Chapter 8. Mars B-Plane Targeting

General Mission Analysis Tool

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Chapter 8. Mars B-Plane Targeting

Audience

Advanced

Length

75 minutes

Prerequisites

Complete Simulating an Orbit, Simple Orbit Transfer and a basic understanding of B-Planes and their usage in targeting is required.

Script File

Tut_Mars_B_Plane_Targeting.script

Objective and Overview

Note

One of the most challenging problems in space mission design is to design an interplanetary transfer trajectory that takes the spacecraft within a very close vicinity of the target planet. One possible approach that puts the spacecraft close to a target planet is by targeting the B-Plane of that planet. The B-Plane is a planar coordinate system that allows targeting during a gravity assist. It can be thought of as a target attached to the assisting body. In addition, it must be perpendicular to the incoming asymptote of the approach hyperbola. Figure 8.1, “Geometry of the B-Plane as seen from a viewpoint perpendicular to the B-Plane” and Figure 8.2, “The B-vector as seen from a viewpoint perpendicular to orbit plane” show the geometry of the B-Plane and B-vector as seen from a viewpoint perpendicular to orbit plane. To read more on B-Planes, please consult the GMATMathSpec document. A good example involving the use of B-Plane targeting is a mission to Mars. Sending a spacecraft to Mars can be achieved by performing a Trajectory Correction Maneuver (TCM) that targets Mars B-Plane. Once the spacecraft gets close to Mars, then an orbit insertion maneuver can be performed to capture into Mars orbit.

Figure 8.1. Geometry of the B-Plane as seen from a viewpoint perpendicular to the B-Plane

Geometry of the B-Plane as seen from a viewpoint perpendicular to the B-Plane

Figure 8.2. The B-vector as seen from a viewpoint perpendicular to orbit plane

The B-vector as seen from a viewpoint perpendicular to orbit plane

In this tutorial, we will use GMAT to model a mission to Mars. Starting from an out-going hyperbolic trajectory around Earth, we will perform a TCM to target Mars B-Plane. Once we are close to Mars, we will adjust the size of the maneuver to perform a Mars Orbit Insertion (MOI) to achieve a final elliptical orbit with an inclination of 90 degrees. Meeting these mission objectives requires us to create two separate targeting sequences. In order to focus on the configuration of the two targeters, we will make extensive use of the default configurations for spacecraft, propagators, and maneuvers.

The first target sequence employs maneuvers in the Earth-based Velocity (V), Normal (N) and Bi-normal (B) directions and includes four propagation sequences. The purpose of the maneuvers in VNB directions is to target BdotT and BdotR components of the B-vector. BdotT is targeted to 0 km and BdotR is targeted to a non-zero value to generate a polar orbit that has inclination of 90 degrees. BdotR is targeted to -7000 km to avoid having the orbit intersect Mars, which has a radius of approximately 3396 km.

The second target sequence employs a single, Mars-based anti-velocity direction (-V) maneuver and includes one propagation sequence. This single anti-velocity direction maneuver will occur at periapsis. The purpose of the maneuver is to achieve MOI by targeting position vector magnitude of 12,000 km at apoapsis. The basic steps of this tutorial are:

  1. Modify the DefaultSC to define spacecraft’s initial state. The initial state is an out-going hyperbolic trajectory that is with respect to Earth.

  2. Create and configure a Fuel Tank resource.

  3. Create two ImpulsiveBurn resources with default settings.

  4. Create and configure three Propagators: NearEarth, DeepSpace and NearMars

  5. Create and configure DifferentialCorrector resource.

  6. Create and configure three DefaultOrbitView resources to visualize Earth, Sun and Mars centered trajectories.

  7. Create and configure three CoordinateSystems: Earth, Sun and Mars centered.

  8. Create first Target sequence to target BdotT and BdotR components of the B-vector.

  9. Create second Target sequence to implement MOI by targeting position magnitude at apoapsis.

  10. Run the mission and analyze the results.

Configure Fuel Tank, Spacecraft properties, Maneuvers, Propagators, Differential Corrector, Coordinate Systems and Graphics

For this tutorial, you’ll need GMAT open, with the default mission loaded. To load the default mission, click New Mission () or start a new GMAT session. DefaultSC will be modified to set spacecraft’s initial state as an out-going hyperbolic trajectory.

