) beside the Final time.2. Select Set Animation Time.3. Bring the 3D Graphics - Earth window to the front.PAGE 40

  • 3D View: Target capture

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    FIGURE 17.

    AerobrakingThe satellite is captured in an elliptical orbit. Now, we need to work our way down to a circular orbit like the one that the space station is in.

    1. Add a Propagate segment ( ) after the EarthCapture target sequence ( ).2. Double-click the new Propagate segment ( ).3. Set the following:

    4. Click OK.

    STOPPING CONDITIONS

    1. Select Aerobraking ( ) in the MCS tree.2. Click the Insert... button.

    TABLE 26. Aerobraking segment properties

    OPTION VALUEName AerobrakingColor Any color not currently being used.Page 41

    3. Select the Periapsis item ( ).

  • Will the Martian Space Vehicle Return to Earth?

    4. Click OK to add the new Stopping Condition to the table.5. Repeat steps 3-5 to add a second Periapsis Stopping Condition.6. Select the Duration stopping condition in the table.7. Click the Remove button.

    Automatic SequencesAutomatic Sequences are MCS elements that are structurally similar to Sequence segments, but are not MCS segments, properly. Rather, Automatic Sequences can be assigned to Propagate and Maneuver (Finite) segments, and function as subroutines by executing in response to specified stopping conditions of those segments.

    THE AUTOMATIC SEQUENCE BROWSERThe Automatic Sequence Browser contains a list of all Automatic Sequences defined for the Astrogator satellite. You define or edit Automatic Sequences, in the Automatic Sequence Browser window.

    1. Click the Automatic Sequence Browser button ( ) on the MCS Controls.2. Click the New Button.3. Rename it SmallBurn.4. Click OK.

    EDIT THE AUTOMATIC SEQUENCETo simulate aerobraking the apoapsis altitude is decreased by firing a thruster at every periapsis in the antivelocity direction.

    1. Click the Edit button.2. Add a Maneuver segment ( ) to the Automatic Sequence.3. Set the following:

    TABLE 27. Small burn sequence values

    OPTION VALUEAttitude Control Antivelocity VectorDelta V Magnitude 0.25 km/secPAGE 42

    4. Click OK.5. Click OK to dismiss the Automatic Sequence Browser.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    The Automatic Sequence for this propagate segment will run for seven periapsides and the propagate segment will stop on the eight periapsis.

    EDIT STOPPING CONDITIONSNow we can use the automatic sequence in the stopping condition to simulate the aerobraking.

    1. Select the first Periapsis entry in the Stopping Condition table.2. Set the following:

    3. Select the second Periapsis entry in the Stopping Condition table.4. Chane the repeat count to 8.

    RUN!

    1. Select EarthCapture ( ) in the MCS tree.2. Ensure that the Action is set to Run active profiles.3. Click Run ( ).

    Did the profile converge? If so, did you achieve the desired values?

    LET ASTROGATOR CHANGE YOUR PERSPECTIVE

    1. Click on the unit selector ( ) beside the Final time.2. Select Set Animation Time.3. Bring the 3D Graphics - Earth window to the front.

    TABLE 28.

    OPTION VALUESequence SmallBurnMax Trip Times 7Page 43

  • 3D View: Aerobraking

    Will the Martian Space Vehicle Return to Earth?

    FIGURE 18.

    4. When you finish, close the status grid.5. Save ( ) the scenario ( ).

    Circular Phasing OrbitWell add another target sequence will result in a phasing orbit. Two Hohmann transfers will be utilized to circularize the orbit at an altitude of 800 km.

    1. Add a new Target Sequence ( ) below the EarthCapture ( ) sequence.2. Change the name to CircularPhasingOrbit.

    Add a Propagate SegmentFirst, well add a propagate segment that will get us to apogee.

    1. Use the same process to add a Propagate segment ( ).2. Double-click the new Propagate segment ( ).3. Enter the following:PAGE 44

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    4. Click OK.

    STOPPING CONDITIONS

    1. Click the Insert... button.2. Select the Apoasis stopping condition ( ).3. Click OK to add the new Stopping Condition to the table.4. Select the Duration stopping condition in the table.5. Click the Remove button.

    Add a Maneuver Segment1. Use the same process to add a Maneuver segment ( ) after ToApogee ( ).2. Rename the new Maneuver segment ( ) BurnOne.3. Select BurnOne ( ) in the MCS tree.4. Ensure that the Attitude tab is selected.5. Set the following:

    6. Click the ( ) beside X(Velocity) to mark it as an independent variable ( ).

    CREATE A NEW CALCULATION OBJECTThe second maneuver should be a half-revolution after the first maneuver. The first maneuver was at apogee, but the maneuver may have pushed the orbit higher so the current location is now perigee. Therefore, we cant use a

    TABLE 29.

