Moon Mission Using B-Plane Targeting

STK Premium (Space) or STK Enterprise
You can obtain the necessary licenses for this tutorial by contacting AGI Support at support@agi.com or 1-800-924-7244.

The results of the tutorial may vary depending on the user settings and data enabled (online operations, terrain server, dynamic Earth data, etc.). It is acceptable to have different results.

Capabilities covered

This lesson covers the following capabilities of the Ansys Systems Tool Kit® (STK®) digital mission engineering software:

  • STK Pro
  • Astrogator
  • STK SatPro

Problem statement

Engineers want to model a mission to the Moon. They decide to use the method of B-plane targeting to utilize the gravity assist to achieve the desired orbit. The B-plane is defined to contain the focus of an idealized two-body trajectory that is assumed to be a hyperbola.

Solution

Use the STK/Astrogator® capability to model a mission to the Moon. Starting from a parking orbit around the Earth, you will perform a trans-lunar injection (TLI) to target the lunar B-plane. You will adjust the size of the maneuver to perform a lunar orbit insertion (LOI) to achieve a final circular lunar orbit with an inclination of 90 degrees.

This is an advanced Astrogator exercise, which presupposes familiarity with the STK software and some previous exposure to Astrogator. If you are new to the STK software, it is recommended that you first work through the STK Beginner training, which gives you a tour of the STK user interface and basic functionality of the STK application. For an entry-level introduction to Astrogator, try the exercise in which you use Target Sequences to model a Hohmann transfer.

What you will learn

Upon completion of this tutorial, you will be able to:

  • Customize the graphics settings for multiple central bodies
  • Use the B-Plane Template tool to configure a B-plane
  • Set a Target Sequence to target on the B-plane
  • Design and model a lunar orbit insertion

Video guidance

Watch the following video. Then follow the steps below, which incorporate the systems and missions you work on (sample inputs provided).

Creating a new scenario

First, you must create a new STK scenario, then build from there.

  1. Launch the STK application ().
  2. Click Create a Scenario in the Welcome to STK dialog box.
  3. Enter the following in the STK: New Scenario Wizard:
    4. Option Value
    Name LunarMission
    Location Default
    Start Tomorrow
    Stop + 30 days
  4. Click OK when you finish.
  5. Click Save () when the scenario loads.

    6. The STK software creates a folder with the same name as your scenario for you.

  6. Verify the scenario name and location in the Save As dialog box.
  7. Click Save.

Save () often during this lesson!

Preparing your workspace

Make some changes to your workspace and the scenario properties to make your mission easier to view.

Closing unneeded windows

Close the Timeline View and the 2D Graphics window. You don't need them in this scenario.

  1. Close the Timeline View to free up more space for other windows.
  2. Close the 2D Graphics window.

Do not resize the 3D Graphics window. You will continue to set up your workspace later in the scenario.

Updating the scenario properties

Update your scenario's Basic Time properties to increase the time interval between animation steps.

  1. Right-click on LunarMission () in the Object Browser.
  2. Select Properties () in the shortcut menu.
  3. Select the Basic - Time page when the Properties Browser opens.
  4. Enter 3 min in the Step Size field in the Animation panel.

    5. The greater this value, the greater the distance a vehicle will move in the 2D and 3D Graphics windows each time the screen is refreshed.

  5. Click Apply to confirm your change and to keep the Properties Browser open.

Setting 2D and 3D Graphics attributes for space situational awareness

2D Graphics attributes at the scenario level enables you to select what to view and how to view it in the 2D and 3D Graphics windows for all objects.

  1. Select the 2D Graphics - Global Attributes page.
  2. Set the following options:
    3. Panel Option Value
    Vehicles Show Orbits/ Trajectories Selected
    Show Orbit Markers Selected
    All other selections Cleared
    Planets Show Orbits Selected
    Show Inertial Positions Selected
    Show Position Labels Selected
    All other selections Cleared
  3. Click OK to confirm your changes and to close the Properties Browser.

Inserting Planet objects into the scenario

When you create a scenario, Globe Manager will automatically include in its hierarchy globes and imagery for central bodies associated with the selected primary central body; in this case, since Earth is the STK application's default primary central body, the Moon and Sun are also populated in the Globe Manager Hierarchy tab and visualized in the 3D Graphics window. However, you also want to model the ephemerides and visualize the orbits of Earth and the Moon for situational awareness. Use Planet objects to model these celestial bodies. A Planet object models orbital and other properties of a planet, a moon, an asteroid, or the Sun.

Adding the Planet object to the Insert STK Objects Tool

The Planet object isn't displayed in the New Object tool by default. If you have not yet added it to the Select An Object To Be Inserted list, do so now.

  1. Go to the Insert STK Objects () tool.
  2. Click Edit Preferences....
  3. Select Planet in the New Object list when the Preferences dialog box opens.
  4. Click OK to confirm your selection and to close the Preferences dialog box.

Inserting Planet objects into the scenario

Insert two Planet objects using the Insert Default method.

  1. Go to the Insert STK Objects () tool.
  2. Select Planet () in the Select An Object To Be Inserted list.
  3. Select Insert Default () in the Select a Method list.
  4. Click Insert... two times.