Create Fuel Tank

We need to create a fuel tank in order to see how much fuel is expended after each impulsive burn. We will modify DefaultSC resource later and attach the fuel tank to the spacecraft.

  1. In the Resources tree, right-click the Hardware folder, point to Add and click ChemicalTank. A new resource called ChemicalTank1 will be created.

  2. Right-clickChemicalTank1 and click Rename.

  3. In theRename box, type MainTank and click OK.

  4. Double click onMainTank to edit its properties.

  5. Set the values shown in the table below.

    Table 8.1. MainTank settings

    Field Value
    Fuel Mass 1718
    Fuel Density 1000
    Pressure 5000
    Volume 2


  6. Click OK to save these changes.

Modify the DefaultSC Resource

We need to make minor modifications to DefaultSC in order to define spacecraft’s initial state and attach the fuel tank to the spacecraft.

  1. In the Resources tree, under Spacecraft folder, right-click DefaultSC and click Rename.

  2. In the Rename box, type MAVEN and click OK.

  3. Double-click on MAVEN to edit its properties. Make sure Orbit tab is selected.

  4. Set the values shown in the table below.

    Table 8.2. MAVEN settings

    Field Value
    Epoch Format UTCGregorian
    Epoch 18 Nov 2013 20:26:24.315
    Coordinate System EarthMJ2000Eq
    State Type Keplerian
    SMA under Elements -32593.21599272796
    ECC under Elements 1.202872548116185
    INC under Elements 28.80241266404142
    RAAN under Elements 173.9693759331483
    AOP under Elements 240.9696529532764
    TA under Elements 359.9465533778069


  5. Click on Tanks tab now.

  6. Under Available Tanks, you'll see MainTank. This is the fuel tank that we created earlier.

  7. We attach MainTank to the spacecraft MAVEN by bringing it under Selected Tanks box. Select MainTank under Available Tanks and bring it over to the right-hand side under the Selected Tanks.

  8. Click OK to save these changes.

Create the Maneuvers

We’ll need two ImpulsiveBurn resources for this tutorial. Below, we’ll rename the default ImpulsiveBurn and create a new one. We’ll also select the fuel tank that was created earlier in order to access fuel for the burns.

  1. In the Resources tree, under the Burns folder, right-click DefaultIB and click Rename.

  2. In the Rename box, type TCM, an acronym for Trajectory Correction Maneuver and click OK to edit its properties.

  3. Double-Click TCM to edit its properties to edit its properties.

  4. Check Decrement Mass under Mass Change.

  5. For Tank field under Mass Change, select MainTank from drop down menu.

  6. Click OK to save these changes.

  7. Right-click theBurns folder, point to Add, and click ImpulsiveBurn. A new resource called ImpulsiveBurn1 will be created.

  8. Rename the new ImpulsiveBurn1 resource to MOI, an acronym for Mars Orbit Insertion and click OK.

  9. Double-click MOI to edit its properties.

  10. For Origin field under Coordinate System, select Mars.

  11. Check Decrement Mass under Mass Change.

  12. For Tank field under Mass Change, select MainTank from the drop down menu.

  13. Click OK to save these changes.

Create the Propagators

We’ll need to add three propagators for this tutorial. Below, we’ll rename the default DefaultProp and create two more propagators.

  1. In the Resources tree, under the Propagators folder, right-click DefaultProp and click Rename.

  2. In the Rename box, type NearEarth and click OK.

  3. Double-click on NearEarth to edit its properties.

  4. Set the values shown in the table below.

    Table 8.3. NearEarth settings

    Field Value
    Initial Step Size under Integrator 600
    Accuracy under Integrator 1e-013
    Min Step Size under Integrator 0
    Max Step Size under Integrator 600
    Model under Gravity JGM-2
    Degree under Gravity 8
    Order under Gravity 8
    Atmosphere Model under Drag None
    Point Masses under Force Model Add Luna and Sun
    Use Solar Radiation Pressure under Force Model Check this field