    OPTION VALUEName ToApogeeColor Select a color that isnt being used by any segment.

    TABLE 30.

    OPTION VALUEAltitude Control Thrust VectorX(Velocity) 0 km/secPage 45

    perigee stopping condition to find the location of the second maneuver.

  • Will the Martian Space Vehicle Return to Earth?

    Instead, well use a mean anomaly difference of 180 degrees. But first, we have to define a calculation object that gives us the difference in mean anomaly.

    1. Select the Astrogator Browser option from the View menu in the STK Workspace to open the component browser.

    2. Expand the component tree as follows:... CalculationObjects... Math

    3. Select Math.4. Select Difference ( ) components table.5. Click the Duplicate button.6. Rename it MeanAnomalyDifference.7. Click OK.8. When the new component (Mean Anomaly Difference) appears in the table,

    double-click it.9. Double-click the CalcObject value.10. Expand the component tree as follows:

    ... Keplerian Elems

    ... MeanAnomaly11. Select MeanAnomaly ( ).12. Click OK.13. Click OK to dismiss the component editing window.14. Click OK to dismiss the Astrogator Browser.

    Add a Second Propagate SegmentSince the maneuver (BurnOne) could have flipped apogee and perigee, we dont know to which apsis were propagating, but we do know that we want to propagate to the next apsis.

    1. Use the same process to add a Propagate segment ( ) after BurnOne ( ).2. Double-click the new Propagate segment ( ).3. Enter the following:

    TABLE 31. Half around properties

    OPTION VALUEPAGE 46

    Name HalfAroundColor Select a color that isnt being used by any segment.

  • WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    4. Click OK.

    STOPPING CONDITIONSWell add the same stopping condition to the second propagate segment that we used for the first to ensure that we stop at the next apsis.

    1. Click the Insert... button.2. Select the UserSelect stopping condition ( ).3. Click OK to add the new Stopping Condition to the table.4. Set the User Calc Object to Mean Anomaly Difference.5. Click OK.6. Set the Trip value to zero (0) deg.7. Select the Duration stopping condition in the table.8. Click the Remove button.

    Add a Second Maneuver Segment1. Use the same process to add a Maneuver segment ( ) after

    HalfAround ( ).2. Rename the new Maneuver segment ( ) BurnTwo.3. Select BurnTwo ( ) in the MCS tree.4. Ensure that the Attitude tab is selected.5. Set the following:

    6. Click the ( ) beside X(Velocity) to mark it as an independent variable ( ).

    RESULTS

    1. Click the Results... button.2. Expand the component tree as follows:

    TABLE 32.

    OPTION VALUEAltitude Control Thrust VectorX(Velocity) 0Page 47

    ... Geodetic

  • Will the Martian Space Vehicle Return to Earth?

    ... Altitude3. Double-click the Altitude component ( ) to add it to the list.4. Expand the component tree as follows:

    ... Keplerian Elems

    ... Eccentricity5. Double-click the Eccentricity component ( ) to add it to the list.6. Click OK.

    Phasing Orbit Differential CorrectorsWell now use the target sequence to enter an 800 km altitude circular phasing orbit above the space stations orbit. Well see the desired values for this run to reflect that.

    1. Select CircularPhasingOrbit ( ) in the MCS tree.2. Select the Differential Corrector.3. Rename it TargetPhasing.4. Click the Properties... button.5. Enable the two maneuvers as active controls:

    6. Enable the equality constraints as active controls:

    7. Set the Tolerance for Eccentricity value to 1e-5.8. Click OK.

    RUN!

    TABLE 33. Target phasing control parameters

    CONTROL PARAMETERS STATEImpulsive Mnvr.Cartesian X OnImpulsive Mnvr.Cartesian X On

    TABLE 34. Target phasing equality constraints

    EQUALITY CONSTRAINTS STATE DESIRED VALUEAltitude On 800 kmEccentricity On 0PAGE 48

    1. Select CircularPhasingOrbit ( ) in the MCS tree.

  • 3D View: Circular phasing orbit

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    2. Ensure that the Action is set to Run active profiles.3. Click Run ( ).

    Did the profile converge? If so, did you achieve the desired values?

    4. Once converged, click the Apply Changes button.5. Change the Action to Run nominal sequence.

    LET ASTROGATOR CHANGE YOUR PERSPECTIVE

    1. Click on the unit selector ( ) beside the Final time.2. Select Set Animation Time.3. Bring the 3D Graphics - Earth window to the front.

    FIGURE 19.

    Final OrbitNow that the targeter has put us in the final phasing orbit, we need to propagate to see the orbit. Well propagate for five days in the final orbit.Page 49

    1. Add a Propagate segment ( ) after the CircularPhasingOrbit target sequence ( ).

  • Will the Martian Space Vehicle Return to Earth?