Adding the Earth to the scenario

Planet objects are defined by their Central Body. The options on a Planet object's Definition page enable you to identify the ephemeris source for a planet by selecting a Central Body component. A Central Body component models the gravitational, atmospheric, ephemeris, and other properties of a celestial body. The catalog of central bodies in the STK application includes the known planets, the Sun, the Moon, and other bodies of common interest. The default Central Body component for Planet objects is the Sun. Update Planet1's properties to add the Earth to your scenario.

  1. Open Planet1's () Properties ().
  2. Select the Basic - Definition page when the Properties Browser opens.
  3. Open the Central Body drop-down list.
  4. Select Earth.
  5. Ensure the Auto-Rename check box is selected.
  6. Click OK to confirm your selection and to close the Properties Browser.

Note that the Planet1 () has automatically been renamed Earth.

Adding the Moon to the scenario

Next, add the Moon.

  1. Open Planet2's () Properties ().
  2. Select the Basic - Definition page when the Properties Browser opens.
  3. Open the Central Body drop-down list.
  4. Select Moon.
  5. Ensure the Auto-Rename check box is selected.
  6. Click OK to confirm your selection and to close the Properties Browser.

Note that the Planet2 () has automatically been renamed Moon.

Preparing two 3D Graphics windows

For situational awareness, set up two 3D Graphics windows — one centered on the Earth and the other on the Moon.

Enabling the ECI Coordinates grid in the 3D Graphics window

Update your 3D Graphics window's Grids properties to display an Earth-centered space grid. Space grids can aid in accurately interpreting distances between objects in space. For ECI Coordinates, the space grid is displayed along the equatorial plane in the Earth-Centered inertial (ECI) coordinate system.

  1. Click Properties () on the 3D Window Defaults toolbar.
  2. Select the Grids page when the Properties Browser opens.
  3. Select the Show check box in the Space Grid - ECI Coordinates panel.
  4. Click Apply to confirm your selection and to keep the Properties Browser open.

You may want to select a relatively muted color for the grid (such as gray or olive green) so that it does not display in a prominent way in the 3D Graphics windows. Otherwise, it may detract from more important objects, such as orbit paths and the B-plane.

Renaming the 3D Graphics window

Rename the 3D Graphics window for clarity by updating its Window Properties.

  1. Select the Window Properties page.
  2. Enter Earth-Centered in the Title field.
  3. Click Apply to confirm your change and to keep the Properties Browser open.

Setting the maximum visible distance

Use the 3D Graphics window's Advanced properties to specify the maximum viewing distance in meters; the default is 10 million meters.

  1. Select the Advanced page.
  2. Enter 1e+010 km in the Max Visible Distance field in the Viewing panel.
  3. Click OK to confirm your changes and to close the Properties Browser.

earth-centered 3D Graphics window

Duplicating the 3D Graphics window

Duplicate the Earth-Centered 3D Graphics window and center it on the Moon.

  1. Select the View menu in the Menu Bar.
  2. Select Duplicate 3D Graphics Window in the View menu.
  3. Select Earth-Centered in the Duplicate 3D Graphics Window submenu.

Renaming the duplicate 3D Graphics window

Rename the 3D Graphics 2 - Earth window for clarity.

  1. Click on the 3D Graphics 2 - Earth window.
  2. Click Properties () on the 3D Graphics 2 - Earth 3D Graphics window's 3D Window Defaults toolbar.
  3. Select the Window Properties page when the Properties Browser opens.
  4. Enter Moon-Centered in the Title field.
  5. Click OK to confirm your change and to close the Properties Browser.

Changing the Moon-Centered 3D Graphics window's central body

Select the central body for the Moon-Centered window.

  1. Click 3D Graphics Window's Central Body () on the Moon-Centered 3D Graphics window's 3D Window Defaults toolbar.
  2. Select Moon in the drop-down list.

    3. Moon-centered 3D Graphics window

  3. Select the Window menu in the Menu Bar.
  4. Select Tile Vertically.

Modeling the lunar probe

You will model your lunar mission from launch to TLI to LOI. Start by inserting a Satellite object.

Inserting a Satellite object

A Satellite object models the properties and behavior of a vehicle in orbit around a central body.

  1. Go to the Insert STK Objects () tool.
  2. Insert a Satellite () object using the Insert Default () method.
  3. Right-click on Satellite1 () in the Object Browser.
  4. Select Rename in the shortcut menu.
  5. Rename Satellite1 () LunarProbe.

Setting the 3D Graphics properties for space situational awareness

Prior to propagating LunarProbe, update its 3D Pass graphics to enhance your space situational awareness.

  1. Open LunarProbe's () Properties ().
  2. Select the 3D Graphics - Pass page when the Properties Browser opens.
  3. Open the Lead Type drop-down list in the Orbit Track panel.
  4. Select All.
  5. Click Apply to confirm your selection and to keep the Properties Browser open.

The Lead Type defines the display of the leading portion of a vehicle tracks. The leading portion of a vehicle's track begins at the vehicle's present position and moves forward half the span of its ephemeris. Selecting All displays the track spanning the entire vehicle ephemeris.

Setting the 3D Graphics model's detail thresholds

Update the detail thresholds on the satellite 3D Graphics Model proprieties for better viewing a large distances. The threshold distance indicates when to switch between levels. Maximizing the detail thresholds sets the maximum viewing distance at which the coarsest detail in the model, label and vectors, attitude sphere, and geostationary box is displayed.