  5. Click on OK to save these changes.

  6. Right-click the Propagators folder and click Add Propagator. A new resource called Propagator1 will be created.

  7. Rename the new Propagator1 resource to DeepSpace and click OK.

  8. Double-click DeepSpace to edit its properties.

  9. Set the values shown in the table below.

    Table 8.4. DeepSpace settings

    Field Value
    Type under Integrator PrinceDormand78
    Initial Step Size under Integrator 600
    Accuracy under Integrator 1e-012
    Min Step Size under Integrator 0
    Max Step Size under Integrator 864000
    Central Body under Force Model Sun
    Primary Body under Force Model None
    Point Masses under Force Model Add Earth, Luna, Sun, Mars, Jupiter, Neptune, Saturn, Uranus, Venus
    Use Solar Radiation Pressure under Force Model Check this field


  10. Click OK to save these changes.

  11. Right-click the Propagators folder and click Add Propagator. A new resource called Propagator1 will be created.

  12. Rename the new Propagator1 resource to NearMars and click OK.

  13. Double-click on NearMars to edit its properties.

  14. Set the values shown in the table below.

    Table 8.5. NearMars settings

    Field Value
    Type under Integrator PrinceDormand78
    Initial Step Size under Integrator 600
    Accuracy under Integrator 1e-012
    Min Step Size under Integrator 0
    Max Step Size under Integrator 86400
    Central Body under Force Model Mars
    Primary Body under Force Model Mars
    Model under Gravity Mars-50C
    Degree under Gravity 8
    Order under Gravity 8
    Atmosphere Model under Drag None
    Point Masses under Force Model Add Sun
    Use Solar Radiation Pressure under Force Model Check this field


  15. Click OK to save the changes.

Create the Differential Corrector

Two Target sequences that we will create later need a DifferentialCorrector resource to operate, so let’s create one now. We'll leave the settings at their defaults.

  1. In the Resources tree, expand the Solvers folder if it isn’t already.

  2. Right-click the Boundary Value Solvers folder, point to Add, and click DifferentialCorrector. A new resource called DC1 will be created.

  3. Rename the new DC1 resource to DefaultDC and click OK.

Create the Coordinate Systems

The BdotT and BdotR constraints that we will define later under the first Target sequence require us to create a coordinate system. Orbit View resources that we will create later also need coordinate system resources to operate. We will create Sun and Mars centered coordinate systems. So let’s create them now.

  1. In the Resources tree, right-click the Coordinate Systems folder and click Add Coordinate System. A new Dialog box is created with a title New Coordinate System.

  2. Type SunEcliptic under Coordinate System Name box.

  3. Under Origin field, select Sun.

  4. For Type under Axes, select MJ2000Ec.

  5. Click OK to save these changes. You’ll see that a new coordinate system SunEcliptic is created under Coordinate Systems folder.

  6. Right-click the Coordinate Systems folder and click Add Coordinate System. A new Dialog Box is created with a title New Coordinate System.

  7. Type MarsInertial under Coordinate System Name box.

  8. Under Origin field, select Mars.

  9. For Type under Axes, select BodyInertial.

  10. Click OK to save these changes. You’ll see that a new coordinate system MarsInertial is created under Coordinate Systems folder.

Create the Orbit Views

We’ll need three DefaultOrbitView resources for this tutorial. Below, we’ll rename the default DefaultOrbitView and create two new ones. We need three graphics windows in order to visualize spacecraft’s trajectory centered around Earth, Sun and then Mars

  1. In the Resources tree, under Output folder, right-click DefaultOrbitView and click Rename.

  2. In the Rename box, type EarthView and click OK.

  3. In the Output folder, delete DefaultGroundTrackPlot.

  4. Double-click EarthView to edit its properties.

  5. Set the values shown in the table below.

    Table 8.6. EarthView settings

    Field Value
    View Scale Factor under View Definition 4
    View Point Vector boxes, under View Definition 0, 0, 30000


  6. Click OK to save these changes.

  7. Right-click the Output folder, point to Add, and click OrbitView. A new resource called OrbitView1 will be created.

  8. Rename the new OrbitView1 resource to SolarSystemView and click OK.

  9. Double-click SolarSystemView to edit its properties.

  10. Set the values shown in the table below.

    Table 8.7. SolarSystemView settings

    Field Value
    From Celestial Object under View Object, add following objects to Selected Celestial Object box Mars, Sun (Do not remove Earth)
    Coordinate System under View Definition SunEcliptic
    View Point Reference under View Definition Sun
    View Point Vector boxes, under View Definition 0, 0, 5e8
    View Direction under View Definition Sun
    Coordinate System under View Up Definition SunEcliptic


