Mission to Sun-Earth L1
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
- Analysis Workbench
Problem statement
Engineers and operators require a quick way to design high-fidelity spacecraft trajectories for mission planning and operations. You want to design a maneuver from an initial state to the Sun-Earth libration (or Lagrange) point, L1.
Libration points in the Sun-Earth system
Solution
Use the STK/Astrogator® and Analysis Workbench capabilities to build and propagate the various sequences of launching a spacecraft to a Libration Point Orbit (LPO) around the Sun-Earth libration point. The goal of this tutorial is to model a mission to the vicinity of the L1 point.
What you will learn
Upon completion of this tutorial, you will be able to:
- Create custom geometry components for libration points
- Customize calculation objects components for use with libration points
- Configure the magnitude of the injection thrust
- Understand the effects of perturbations on the mission
- Model orbital station-keeping maneuvers around the L1 point with an Automatic Sequence
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 scenario, then build from there.
- Launch the STK application (
). - Click when the Welcome to STK dialog box opens.
- Enter the following in the STK: New Scenario Wizard:
- Click when you finish.
- Click Save (
) when the scenario loads. - Verify the scenario name and location in the Save As dialog box.
- Click .
| Option | Value |
|---|---|
| Name | Sun_Earth_L1 |
| Start | 15 Jan 2025 00:00:00.000 UTCG |
| Stop | 15 Aug 2026 00:00:00.000 UTCG |
The STK software creates a folder with the same name as your scenario for you.
Save (
) often during this scenario!
Modeling the Sun, Earth, and Moon
A
Adding the Planet object to the Insert STK Objects tool
You must first add the Planet object to the Insert STK Objects tool to be able to add them into your scenario.
- Bring the Insert STK Objects tool (
) to the front. - Click in the Insert STK Objects tool.
- Ensure the New Object page is selected when the Preferences dialog box opens.
- Select the Show check box for the Planet option in the Define Default Creation Methods panel.
- Click to confirm your selection and to close the Preferences dialog box.
Inserting Planet objects into the scenario
Start by inserting three Planet objects to model the Sun, Earth and Moon.
- Select Planet (
) in the Select An Object To Be Inserted list. - Select Insert Default (
) in the Select A Method list. - Click three times to insert three Planet objects.
Modeling the Sun
Planet objects are defined by their Central Body. The default Central Body for Planet objects is the Sun, so you only need to rename one of the Planet objects as the Sun for it to show in your scenario. The catalog of central bodies in the STK application includes the known planets, the Sun, the Moon, and other bodies of common interest.
- Right-click on Planet1 (
) in the Object Browser. - Select Rename in the shortcut menu.
- Rename Planet1 (
) Sun.
Selecting the Earth
The options on a Planet object's
- Right-click on Planet2 (
) in the Object Browser. - Select Properties (
) in the shortcut menu. - Select the Basic - Definition page when the Properties Browser opens.
- Open the Central Body drop-down list.
- Select Earth.
- Ensure the Auto-Rename check box is selected.
- Click to confirm your selection and to close the Properties Browser.
Note the Ephemeris Source is set to Default. Keep this default option to use the STK's internal definition of the Central Body to generate the ephemeris. Radius values are read-only and update automatically.
Note the name of the Planet object was automatically updated to Earth.
Selecting the Moon
Select the Moon as the central body of the third planet object.
- Open Planet3's (
) Properties (
). - Select the Basic - Definition page when the Properties Browser opens.
- Open the Central Body drop-down list.
- Select Moon.
- Ensure the Auto-Rename check box is selected.
- Click to confirm your selection and to close the Properties Browser.
Note the name of the Planet object was automatically updated to Moon.
Configuring the 2D and 3D Graphics windows
The
Setting the display options
Configure the scenario's global 2D Graphics attributes to visualize the orbit tracks of the planets in relation to the L1 point. You can choose to have individual objects inherit these attributes from the scenario or you can override these options in the object's properties. By definition, overridable attributes are global; these will also be applied to the 3D Graphics window.
- Open Sun_Earth_L1's (
) Properties (
). - Select the 2D Graphics - Global Attributes page when the Properties Browser opens.
- Clear Show Ground Tracks/Routes in the Vehicles panel.
- Set the following options in the Planets panel:
- Click to confirm your changes and to close the Properties Browser.
| Option | Value |
|---|---|
| Show Orbits | Selected |
| Show Inertial Positions | Selected |
| Show Position Labels | Selected |
| Show Subplanet Points | Cleared |
| Show Subplanet Labels | Cleared |
Subplanet points and labels show the point and label directly below the planet and appears in the 2D and 3D Graphics windows on the central body.
Configuring the 3D Graphics window properties
When viewing a scenario in 3D, a virtual camera is placed among the objects in the scenario. Use the
- Bring the 3D Graphics window to the front.