  1. Select the 3D Graphics - Model page.
  2. Drag the All slider all the way to the right in the Detail Thresholds panel to maximize the viewing distance.
  3. Click Apply to confirm your changes and to keep the Properties Browser open.

Targeting the Moon with Astrogator

The Astrogator capability contains specialized analyses for interactive orbit maneuver and spacecraft trajectory design. Astrogator calculates a satellite's ephemeris by running a Mission Control Sequence, or MCS, that you define according to the requirements of your mission. The Mission Control Sequence functions as a graphical programming language in which mission segments dictate how the Astrogator capability calculates the trajectory of the spacecraft based on the general settings that you specify for the MCS itself. Use the Astrogator capability to set up a Mission Control Sequence, make a first guess for the trans-lunar injection, set up a Target Sequence to calculate launch epoch and coast duration, and run the Target Sequence to bring the lunar probe close within the Moon's vicinity.

Propagating the Satellite object using Astrogator

The STK application offers a variety of analytic and numerical orbit propagators. Update the satellite's Basic Orbit properties to use Astrogator as the propagator.

  1. Select the Basic - Orbit page.
  2. Open the Propagator drop-down list.
  3. Select Astrogator.
  4. Click Apply to confirm your selection and to keep the Properties Browser open.

Setting up Mission Control Sequence segments

MCS segments are the building blocks of an Astrogator space mission. There are two general types of segments: those that generate ephemerides and those that affect the execution of the MCS. These segments can be used interactively so that ephemeris generated by one segment can cause another segment to change the way in which the MCS continues to run. Before configuring your MCS, you must first remove the default segments.

  1. Select the Basic - Orbit page.
  2. Select Initial State () in the MCS.
  3. Click Delete Segment () on the MCS toolbar.
  4. Click Yes in the Question dialog box to confirm the deletion.
  5. Select Propagate () in the MCS.
  6. Click Delete Segment () on the MCS toolbar.
  7. Click Yes in the Question dialog box to confirm the deletion.

Adding a Target Sequence

Use a Target Sequence as a structural element to define maneuvers and propagations in terms of the goals they are intended to achieve.

  1. Right-click on the Return Segment () in the MCS.
  2. Select Insert Before... in the shortcut menu.
  3. Select Target Sequence () when the Segment Selection dialog box opens.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.
  5. Right-click on Target Sequence () in the MCS.
  6. Select Rename in the shortcut menu.
  7. Rename Target Sequence () First Guess.

Adding a Launch segment

Use a Launch segment to model a simple spacecraft launch from Earth.

  1. Right-click on the Return segment () nested within First_Guess () in the MCS.
  2. Select Insert Before... in the shortcut menu.
  3. Select Launch () when the Segment Selection dialog box opens.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.

Adding a Propagate segment

Use a Propagate segment to model the movement of the spacecraft along its current trajectory until meeting specified stopping conditions.

  1. Right-click on Launch () in the MCS.
  2. Select Insert After... in the shortcut menu.
  3. Select Propagate () when the Segment Selection dialog box opens.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.

Adding a Maneuver segment

Use a Maneuver segment to model an Impulsive, Finite, or Optimal Finite maneuver.

  1. Right-click on Propagate () in the MCS.
  2. Select Insert After... in the shortcut menu.
  3. Select Maneuver () when the Segment Selection dialog box opens.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.

Adding two more Propagate segments

Two additional Propagate segments are required.

  1. Right-click on Maneuver () in the MCS.
  2. Select Insert After... in the shortcut menu.
  3. Select Propagate () when the Segment Selection dialog box opens.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.
  5. Right-click on Propagate1 () in the MCS.
  6. Select Insert After... in the shortcut menu.
  7. Select Propagate () when the Segment Selection dialog box opens.
  8. Click OK to confirm your selection and to close the Segment Selection dialog box.
  9. Click Apply to confirm your changes and to keep the Properties Browser open.

Updating the Launch segment's epoch

Specify the date and start time of the launch.

  1. Select Launch () in the MCS.
  2. Select the Launch tab.
  3. Open the Epoch drop-down menu ().
  4. Select Use Analysis Start Time.
  5. Click Apply to confirm your changes and to keep the Properties Browser open.

Updating the first Propagate segment's properties

Change the Propagate segment's name and color.

  1. Select Propagate () in the MCS.
  2. Click Segment Properties () on the MCS toolbar.
  3. Enter Coast in the Name field when the Edit Segment dialog box opens.
  4. Open the Color drop-down list.
  5. Select a color different from Launch ().

    6. In selecting a color for this and other MCS segments, make sure that the color you choose will show up well against the backgrounds of the 2D and 3D Graphics windows.

  6. Click OK to confirm your changes and to close the Edit Segment dialog box.

Setting Coast's Trip value

Stopping conditions are Astrogator components that are used by Propagate, Follow, and Finite Maneuver segments to define the point at which propagation should stop. The current stopping condition for the Coast Propagate segment is Duration; specify the Trip value at which the condition will be satisfied.

  1. Enter 5400 sec in the Trip field.

    2. This is equivalent to 90 minutes, which is about one orbit.

  2. Click Apply to confirm your changes and to keep the Properties Browser open.

Updating the Maneuver segment's properties

Change the name and color of the Maneuver segment.