  11. Click OK to save these changes.

  12. Right-click the Output folder, point to Add, and click OrbitView. A new resource called OrbitView1 will be created.

  13. Rename the new OrbitView1 resource to MarsView and click OK.

  14. Double-click MarsView to edit its properties.

  15. Set the values shown in the table below.

    Table 8.8. MarsView settings

    Field Value
    From Celestial Object under View Object, add following object to Selected Celestial Object box Mars (You don’t have to remove Earth)
    Coordinate System under View Definition MarsInertial
    View Point Reference under View Definition Mars
    View Point Vector boxes, under View Definition 22000, 22000, 0
    View Direction under View Definition Mars
    Coordinate System under View Up Definition MarsInertial


  16. Click OK to save the changes.

Configure the Mission Sequence

Now we will configure first Target sequence to solve for the maneuver values required to achieve BdotT and BdotR components of the B-vector. BdotT will be targeted to 0 km and BdotR is targeted to a non-zero value in order to generate a polar orbit that will have an inclination of 90 degrees. To allow us to focus on the first Target sequence, we’ll assume you have already learned how to propagate an orbit by having worked through Chapter 5, Simulating an Orbit tutorial.

The second Target sequence will perform the MOI maneuver so that the spacecraft can orbit around Mars, but that sequence will be created later.

Create the First Target Sequence

Now create the commands necessary to perform the first Target sequence. Figure 8.3, “Mission Sequence for the First Target sequence” illustrates the configuration of the Mission tree after you have completed the steps in this section. We’ll discuss the first Target sequence after it has been created.

Figure 8.3. Mission Sequence for the First Target sequence

Mission Sequence for the First Target sequence

To create the first Target sequence:

  1. Click on the Mission tab to show the Mission tree.

  2. You’ll see that there already exists a Propagate1 command. We need to delete this command

  3. Right-click on Propagate1 command and click Delete.

  4. Right-click on Mission Sequence folder, point to Append, and click Target. This will insert two separate commands: Target1 and EndTarget1.

  5. Right-click Target1 and click Rename.

  6. Type Target desired B-plane Coordinates and click OK.

  7. Right-click Target desired B-plane Coordinates, point to Append, and click Propagate. A new command called Propagate1 will be created.

  8. Right-click Propagate1 and click Rename.

  9. In the Rename box, type Prop 3 Days and click OK.

  10. Complete the Target sequence by appending the commands in Table 8.9, “Additional First Target Sequence Commands”.

    Table 8.9. Additional First Target Sequence Commands

    Command Name
    Propagate Prop 12 Days to TCM
    Vary Vary TCM.V
    Vary Vary TCM.N
    Vary Vary TCM.B
    Maneuver Apply TCM
    Propagate Prop 280 Days
    Propagate Prop to Mars Periapsis
    Achieve Achieve BdotT
    Achieve Achieve BdotR


Note

Let’s discuss what the first Target sequence does. We know that a maneuver is required to perform the B-Plane targeting. We also know that the desired B-Plane coordinate values for BdotT and BdotR are 0 and -7000 km, resulting in a polar orbit with 90 degree inclination. However, we don’t know the size (or ΔV magnitude) and direction of the TCM maneuver that will precisely achieve the desired orbital conditions. We use the Target sequence to solve for those precise maneuver values. We must tell GMAT what controls are available (in this case, three controls associated with three components of the TCM maneuver) and what conditions must be satisfied (in this case, BdotT and BdotR values). You accomplish this by using the Vary and Achieve commands. Using the Vary command, you tell GMAT what to solve for—in this case, the ΔV value and direction for TCM. You use the Achieve command to tell GMAT what conditions the solution must satisfy—in this case, BdotT and BdotR values that result in a 90 degree inclination.

Configure the First Target Sequence

Now that the structure is created, we need to configure various parts of the first Target sequence to do what we want.

Configure the Target desired B-plane Coordinates Command

  1. 1Double-click Target desired B-plane Coordinates to edit its properties.

  2. In the ExitMode list, click SaveAndContinue. This instructs GMAT to save the final solution of the targeting problem after you run it.