- Click Properties (
) on the 3D Graphics window's 3D Window Defaults toolbar. - Select the Advanced page when the Properties Browser opens.
- Enter 1e+12 km in the Max Visible Distance field.
- Enter 55 deg in the Field of View field.
- Click to confirm your changes and to close the Properties Browser.
The default value is 10 million (1e+07) kilometers.
The Field of View specifies how wide of an angle you can see, in degrees, in the 3D Graphics window. The larger the value, the more you can see. The maximum angle is 160 degrees. A large field of view is similar to a wide-angle lens in photography, where size differences are exaggerated due to proximity to the camera. A small field of view is similar to a telescopic lens.
3D graphics view of the Sun, Earth, and Moon
Configuring an orthographic projection in the 2D Graphics window
The
- Bring the 2D Graphics window to the front.
- Click Properties (
) on the 2D Graphics window's 2D Window Defaults toolbar. - Select the Projection page when the Properties Browser opens.
- Open the Type drop-down list in the Projection Format panel.
- Select Orthographic.
- Open the Display Coordinate Frame drop-down list.
- Select BBR.
- Use the default Sun selection for the Secondary Body.
- Enter 2e+06 km in the Display Height field.
BBR stands for Body-to-body Rotating.
With the BBR Display Coordinate Frame, you must select a secondary celestial body. This list may include asteroids and other celestial bodies in addition to the planets typically available in the STK application.
When you select the orthographic map projection, you can specify the height of the viewing plane. In all cases, the observer's position is fixed in the ECF reference frame at the Projection Center Position.
Displaying and formatting the axes for the orthographic projection
After selecting the Orthographic projection type,
- Select the Show Axes check box to show the X, Y, and Z axes for that view.
- Click .
- Open the Coordinate Frame drop-down list when the Format Axes dialog box opens.
- Use the default Sun selection for the Secondary Body.
- Open the +X Axis Color drop-down list.
- Select yellow.
- Enter 250 in the +X Axis Scale field.
- Click to confirm your changes and to close the Format Axes dialog box.
Selecting the orthographic projection's center point
Use the options in the Center panel to select the center point for the map projection on the North Pole. Enter the exact latitude and longitude degrees in the respective fields.
- Enter the following in the Center panel:
- Click to confirm your changes and to close the Properties Browser.
| Option | Value |
|---|---|
| Lat | 90 deg |
| Lon | 90 deg |
2D graphics orthographic projection
Creating custom geometry components for the L1 point
Create and display the proper geometry for the L1 point using the Analysis Workbench capability's
Selecting the central body
A
- Right-click on Sun_Earth_L1 (
) in the Object Browser. - Select Analysis Workbench... (
) in the shortcut menu. - Select the Vector Geometry tab when the Analysis Workbench opens.
- Open the Filter by drop-down list.
- Select Primary Central Bodies.
- Select Sun (
) in the object tree.
Creating an assembled system
A System component defines the location and translation motion of the origin orientation, and rotational motion of a triad of mutually orthogonal unit vectors in three-dimensional space.
- Click Create new System (
) on the Vector Geometry toolbar. - Keep the default Assembled type when the Add Geometry Component dialog box opens.
- Enter Syst_SEM_L1 in the Name field.
The SEM acronym denotes Sun, Earth-Moon.
Selecting the origin point
An assembled system is a system composed of an origin point and a set of reference axes. Add the SEM_L1 libration point as the reference point for the system. The corresponding L1 point is the interior collinear libration point associated with the system comprised of the Sun and the Earth-Moon barycenter.
- Click the Origin Point ellipsis (
). - Select Sun (
) in the object tree when the Select Reference Point dialog box opens. - Select SEM_L1 (
) in the Points for: Sun list. - Click to confirm your selection and to close the Select Reference Point dialog box.
Selecting the reference axes
Select the SEM_L1 axes for the reference axes. The SEM axes are the central-body aligned axes of the selected libration point between one primary and multiple secondary central bodies, with the X axis along the position of the libration point relative to the primary center of mass and the Z axis along the orbit normal of the libration point relative to the primary center of mass.
- Click the Reference Axes ellipsis (
). - Select Sun (
) in the object tree when the Select Reference Axes dialog box opens. - Select SEM_L1 (
) in the Axes for: Sun list. - Click to confirm your selection and to close the Select Reference Axes dialog box.
- Click to confirm your changes and to close the Add Geometry Component dialog box.
Displaying geometry components in the 3D Graphics window
Configure custom planes for display of the assembled SEM_L1 system in the 3D Graphics window.
Displaying the Syst_SEM_L1 planes
You can control the display of geometric elements related to central bodies using the
- Bring the 3D Graphics window to the front.
- Click Properties (
) on the 3D Window Defaults toolbar. - Select the Vector page when the Properties Browser opens.
- Select the Planes tab.