  1. Select Maneuver () in the MCS.
  2. Click Segment Properties () on the MCS toolbar.
  3. Enter Trans-Lunar Injection the Name field when the Edit Segment dialog box opens.
  4. Open the Color drop-down list.
  5. Select white.
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.

You can't see the Maneuver segment in the 3D Graphics windows, so changing the color to white is just a way to make the segment stand out in the MCS.

Setting the Delta-V Magnitude for a first guess

The Maneuver segment defaults to an Impulsive maneuver type. For an Impulsive Maneuver, Astrogator calculates the new state of the spacecraft by adding a Delta-V vector to the final state velocity of the previous segment. This new state is then added to the ephemeris and passed to the next segment. You can apply a first guess for the magnitude of the thrust to correctly put the probe into position for TLI.

  1. Select Trans-Lunar Injection () in the MCS.
  2. Verify that the Maneuver Type is Impulsive.
  3. Select the Attitude tab.
  4. Ensure Along Velocity Vector is selected for the Attitude Control.

    5. The Attitude Control field enables you to select the mode in which the maneuver pointing direction is prescribed. The satellite object’s attitude is such that the Delta-V vector aligns with or is opposite to the spacecraft's inertial velocity vector. The inertial reference frame depends on the central body of the satellite object.

  5. Enter 3200 m/sec in the Delta-V Magnitude field as a first guess value.

    6. This is the magnitude of the impulse to be added to the spacecraft velocity vector in distance / time.

  6. Click Apply to confirm your change and to keep the Properties Browser open.

Updating Propagate1's Segment Properties

Change the name and color of the Propagate1 segment.

  1. Select Propagate1 () in the MCS.
  2. Click Segment Properties () on the MCS toolbar.
  3. Enter To Swing By in the Name field when the Edit Segment dialog box opens.
  4. Open the Color drop-down list.
  5. Select a color different from Launch () and Coast ().
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.
  7. Click Apply to confirm your change and to keep the Properties Browser open.

Updating To Swing By's Propagator component

Astrogator also utilizes a component catalog and editor in the STK application called the Component Browser. The Component Browser enables you to define and customize engine models, force models, propagators, central bodies, atmospheric models, and other elements of a space mission analysis scenario. A Propagator component comprises a numerical integrator and a set of propagator functions. You will use the Cislunar (between the Earth and the Moon) Propagator to model an Earth-centered orbit within the Moon's orbit.

  1. Select To Swing By () in the MCS.
  2. Click on the Propagator ellipsis ().
  3. Select Cislunar () when the Select Component dialog box opens.
  4. Click OK to confirm your selection and to close the Select Component dialog box.

Creating a new stopping condition for To Swing By

You will use the R Magnitude stopping condition to stop at a specified distance from the origin.

  1. Click New... () on the Stopping Conditions panel toolbar.
  2. Select R Magnitude () when the New Stopping Condition dialog box opens.
  3. Click OK to accept your selection and to close the New Stopping Condition dialog box.
  4. Enter 300000 km in the Trip field.
  5. Select the Duration stopping condition in the Stopping Conditions list.
  6. Click Delete () in the Stopping Conditions panel toolbar.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Updating Propagate2's Segment Properties

Update the name and color of the Propagate2 segment.

  1. Select Propagate2 () in the MCS.
  2. Click Segment Properties () on the MCS toolbar.
  3. Enter To Periselene in the Name field when the Edit Segment dialog box opens.
  4. Open the Color drop-down list.
  5. Select a color different from Launch (), Coast () and To Swing By ().
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Updating To Periselene's Propagator component

Change the Propagator for the To Periselene Propagate segment to Cislunar.

  1. Select To Periselene () in the MCS.
  2. Click on the Propagator ellipsis ().
  3. Select Cislunar () when the Select Component dialog box opens.
  4. Click OK to confirm your selection and to close the Select Component dialog box.

Updating To Periselene's Duration stopping condition

Update the Duration stopping condition for the To Periselene Propagate segment.

  1. Enter 10 day in the Trip field.
  2. Click Apply to confirm your changes and to keep the Properties Browser open.

Creating a new Altitude stopping condition

Create a new Altitude stopping condition for the To Periselene Propagate segment to stop at a specified altitude from the Earth, near the Moon.

  1. Click New... () on the Stopping Conditions panel toolbar.
  2. Select Altitude () when the New Stopping Condition dialog box opens.
  3. Click OK to confirm your selection and to close the New Stopping Condition dialog box.
  4. Enter 0 km in the Trip field.
  5. Click on the Central Body ellipsis ().
  6. Select Moon () when the Select Component dialog box opens.

    7. Recall that Central Body components model the gravitational, atmospheric, ephemeris, and other properties of celestial bodies.

  7. Click OK to confirm your selection and to close the Select Component dialog box.
  8. Click Apply to confirm your changes and to keep the Properties Browser open.

Creating a new Periapsis stopping condition

Next, create a Periapsis stopping condition for To Periselene with the Moon as a central body.

  1. Click New... () on the Stopping Conditions panel toolbar.
  2. Select Periapsis () when the New Stopping Condition dialog box opens.
  3. Click OK to confirm your selection and to close the Select Component dialog box.
  4. Click on the Central Body ellipsis ().
  5. Select Moon () when the Select Component dialog box opens.
  6. Click OK to confirm your selection and to close the Select Component dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Configuring MCS segment propagators

In the MCS toolbar, you can Configure the MCS by clicking Configure MCS Segment Propagators () to view and adjust the propagator and integrator settings for each segment. When you click the icon, the Configure MCS Propagators dialog box appears, enabling you to set parameters if required.