  3. Click OK to save these changes.

Figure 8.4. Target desired B-plane Coordinates Command Configuration

Target desired B-plane Coordinates Command Configuration

Configure the Prop 3 Days Command

  1. Double-click Prop 3 Days to edit its properties.

  2. Under Propagator, make sure that NearEarth is selected

  3. Under Parameter, replace MAVEN.ElapsedSeconds with MAVEN.ElapsedDays.

  4. Under Condition, replace 0.0 with 3.

  5. Click OK to save these changes.

Figure 8.5. Prop 3 Days Command Configuration

Prop 3 Days Command Configuration

Configure the Prop 12 Days to TCM Command

  1. Double-click Prop 12 Days to TCM to edit its properties.

  2. Under Propagator, replace NearEarth with DeepSpace.

  3. Under Parameter, replace MAVEN.ElapsedSeconds with MAVEN.ElapsedDays.

  4. Under Condition, replace 0.0 with 12.

  5. Click OK to save these changes.

Figure 8.6. Prop 12 Days to TCM Command Configuration

Prop 12 Days to TCM Command Configuration

Configure the Vary TCM.V Command

  1. Double-click Vary TCM.V to edit its properties. Notice that the variable in the Variable box is TCM.Element1, which by default is the velocity component of TCM in the local Velocity-Normal-Binormal (VNB) coordinate system. That’s what we need, so we’ll keep it.

  2. In the Initial Value box, type 1e-005.

  3. In the Perturbation box, type 0.00001.

  4. In the Lower box, type -10e300.

  5. In the Upper box, type 10e300.

  6. In the Max Step box, type 0.002.

  7. Click OK to save these changes.

Figure 8.7. Vary TCM.V Command Configuration

Vary TCM.V Command Configuration

Configure the Vary TCM.N Command

  1. Double-click Vary TCM.N to edit its properties. Notice that the variable in the Variable box is still TCM.Element1, which by default is the velocity component of TCM in the local VNB coordinate system. We need to insert TCM.Element2 which is the normal component of TCM in the local VNB coordinate system. So let’s do that.

  2. Next to Variable, click the Edit button..

  3. Under Object List, click TCM.

  4. In the Object Properties list, double-click Element2 to move it to the Selected Value(s) list. See the image below for results.

  5. Click OK to close the ParameterSelectDialog window.

  6. Notice that the variable in the Variable box is now TCM.Element2.

  7. In the Initial Value box, type 1e-005.

  8. In the Perturbation box, type 0.00001.

  9. In the Lower box, type -10e300.

  10. In the Upper box, type 10e300.

  11. In the Max Step box, type 0.002.

  12. Click OK to save these changes.

Figure 8.8. Vary TCM.N Parameter Selection

Vary TCM.N Parameter Selection

Figure 8.9. Vary TCM.N Command Configuration

Vary TCM.N Command Configuration

Configure the Vary TCM.B Command

  1. Double-click Vary TCM.B to edit its properties. Notice that the variable in the Variable box is still TCM.Element1, which by default is the velocity component of TCM. We need to insert TCM.Element3 which is the bi-normal component of TCM in the local VNB coordinate system. So let’s do that.

  2. Next to Variable, click the Edit button.

  3. Under Object List, click TCM.

  4. In the Object Properties list, double-click Element3 to move it to the Selected Value(s) list. See the image below for results.

  5. Click OK to close the ParameterSelectDialog window.

  6. Notice that the variable in the Variable box is now TCM.Element3.

  7. In the Initial Value box, type 1e-005.

  8. In the Perturbation box, type 0.00001.

  9. In the Lower box, type -10e300.

  10. In the Upper box, type 10e300.

  11. In the Max Step box, type 0.002.

  12. Click OK to save these changes.

Figure 8.10. Vary TCM.B Parameter Selection

Vary TCM.B Parameter Selection

Figure 8.11. Vary TCM.N Command Configuration

Vary TCM.N Command Configuration

Configure the Apply TCM Command

  • Double-click Apply TCM to edit its properties. Notice that the command is already set to apply the TCM burn to the MAVEN spacecraft, so we don’t need to change anything here.