    2. Double-click the new Propagate segment ( ).3. Enter the following:

    4. Set the Trip value under the Stopping Conditions to 5 days.

    RUN!

    1. Select CircularPhasingOrbit ( ) in the MCS tree.2. Ensure that the Action is set to Run active profiles.3. Click Run ( ).

    Did the profile converge? If so, did you achieve the desired values?

    LET ASTROGATOR CHANGE YOUR PERSPECTIVE

    1. Select the Final Propagate ( ) segement in the MCS tree.2. Click on the unit selector ( ) beside the Final time.3. Select Set Animation Time.4. Bring the 3D Graphics - Earth window to the front.

    TABLE 35. Half around properties

    OPTION VALUEName Final OrbitColor Select a color that isnt being used by any segment.PAGE 50

  • 3D View: Final prop to station

    WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?

    FIGURE 20.

    Data ReportingMCS ephemeris segments just give a listing of the segments run. It will show the autosequences and MCS segments and is good for getting an idea of how the run progressed.

    The Maneuver Summary report style is available only to Astrogator satellites. This report shows a summary of the maneuver segments in the MCS that have been run.

    1. Select SampleReturn( ) in the Object Browser.2. Open the Report & Graph Manager ( ).3. Select the Maneuver Summary Report style ( ).4. Click Generate...

    How much Delta-V does this mission require? What is the estimated fuel usage based on the engine models selected for

    the maneuvers?

    The MCS Ephemeris Segments report style shows which Astrogator segment produced each interval of ephemeris.

    1. Bring the Report & Graph Manager ( ) to the front.2. Select the MCS Ephemeris Segments Report style ( ).3. Click Generate...Page 51

    4. Take a moment to discuss the report contents with your instructor.

  • Will the Martian Space Vehicle Return to Earth?

    When You Finish1. Close all open status grids.2. Close any open reports.3. Close the Report & Graph Manager ( ).4. Click OK to dismiss SampleReturns ( ) properties ( ) and save your

    changes.5. Save ( ) the scenario ( ).PAGE 52

    Will the Martian Space Vehicle Return to Earth?Problem StatementBreak It DownSolution

    Model the World!Model a SpacecraftObject GraphicsSelect a Propagator

    What Is Astrogator?Mission Control SequenceMCS Controls

    Model the Martian LaunchAdd a Launch SegmentLaunch ParametersBurnout Velocity

    Model the Coast to the Martian OrbitThe Component BrowserCustomize ComponentsEdit the Propagator

    Propagate Segment PropertiesAdd a Maneuver SegmentThrust VectorAttitude Parameters

    Add a Second Propagate SegmentDefine the Properties of the Second Propagator

    Change Your PerspectiveCreate a Target SequenceVector Geometry ToolCreate the Orbit Normal VectorCreate the Orbital PlaneCreate the Angle Between

    Target Sequence ProfilesAdd the Segments to the Target Sequence

    Linking Independent VariablesLaunch Variables

    ResultsTarget the Launch

    Search ProfilesOrbit Plane Matching Differential Corrector

    Run the Active ProfileInitial & Final Date and TimeLet Astrogator Change Your Perspective

    Asymptote Targeting ProfilePropagate VariablesManeuver Variables

    Maneuver Targeting ComponentsAdd C3 EnergyAdd Outgoing Asymptote Parameters

    Asymptote Targeting ProfileControl ParametersEquality ConstraintsRun the Active ProfileChange Your Perspective

    Are We Headed In the Right Direction?Change Your Perspective

    Earth ArrivalModel the Mid-Course ManeuverPropagate to Earth SOIStopping ConditionsPropagate to Earth PeriapsisStopping ConditionsTarget the B-PlaneUser Selected Results

    Earth Arrival Differential CorrectorsRun the Active ProfileLet Astrogator Change Your Perspective

    Target Keplerian ElementsAltitude of PeriapsisRelative InclinationRelative RAANKeplerian Elements Differential CorrectorRun the Active ProfileLet Astrogator Change Your Perspective

    Earth CaptureManeuverResultsPropagateStopping Conditions

    Earth Capture Differential CorrectorRun!Let Astrogator Change Your Perspective

    AerobrakingStopping Conditions

    Automatic SequencesThe Automatic Sequence BrowserEdit the Automatic SequenceEdit Stopping ConditionsRun!Let Astrogator Change Your Perspective

    Circular Phasing OrbitAdd a Propagate SegmentStopping Conditions

    Add a Maneuver SegmentCreate a New Calculation Object

    Add a Second Propagate SegmentStopping Conditions

    Add a Second Maneuver SegmentResults

    Phasing Orbit Differential CorrectorsRun!Let Astrogator Change Your Perspective

    Final OrbitRun!Let Astrogator Change Your Perspective

    Data ReportingWhen You Finish

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