- Click .
- Select Sun (
) in the object tree when the Add Components dialog box opens. - Expand (
) Syst_SEM_L1 (
) in the Components for: Sun list. - Using the CTRL key, multi-select both the YZ (
) and XZ (
) planes. - Click to confirm your selections and to close the Add Components dialog box.
Configuring the Y-Z plane
Change the view and scale for the Y-Z plane.
- Double click the Color cell for Sun Syst_Sem_L1.YZ Plane.
- Open the Color drop-down list.
- Select gray.
- Clear the Draw at object check box.
- Select the Translucent plane check box to make the plane semi-transparent.
- Enter 50 in the Scale field in the Component Size panel of the Common Options panel.
Set the scale to 50, since the scenario deals with very large distances.
Configuring the X-Z plane
Change the view for the X-Z plane.
- Double click the Color cell for Sun Syst_Sem_L1.XZ Plane.
- Open the Color drop-down list.
- Select gray.
- Clear the Draw at object check box.
- Select the Translucent plane check box.
- Click to confirm your changes and to keep the Properties Browser open.
Viewing the planes in the 3D Graphics window
Review your changes in the 3D graphics window.
- Bring the 3D Graphics window to the front.
- Right-click on Earth (
) in the Object Browser. - Select Zoom To in the shortcut menu.
- Use your mouse to zoom out to view the planes and the L1 point.
L1 Y-Z and X-Z planes
You now see the two planes are displayed at the L1 point.
Creating a second assembled system
The strategy you will use to launch from an initial state to the L1 point is a ballistic transfer from the defined low Earth orbit. The first burn will happen when the probe intersects the anti-Sun line for a proper alignment. The anti-Sun line joins the Sun and Earth as it extends through and beyond the Earth from the umbra side.
Creating a new system
To better understand the geometry, create a new Assembled System component using the VGT.
- Return to the Analysis Workbench.
- Select the Vector Geometry tab.
- Select Earth (
) in the object tree. - Click Create new System (
) on the Vector Geometry toolbar. - Keep Assembled as the default type.
- Enter L1_LEO in the Name field.
- Notice that Earth Center is the default Origin Point.
- Keep the Earth Center point as the reference point for the system.
Selecting the reference axes
Select the SEM_L1 axes for the reference axes.
- Click the Reference Axes ellipsis (
). - Select Sun (
) in the object tree when the Select Reference Axes dialog box opens. - Select SEM_L1 (
) in the Axes for: Sun list. - Click to confirm your selection and to close the Select Reference Axes dialog box.
- Click to confirm your changes and to close the Add Geometry Component dialog box.
Adding the custom axes to the 3D Graphics window
Add the Earth L1_LEO system's axes for display in the 3D Graphics window.
- Return to the 3D Graphics window's Vector properties page.
- Select the Axes tab.
- Click .
- Select Earth (
) in the object tree when the Add Components dialog box opens. - Extend (
) L1_LEO (
) in the Components for: Earth list. - Select Axes (
). - Click to confirm your selection and to close the Add Components dialog box.
Adding the custom plane to the 3D Graphics window
Add the Earth L1_LEO system's XY plane to the 3D Graphics window.
- Select the Planes tab.
- Click .
- Select Earth (
) in the object tree when the Add Components dialog box opens. - Expand (
) L1_LEO (
) in the Components for: Earth list. - Select XY (
). - Click to confirm your selection and to close the Add Components dialog box.
Updating the plane's display
Change the color and transparency of the Earth L1_LEO.XY Plane.
- Double click on the Earth L1_LEO.XY Plane color cell.
- Open the Color drop-down list.
- Select yellow.
- Clear the Draw at object check box.
- Select the Translucent plane check box.
- Click to confirm your changes and to close the Properties Browser.
Viewing the custom plane and axes in the 3D Graphics window
The newly added plane is the reference and the stopping condition for the initial (coasting) spacecraft propagation. View your changes in the 3D Graphics window.
- Bring the 3D Graphics window to the front.
- Use your mouse to obtain situational awareness of the plane and axes.
custom axes and plane
Modeling the orbit injection maneuver
Use a Satellite object to model the probe and configure a Mission Control Sequence to model the maneuver to reach the L1 point.
Inserting a Satellite object
Insert a Satellite object and name it L1_Probe.
- Bring the Insert STK Objects tool (
) to the front. - Insert a Satellite (
) object using the Insert Default (
) method. - Rename Satellite1 (
) L1_Probe.
Setting L1_Probe's orbit tracks
The display of leading and trailing portions of a route, ground track, trajectory or orbit is determined on the basis of the current animation time. A lead type of All displays the track spanning the entire vehicle ephemeris.
- Open L1_Probe's (
) Properties (
). - Select the 2D Graphics - Pass page when the Properties Browser opens.