Figure 8.12. Apply TCM Command Configuration

Apply TCM Command Configuration

Configure the Prop 280 Days Command

  1. Double-click Prop 280 Days to edit its properties.

  2. Under Propagator, replace NearEarth with DeepSpace.

  3. Under Parameter, replace MAVEN.ElapsedSeconds with MAVEN.ElapsedDays.

  4. Under Condition, replace 0.0 with 280.

  5. Click OK to save these changes.

Figure 8.13. Prop 280 Days Command Configuration

Prop 280 Days Command Configuration

Configure the Prop to Mars Periapsis Command

  1. Double-click Prop to Mars Periapsis to edit its properties.

  2. Under Propagator, replace NearEarth with NearMars.

  3. Under Parameter, replace MAVEN.ElapsedSeconds with MAVEN.Mars.Periapsis.

  4. Click OK to save these changes.

Figure 8.14. Prop to Mars Periapsis Command Configuration

Prop to Mars Periapsis Command Configuration

Configure the Achieve BdotT Command

  1. Double-click Achieve BdotT to edit its properties.

  2. Next to Goal, click the Edit button.

  3. In the Object Properties list, click BdotT.

  4. Under Coordinate System, select MarsInertial and double-click on BdotT.

  5. Click OK to close the ParameterSelectDialog window.

  6. In the Value box, type 0.

  7. In the Tolerance box, type 0.00001.

  8. Click OK to save these changes.

Figure 8.15. Achieve BdotT Command Configuration

Achieve BdotT Command Configuration

Configure the Achieve BdotR Command

  1. Double-click Achieve BdotR to edit its properties.

  2. Next to Goal, click the Edit button.

  3. In the Object Properties list, click BdotR.

  4. Under Coordinate System, select MarsInertial and double-click on BdotR.

  5. Click OK to close the ParameterSelectDialog window.

  6. In the Value box, type -7000.

  7. In the Tolerance box, type 0.00001.

  8. Click OK to save these changes.

Figure 8.16. Achieve BdotR Command Configuration

Achieve BdotR Command Configuration

Run the Mission with first Target Sequence

Before running the mission, click Save () and save the mission to a file of your choice. Now click Run (). As the mission runs, you will see GMAT solve the targeting problem. Each iteration and perturbation is shown in EarthView, SolarSystemView and MarsView windows in light blue, and the final solution is shown in red. After the mission completes, the 3D views should appear as in the images shown below. You may want to run the mission several times to see the targeting in progress.

Figure 8.17. 3D View of departure hyperbolic trajectory (EarthView)

3D View of departure hyperbolic trajectory (EarthView)

Figure 8.18. 3D View of heliocentric transfer trajectory (SolarSystemView)

3D View of heliocentric transfer trajectory (SolarSystemView)

Figure 8.19. 3D View of approach hyperbolic trajectory. MAVEN stopped at periapsis (MarsView)

3D View of approach hyperbolic trajectory. MAVEN stopped at periapsis (MarsView)

Since we are going to continue developing the mission tree by creating the second Target sequence, we will store the final solution of the first Target sequence as the initial conditions of the TCM resource. This is so that when you make small changes, the subsequent runs will take less time. To do this, follow these steps:

  1. In the Mission tree, double-click Target desired B-plane Coordinates to edit its properties.

  2. Click Apply Corrections.

  3. Click OK to save these changes.

  4. Now re-run the mission. If you inspect the results in the message window, you will see that the first Target sequence converges in one iteration. This is because you stored the solution as the initial conditions.

  5. In the Mission tree, double-click Vary TCM.V, Vary TCM.N and Vary TCM.B, you will notice that the values in Initial Value box have been updated to the final solution of the first Target sequence.

If you want to know TCM maneuver’s delta-V vector values and how much fuel was expended during the maneuver, do the following steps:

  1. In the Mission tree, right-click Apply TCM, and click on Command Summary.

  2. Scroll down and under Maneuver Summary heading, values for delta-V vector are:

    Delta V Vector:

    Element 1: 0.0039376963731 km/s

    Element 2: 0.0060423170483 km/s

    Element 3: -0.0006747125434 km/s

  3. Scroll down and under Mass depletion from MainTank heading, Delta V and Mass Change tells you TCM maneuver’s magnitude and how much fuel was used for the maneuver:

    Delta V: 0.0072436375569 km/s

    Mass change: -6.3128738639690 kg

  4. Click OK to close Command Summary window.

Just to make sure that the goals of first Target sequence were met successfully, let us access command summary for Prop to Mars Periapsis command by doing the following steps:

  1. In the Mission tree, right-click Prop to Mars Periapsis, and click on Command Summary.

  2. Under Coordinate System, select MarsInertial.

  3. Under Hyperbolic Parameters heading, see the values of BdotT and BdotR. Under Keplerian State, see the value for INC. You can see that the desired B-Plane coordinates were achieved which result in a 90 degree inclined trajectory:

    BdotT = -0.0000053320678 km

    BdotR = -7000.0000019398 km

    INC = 90.000000039301 deg

Create the Second Target Sequence

Recall that we still need to create second Target sequence in order to perform Mars Orbit Insertion maneuver to achieve the desired capture orbit. In the Mission tree, we will create the second Target sequence right after the first Target sequence.