  1. Click Configure MCS Segment Propagators () on the MCS toolbar.
  2. Ensure First_Guess.Coast and First_Guess.Trans_Lunar_Injection are using the Earth_Default_High_Fidelity_v13 propagator when the Configure MCS Propagators dialog box opens.
  3. Ensure First_Guess.To_Swing_By and First_Guess.To_Periselene are using the Cislunar propagator.
  4. Click Cancel to close the Configure MCS Propagators dialog box.

Performing a first guess at TLI

You are now ready to perform an impulsive maneuver that will send the lunar probe near the Moon's orbit. This trajectory is a good first guess to use in running Target Sequence to calculate the correct launch time and the correct coast time in the parking orbit.

  1. Click Run Entire Mission Control Sequence () on the MCS toolbar.
  2. Click on the Earth-Centered tab at the bottom of STK to bring the Earth-Centered 3D Graphics window to the front.
  3. Adjust your view so that you can see the Earth, Moon and LunarProbe.

    4. Trans-Lunar Injection First Guess

    Your view will be similar to but different from the above image depending on your analysis time period.

  4. Click Start () on the Animation toolbar to animate the scenario.
  5. Click Reset () when finished.

Your first guess at a trans-lunar injection is not that close. Use a control parameter to make a targeted approach.

Setting up the control parameters to calculate launch and coast times

A Target Sequence's differential corrector profile uses a differential correction algorithm to achieve a goal value or set of values. The values that the profile targets are called independent variables, or control parameters. The values that define the goal of the profile are called dependent variables, or equality constraints or results. When the Target Sequence runs, it will change the values of the independent variables to achieve the goal. You need to target the Moon. To achieve that, you will use the launch epoch and the coast time as control parameters. Astrogator will calculate new values that meet a set of constraints.

  1. Return to LunarProbe's () Properties () by clicking on the LunarProbe tab at the bottom of STK.
  2. Select Launch () in the MCS.
  3. Select the Launch tab.
  4. Open the Epoch drop-down menu ().
  5. Select Replace With Time.

    6. The Epoch time should match your scenario analysis start time.

  6. Click on the Epoch () target icon.

    7. Any element of a nested MCS segment or linked component that you can use as a control parameter (independent variable) is marked by a target icon (). To select an element as an independent variable, click its target icon. A check mark appears over the target (). You can click the target again to clear the selection of that element if not needed.

  7. Select Coast () in the MCS.
  8. Click on the Trip () target icon.

Selecting To Periselene's results

Dependent variables, or equality constraints, for a Target Sequence's differential corrector profiles are defined in terms of Calculation objects. You will use Delta Right Ascension and Delta Declination as the equality constraints. The constraints are the targeted differences in the right ascension and declination angles between the spacecraft and the selected central body with respect to its parent body. Use the multi-component select window to select and define your results.

  1. Select To Periselene () in the MCS.
  2. Click Results... at the bottom of the MCS.
  3. Expand () MultiBody () in the Available Components list when the User-Selected Results - To Periselene dialog box opens.
  4. Select Delta Declination ().
  5. Move () Delta Declination () to the selected component list.
  6. Select Delta Right Asc ().
  7. Move () Delta Right Asc () to the selected component list.
  8. Verify that the Moon is selected as the CentralBody for both components in the Component Details list.
  9. Click OK to confirm your selections and to close the User-Selected Results - To Periselene dialog box.
  10. Click Apply to confirm your changes and to keep the Properties Browser open.

Setting First_Guess' Differential Corrector

Update the Differential Corrector's name to be more descriptive.

  1. Select First_Guess () in the MCS.
  2. Click on Differential Corrector in the Name field of the Profiles panel.
  3. Enter Delta RA as a new name for Differential Corrector.
  4. Select the Tab key.
  5. Click Properties... () on the Profiles panel toolbar.

You can also double-click on the Differential Corrector to open its properties.

Selecting Delta RA's Control Parameters

Use the launch epoch and the coast time as the independent variables. These are the elements you selected previously.

  1. Select the Use check box for Launch.Epoch in the Control Parameters panel when the Delta RA dialog box opens.
  2. Enter 1 min in the Perturbation field.

    3. Perturbation is the value that you want the profile to use in calculating numerical derivatives.

  3. Enter 1 hr in the Max. Step field.

    4. Max Step is the maximum increment to the value of the parameter in a step.

  4. Select the Use check box for StoppingConditions.Duration.TripValue.
  5. Enter 5 min in the Max. Step field.

Selecting Delta RA's Equality Constraints (Results)

Use Delta Right Ascension and Delta Declination. These are results you previously selected.

  1. Select the Use check box for Delta_Declination in the Equality Constraints (Results) panel.
  2. Select the Use check box for Delta_Right_Asc.
  3. Keep Desired Value at 0 deg for both.

Setting Delta RA's convergence criteria

Use the Convergence tab to specify convergence criteria and related parameters for the profile. You will set the maximum number of iterations your desire in your analysis. This property defines the maximum number of evaluations that the profile will execute. If the profile does not reach the Desired Value, it will stop after the last iteration. The iteration count includes steps taken while searching for bounds as well as bisection iterations.