Now let’s create the commands necessary to perform the second Target sequence. Figure 8.20, “Mission Sequence showing first and second Target sequences” illustrates the configuration of the Mission tree after you have completed the steps in this section. Notice that in Figure 8.20, “Mission Sequence showing first and second Target sequences”, the second Target sequence is created after the first Target sequence. We’ll discuss the second Target sequence after it has been created.

Figure 8.20. Mission Sequence showing first and second Target sequences

Mission Sequence showing first and second Target sequences

To create the second Target sequence:

  1. Click on the Mission tab to show the Mission tree.

  2. In the Mission tree, right-click on Mission Sequence folder, point to Append, and click Target. This will insert two separate commands: Target2 and EndTarget2.

  3. Right-click Target2 and click Rename.

  4. Type Mars Capture and click OK.

  5. Right-click Mars Capture, point to Append, and click Vary. A new command called Vary4 will be created.

  6. Right-click Vary4 and click Rename.

  7. In the Rename box, type Vary MOI.V and click OK.

  8. Complete the Target sequence by appending the commands in Table 8.10, “Additional Second Target Sequence Commands”.

    Table 8.10. Additional Second Target Sequence Commands

    Command Name
    Maneuver Apply MOI
    Propagate Prop to Mars Apoapsis
    Achieve Achieve RMAG


Note

Let’s discuss what the second Target sequence does. We know that a maneuver is required for the Mars capture orbit. We also know that the desired radius of capture orbit at apoapsis must be 12,000 km. However, we don’t know the size (or ΔV magnitude) of the MOI maneuver that will precisely achieve the desired orbital conditions. You use the second Target sequence to solve for that precise maneuver value. You must tell GMAT what controls are available (in this case, a single maneuver) and what conditions must be satisfied (in this case, radius magnitude value). Once again, just like in the first Target sequence, here we accomplish this by using the Vary and Achieve commands. Using the Vary command, you tell GMAT what to solve for—in this case, the ΔV value for MOI. You use the Achieve command to tell GMAT what conditions the solution must satisfy—in this case, RMAG value of 12,000 km.

Create the Final Propagate Command

We need a Propagate command after the second Target sequence so that we can see our final orbit.

  1. In the Mission tree, right-click End Mars Capture, point to Insert After, and click Propagate. A new Propagate6 command will appear.

  2. Right-click Propagate6 and click Rename.

  3. Type Prop for 1 day and click OK.

  4. Double-click Prop for 1 day to edit its properties.

  5. Under Propagator, replace NearEarth with NearMars.

  6. Under Parameter, replace MAVEN.ElapsedSeconds with MAVEN.ElapsedDays.

  7. Under Condition, replace the value 0.0 with 1.

  8. Click OK to save these changes

Figure 8.21. Prop for 1 day Command Configuration

Prop for 1 day Command Configuration

Configure the second Target Sequence

Now that the structure is created, we need to configure various parts of the second Target sequence to do what we want.

Configure the Mars Capture Command

  1. Double-click Mars Capture to edit its properties.

  2. In the ExitMode list, click SaveAndContinue. This instructs GMAT to save the final solution of the targeting problem after you run it.

  3. Click OK to save these changes

Figure 8.22. Mars Capture Command Configuration

Mars Capture Command Configuration

Configure the Vary MOI.V Command

  1. Double-click Vary MOI.V to edit its properties. Notice that the variable in the Variable box is TCM.Element1. We want MOI.Element1 which is the velocity component of MOI in the local VNB coordinate system. So let’s change that.

  2. Next to Variable, click the Edit button.

  3. Under Object List, click MOI.

  4. In the Object Properties list, double-click Element1 to move it to the Selected Value(s) list. See the image below for results.

  5. Click OK to close the ParameterSelectDialog window.

  6. In the Initial Value box, type -1.0.

  7. In the Perturbation box, type 0.00001.

  8. In the Lower box, type -10e300.

  9. In the Upper box, type 10e300.

  10. In the Max Step box, type 0.1.

  11. Click OK to save these changes.

Figure 8.23. Vary MOI Parameter Selection

Vary MOI Parameter Selection

Figure 8.24. Vary MOI Command Configuration

Vary MOI Command Configuration

Configure the Apply MOI Command

  1. Double-click Apply MOI to edit its properties.

  2. In the Burn list, click MOI.

  3. Click OK to save these changes.

Figure 8.25. Apply MOI Command Configuration

Apply MOI Command Configuration

Configure the Prop to Mars Apoapsis Command

  1. Double-click Prop to Mars Apoapsis to edit its properties.

  2. Under Propagator, replace NearEarth with NearMars.

  3. Under Parameter, replace MAVEN.ElapsedSeconds with MAVEN.Mars.Apoapsis.

  4. Click OK to save these changes.

Figure 8.26. Prop to Mars Apoapsis Command Configuration

Prop to Mars Apoapsis Command Configuration

Configure the Achieve RMAG Command

  1. Double-click Achieve RMAG to edit its properties.

  2. Next to Goal, click the Edit button.

  3. In the Object Properties list, click RMAG.

  4. Under Central Body, select Mars and double-click on RMAG.

  5. Click OK to close the ParameterSelectDialog window.

  6. In the Value box, type 12000.

  7. Click OK to save these changes.

Figure 8.27. Achieve RMAG Command Configuration

Achieve RMAG Command Configuration

Run the Mission with first and second Target Sequences

Before running the mission, click Save (). This will save the additional changes that we implemented in the Mission tree. Now click Run (). The first Target sequence will converge in one-iteration. This is because earlier, we stored the solution as the initial conditions. The second Target sequence may converge after 10 to11 iterations.

As the mission runs, you will see GMAT solve the second Target sequence’s targeting problem. Each iteration and perturbation is shown in MarsView windows in light blue, and the final solution is shown in red. After the mission completes, the MarsView 3D view should appear as in the image shown below. EarthView and SolarSystemView 3D views are same as before. You may want to run the mission several times to see the targeting in progress.

Figure 8.28. 3D view of Mars Capture orbit after MOI maneuver (MarsView)

3D view of Mars Capture orbit after MOI maneuver (MarsView)

If you were to continue developing this mission, you can store the final solution of the second Target sequence as the initial condition of MOI resource. This is so that when you make small changes, the subsequent runs will take less time. To do this, follow these steps:

  1. In the Mission tree, double-click Mars Capture to edit its properties.

  2. Click Apply Corrections.

  3. Now re-run the mission. If you inspect the results in the message window, you will see that now the second Target sequence also converges in one iteration. This is because you stored the solution as the initial condition. Now whenever you re-run the mission, both first and second Target sequences will converge in just one iteration.

  4. In the Mission tree, double-click Vary MOI.V, you will notice that the values in Initial Value box have been updated to the final solution of the second Target sequence.

If you want to know MOI maneuver’s delta-V vector values and how much fuel was expended during the maneuver, do the following steps:

  1. In the Mission tree, right-click Apply MOI, and click on Command Summary.

  2. Scroll down and under Maneuver Summary heading, values for delta-V vector are:

    Delta V Vector:

    Element 1: -1.6034665169868 km/s

    Element 2: 0.0000000000000 km/s

    Element 3: 0.0000000000000 km/s

  3. Scroll down and under Mass depletion from MainTank heading, Delta V and Mass Change tells you MOI maneuver’s magnitude and how much fuel was used for the maneuver:

    Delta V: 1.6034665169868 km/s

    Mass change: -1076.0639629424 kg

Just to make sure that the goal of second Target sequence was met successfully, let us access command summary for Achieve RMAG command by doing the following steps:

  1. In the Mission tree, right-click Achieve RMAG, and click on Command Summary.

  2. Under Coordinate System, select MarsInertial.

  3. Under Keplerian State and and Spherical State headings, see the values of TA and RMAG. You can see that the desired radius of the capture orbit at apoapsis was achieved successfully:

    TA = 180.00000241484 deg

    RMAG = 12000.019889021 km

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