  1. Select the Convergence tab.
  2. Enter 200 in the Maximum Iterations field.
  3. Click OK to confirm your changes and to close the Delta RA dialog box.

Rerunning the First_Guess Target Sequence

By default, the Action field of the Target Sequence is set to Run nominal sequence. If you run the MCS, the values you have set for the various segments (e.g. 90 min Duration for the Coast segment) will be used. Here, instead, you will let the Target Sequence calculate new values to help achieve your goal of reaching the Moon.

  1. Select First_Guess () in the MCS.
  2. Open the Action drop-down list.
  3. Select Run active profiles.

    4. Selecting run active profiles runs the mission control sequence allowing the active profiles to operate.

  4. Click Run Entire Mission Control Sequence () on the MCS toolbar.
  5. Look at the data in the Target Status window.

    6. The Target Sequence will run through several iterations and, after a short time, will converge on a solution that meets your constraints within the specified tolerances. A Target Status window will indicate the number of iterations that were required and, again, the differences (now small enough to be acceptable) between the achieved and desired values for the constraints. It will also show the new values calculated for the control variables (launch epoch and coast time).

    If your setup doesn't work, you will see DID NOT CONVERGE in the in the Target Status window, at which point you will need to go back and troubleshoot your setup. Depending on the date of your launch epoch, you may need to increase the Delta-V Magnitude of the Trans-Lunar Injection Maneuver segment to achieve TLI. See the Analyzing a Lunar Launch with Astrogator and ModelCenter tutorial for an example of how Delta-V changes with a launch epoch.

  6. When finished, close the Target Status window.

Viewing the iterations in the Moon-Centered window

Review the results of the solution in the Moon-Centered 3D Graphics window.

  1. Click on the Moon-Centered tab at the bottom of STK to bring the Moon-Centered 3D Graphics window to the front.
  2. Right-click on Moon () in the Object Browser.
  3. Select Zoom To in the shortcut menu.
  4. Select Moon-Centered in the shortcut sub-menu.
  5. Use your mouse so that you can see the iterations and the final solution of LunarProbe () reaching the Moon.

Trans-lunar injection: moon targeted

Your view will look different from the above image. The iteration closest to the Moon is the final iteration.

Understanding B-plane targeting

The B-plane is a planar coordinate system that allows targeting during a gravity assist. You can think of it as a target attached to the assisting body. The B-plane is defined to contain the focus of an idealized two-body trajectory that is assumed to be a hyperbola. Also, it must be 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.

B-plane targeting

Creating a B-plane template with the B-Plane Template tool

The SatPro capability extends the STK software into the realm of high-fidelity satellite systems modeling and analysis. SatPro provides you with a collection of satellite engineering tools, including the B-Plane Template tool, that model a satellite's surface area, mass, solar panel configuration, and more. The B-Plane Template tool allows you to create templates that define the configuration of B-planes that can be displayed in the 3D Graphics window. A template created using this tool will be saved along with the scenario in which it is created, allowing you to utilize the template with any satellite in the scenario. Use the B-Plane Template tool to create a new B-plane template with the Moon as the Central Body.

  1. Select LunarProbe () in the Object Browser.
  2. Select the Satellite menu in the menu bar.
  3. Select B-Plane Template... in the Satellite submenu.
  4. Click Add in the B-Planes panel when the B-Plane Template dialog box opens.
  5. Open the Central Body drop-down list.
  6. Select Moon.
  7. Click OK to confirm your selection and to close the B-Plane Template dialog box.

Visualizing the B-plane

You can add the B-plane for visualization, enabling you to see what the Target Sequence is trying to achieve, by updating the satellite's B-Plane properties.

  1. Return to LunarProbe's () Properties ().
  2. Select the 3D Graphics - B-Plane page.
  3. Click Add....

Selecting the event epoch

Enter the epoch of the event. You'll use the Stop time of the First_Guess_To_Periselne Time Instant. A Time Instant is a component that produces a single moment in time.

  1. Open the Event Epoch drop-down menu ().
  2. Select Time Component....
  3. Select LunarProbe () in the object list when the Select Time Instance dialog box opens.
  4. Expand () MCSEphemerisSegments () in the Time Instants for: LunarProbe list.
  5. Expand () First_Guess_To_Periselne ().
  6. Select Stop ().
  7. Click OK to confirm your selection and to close the Select Time Instance dialog box.
  8. Click OK to close the Add B-Plane dialog box.

Updating the display of the target points

The position of the target points can be defined manually.

  1. Enter 0 km in the B*T field in the Target Point panel.
  2. Enter 5000 km in the B*R field.
  3. Click Apply to confirm your changes and to keep the Properties Browser open.

Clearing the graphics

Clear the iteration graphics from the run.

  1. Select the Basic - Orbit page.
  2. Click Clear Graphics () on the MCS toolbar.
  3. Click Apply to confirm your changes and to keep the Properties Browser open.

Setting up the Moon-Centered view

View the changes in the Moon-Centered 3D Graphics window.

  1. Bring the Moon-Centered 3D Graphics window to the front.
  2. Use your mouse to set up your view so that it looks similar to the following image:

B-plane reference with vectors

You view will be similar to the above image.

Targeting the B-plane

Assume that you want to capture the Moon in an orbit with a 90-degree inclination. Duplicate your existing Differential Corrector Profile and modify it from there.

  1. Bring LunarProbe's () Properties () to the front.
  2. Select First_Guess () in the MCS.
  3. Select Delta RA in the Profiles panel.
  4. Click Duplicate () on the Profiles panel toolbar.
  5. Rename Copy of Delta RA B-Plane Targeting.
  6. Select the Tab key.

Selecting the results of the To Periselene Propagate segment

Select the BdotR and BDotT vector dot products objects as the results of the To Periselene Propagate segment.

  1. Select To Periselene () in the MCS.
  2. Click Results....
  3. Expand () MultiBody () in the Available Components list when the User-Selected Results - To Periselene dialog box opens.
  4. Move () BDotR () to the selected components list.
  5. Move () BDotT () to the selected components list.
  6. Click OK to confirm your selections and to close the User-Selected Results - To Periselene dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Setting up the B-Plane targeting profile

Select the control parameters and equality constraints of the B-Plane Target Sequence.

  1. Select First_Guess () in the MCS.
  2. Select B-Plane Targeting in the Profiles panel.
  3. Click Properties... () on the Profiles panel toolbar.
  4. Verify that the two Control Parameters remain selected when the B-Plane Targeting dialog box opens.
  5. Clear the Use check boxes for the following in the Equality Constraints (Results) list:
    • Delta_Declination
    • Delta_Right_Asc
  6. Select the Use check boxes for the following in the Equality Constraints (Results) list:
    • BDotR
    • BDotT
  7. Select BDotR.
  8. Enter 5000 km in the Desired Value field.

    9. BDotT is targeted to 0 km and BDotR is targeted to a non-zero value to generate a polar orbit. BDotR is targeted to 5,000 kilometers to avoid having the orbit intersect the Moon, which has a radius of approximately 1,738 kilometers.

  9. Click OK to confirm your changes and to close the B-Plane Targeting dialog box.

Resetting profiles and corrections

Although not always required, it won't hurt to reset the controls of the search profiles to the segments' values.

  1. Select First_Guess () in the MCS.
  2. Click Reset in the Profiles and Corrections panel.

Running the Target Sequence to achieve B-plane parameters

With your parameters updated, run the First_Guess Target Sequence.

  1. Ensure First_Guess () is selected in the MCS.
  2. Click Run Entire Mission Control Sequence () on the MCS toolbar.
  3. In the Target Status windows, note that targeting has converged and that new values have been calculated for the control variables

    4. It is important to remember that the B vector ends at the point where the asymptote pierces the plane, not where the trajectory does. Think of the asymptote as the trajectory that the spacecraft would follow if the central body had no gravity. As a result, the trajectory is always closer to the central body than the B vector, as is the case in the B-plane reference with vectors illustration above.

  4. Close the Target Status windows.

Approaching the Moon

You have reached Periselene, but unless you perform some kind of maneuver, the spacecraft will swing by the Moon. Before you add the lunar orbital insertion sequence, observe the effects of the Moon's gravity field by inserting a new Propagate segment.

  1. Right-click on the last (bottom) Return segment () in the MCS.
  2. Select Insert Before... in the shortcut menu.
  3. Select Propagate () when the Segment Selection dialog box opens.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.

Updating the Propagate segment's properties

Rename the Propagate segment and change its color.

  1. Select Propagate () in the MCS.
  2. Click Segment Properties () on the MCS toolbar.
  3. Enter Prop 3 Days in the Name field when the Edit Segment dialog box opens.
  4. Open the Color drop-down list.
  5. Select a color that contrasts with those of the other Propagate segments.
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Changing Prop 3 Days' parameters

Update the Prop 3 Days Propagate segment's propagator and trip time.

  1. Select Prop 3 Days () in the MCS.
  2. Click on the Propagator ellipsis ().
  3. Select Moon HPOP Default v10 () when the Select Component dialog box opens.
  4. Click OK to confirm your selection and to close the Select Component dialog box.
  5. Enter 3 day in the Trip field.
  6. Click Apply to confirm your changes and to keep the Properties Browser open.
  7. Click Run Entire Mission Control Sequence () on the MCS toolbar.
  8. Close the Target Status windows.

Clearing the graphics

Clear the iteration graphics from the run.

  1. Click Clear Graphics () on the MCS toolbar.
  2. Click Apply to confirm your changes and to keep the Properties Browser open.

Visualizing the LunarProbe swinging by the Moon

View the results of the run in the Moon-Centered 3D Graphics window.

  1. Bring the Moon-Centered 3D Graphics window to the front.
  2. Set your view so that you can see the route LunarProbe () as it swing by the Moon.

LunarProbe swings past the Moon

Creating a new Target Sequence to achieve LOI

Without any targeting parameters, LunarProbe will swing by the Moon. Use a Target Sequence to conduct a burn and enter an orbit around the Moon.

Inserting a new Target Sequence

Create a new Target Sequence and nest the Prop 3 Days Propagate segment in it.

  1. Return to LunarProbe's () Properties ().
  2. Right-click on Prop 3 Days () in the MCS.
  3. Select Insert Before... in the shortcut menu.
  4. Select Target Sequence () when the Segment Select dialog box opens.
  5. Click OK to confirm your selection and to close the Segment Select dialog box.
  6. Click and drag Prop 3 Days () and nest it in Target Sequence ().
  7. Right-click on Target Sequence () in the MCS.
  8. Select Rename in the shortcut menu.
  9. Rename Target Sequence () Lunar Orbit Insertion.

Inserting a Maneuver segment

Insert a Maneuver segment before the Prop 3 Days Propagate segment in the Lunar Orbit Insertion Target Sequence.

  1. Right-click on Prop 3 Days () in the MCS.
  2. Select Insert Before... in the shortcut menu.
  3. Select Maneuver () when the Segment Selection dialog box opens.
  4. Click OK to confirm your selection and to close the Segment Select dialog box.

Updating the Maneuver segment properties

Rename the Maneuver segment and change its color.

  1. Select Maneuver () in the MCS.
  2. Click Segment Properties () on the MCS toolbar.
  3. Enter LOI in the Name field when the Edit Segment dialog box opens.
  4. Open the Color drop-down list.
  5. Select white.
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.

Updating LOI's parameters

You will now perform an impulsive maneuver to capture the Moon in a circular orbit. You will need to do a burn in a direction opposite to Moon-centered velocity to slow down and capture into a lunar orbit.

  1. Select LOI () in the MCS.
  2. Select the Attitude tab.
  3. Open the Attitude Control drop-down list.
  4. Select Thrust Vector in the shortcut menu.

    5. With this attitude control setting, you specify the Delta-V vector in some reference frame using either Cartesian or spherical components. Astrogator then computes the attitude so that the total thrust vector in the body frame, as specified by the thruster set or engine model, aligns with this vector in the reference axes.

  5. Click on the Thrust Axes ellipsis ().
  6. Select Satellite in the object list when the Select Reference dialog box opens.
  7. Select VNC(Moon) () in the Templates for Satellite list.
  8. Click OK to confirm your selection and to close the Select Reference dialog box.
  9. Click on the X (Velocity) () target icon to set the control variable.
  10. Click Apply to confirm your changes and to keep the Properties Browser open.

Setting LOI's results

Set the Results of the LOI Maneuver segment to achieve an eccentric orbit around the Moon.

  1. Select LOI () in the MCS.
  2. Click Results....
  3. Expand () Keplerian Elements () in the Available Components list when the User-Selected Results - LOI dialog box opens.
  4. Move () Eccentricity () to the selected components list.
  5. Double-click on CentralBody in the Component Details list.
  6. Select Moon () when the Component Selection dialog box opens.
  7. Click OK to confirm your selection and to close the Component Selection dialog box.
  8. Click OK to confirm your changes and to close the User-Selected Results - LOI dialog box.

Setting up Lunar_Orbit_Insertion's Differential Corrector

Select the control parameters and equality constraints of the Lunar_Orbit_Insertion Target Sequence.

  1. Select Lunar_Orbit_Insertion () in the MCS.
  2. Click Properties... () on the Profiles panel toolbar.
  3. Select the Use - ImpulsiveMnvr.Pointing.Cartesian.X check box in the Control Parameters panel when the Differential Corrector dialog box opens.
  4. Select the Use - Eccentricity check box in the Equality Constraints (Results) panel.
  5. Leave the Desired Value for Eccentricity at 0 since you want to circularize the orbit.
  6. Click OK to confirm your changes and to close the Differential Corrector dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Running the entire mission control sequence

Run the entire mission control sequence using the Lunar Orbit Insertion Target Sequence.

  1. Open the Action drop-down list.
  2. Select Run active profiles.
  3. Click Run Entire Mission Control Sequence () on the MCS toolbar.

    4. When the Target Sequence converges, the Target Status window will indicate that a near-zero value for eccentricity has been achieved.

  4. Close the Target Status windows.
  5. Click Clear Graphics () on the MCS toolbar.
  6. Click OK to confirm your changes and to close the Properties Browser.

Visualizing LunarProbe entering a Moon orbit

View the lunar orbit insertion in the Moon-Centered 3D Graphics window.

  1. Look at the Moon-Centered 3D Graphics window.
  2. Set your view so that you can see LunarProbe () entering a circular orbit around the Moon.

LunarProbe orbiting the moon

Creating an MCS Summary report

You can also confirm the value of eccentricity and other targeted orbital elements by generating an MCS Summary report, which gives the segment summary report for every segment in the MCS. This includes initial state, final state, maneuver information, and spacecraft configuration information.

  1. Right-click on LunarProbe () in the Object Browser.
  2. Select Report & Graph Manager... () in the shortcut menu.
  3. Select the MCS Summary report () in the Installed Styles () folder in the Styles panel when the Report & Graph Manager opens.
  4. Click Generate....
  5. Scroll through the report to get an idea of the provided data.

Among other things, you will find that the targeted value for eccentricity (0) was achieved within tolerance for the final maneuver.

Saving your work

Close out your scenario and save your work.

  1. Close any open reports, properties and tools.
  2. Save () your work.

Summary

In this exercise, you explored a mission to the Moon using the B-plane targeting method. After setting up the scenario, running the MCS, and using a trans-lunar injection first guess, you ran the B-plane targeting tool and set up a Target Sequence to approach the Moon. This calculated the launch epoch and coast duration. Finally, after completing a lunar orbit insertion, the satellite finally entered a circular orbit around the Moon.