- Open the Lead Type drop-down list in the Orbit Track panel.
- Select All.
- Select the 3D Graphics - Pass page.
- Select the Inherit from 2D Graphics check box in the Leading/Trailing panel.
- Click to confirm your changes and to keep the Properties Browser open.
Selecting a trajectory frame
Set the BBR orbit system for the L1_Probe to display in the 3D Graphics window on the
- Select the 3D Graphics - Orbit System page.
- Select 3D Graphics 1 - Earth in the 3D Windows list.
- Click .
- Keep Earth as the Primary Central Body when the Select BBR Orbit System dialog box opens.
- Open the Secondary Central Body drop-down list.
- Select Sun.
- Click to confirm your selection and to close the Select BBR Orbit System dialog box.
- Clear the Show check box for the Inertial by Window in the System list.
- Click to confirm your changes and to keep the Properties Browser open.
Changing the propagator to Astrogator
The Astrogator capability contains specialized analysis for interactive orbit maneuver and spacecraft trajectory design. Astrogator acts as one of the propagators available for a Satellite object. Astrogator calculates the Satellite's ephemeris by running a Mission Control Sequence, or MCS, that you define according to the requirements of your mission.
- Select the Basic - Orbit page.
- Open the Propagator drop-down list.
- Select Astrogator.
Adding a Target Sequence
The
Add a
- Right-click on the Return (
) segment in the MCS. - Select Insert Before... in the shortcut menu.
- Select Target Sequence (
) when the Segment Selection dialog box opens. - Click to confirm your selection and to close the Segment Selection dialog box.
- Right-click on Target Sequence (
) in the MCS. - Select Rename in the shortcut menu.
- Rename Target Sequence (
) Target Plane Crossing. - Click and drag the Initial State (
) segment and nest it in the Target Plane Crossing (
) Target Sequence. - Click and drag the Propagate (
) segment and nest it in the Target Plane Crossing (
) Target Sequence below the Initial State (
) segment. - Click to confirm your changes and to keep the Properties Browser open.
Defining the Initial State segment
Use the
- Select Initial State (
) in the MCS. - Select the Elements tab.
- Make sure the Orbit Epoch matches your scenario start time.
- Open the Coordinate Type drop-down list.
- Select Keplerian.
- Click on the Right Asc. of Asc. Node target icon (
). - Keep the rest of the default settings.
- Click to confirm your changes and to keep the Properties Browser open.
orbital parameters
Your Target Sequence uses a
). By selecting the Right Ascension of the Ascending Node (RAAN) as an independent variable, you are telling Astrogator to determine the value for you later on when you run the MCS.
Defining the Propagate segment
Use the
- Right-click on Propagate (
) in the MCS. - Select Rename in the shortcut menu.
- Rename Propagate (
) Coast.
Adding a new stopping condition
Use an X-Y Plane Cross
- Click New... (
) on the toolbar in the Stopping Conditions panel. - Select X-Y Plane Cross (
) when the New Stopping Condition dialog box opens. - Click to confirm your selection and to close the New Stopping Condition dialog box.
- Select the Duration stopping condition.
- Click Delete (
) on the toolbar in the Stopping Conditions panel.
Setting the X-Y Plane Cross stopping condition's parameters
Set the stopping condition to take the custom L1_LEO coordinate system that you created earlier into account and set its Criterion to Cross Decreasing. A criterion is an extra condition to meet for the stopping condition to be satisfied; Cross Decreasing means the stopping condition is satisfied when the parameter reaches a value equal to the trip value while decreasing.
- Click the Coord. System ellipsis (
). - Select Earth (
) in the object tree when the Select Reference dialog box opens. - Select L1_LEO (
) in the System for: Earth list. - Click to confirm your selections and to close the Select Reference dialog box.
- Open the Criterion drop-down list.
- Select Cross Decreasing.
- Click to confirm your changes and to keep the Properties Browser open.
Adding a result
Recall that you selected the RAAN as an independent variable when setting up the initial state. Select the right ascension
- Click .
- Expand (
) the Spherical Elems (
) folder in the Available Components list when the User-Selected Results - Coast dialog box opens. - Select Right Asc (
). - Click Insert Component (
).
Selecting the calculation component's coordinate system
You can update the coordinate system used with the built- in Calculation Object component so that it takes the correct coordinate system into account for the calculations.
- Double-click on the CoordSystem row in the Component Details list.
- Select Earth (
) in the object tree when the Select Reference dialog box opens. - Select L1_LEO (
) in the Systems for: Earth list. - Click to confirm your selection and to close the Select Reference dialog box.
- Click to confirm your selections and to close the User-Selected Results - Coast dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Defining the Differential Corrector
Set up the Differential Corrector search profile for your target sequence.
- Select Target_Plane_Crossing (
) in the MCS. - Slowly click twice in the Differential Corrector cell in the Profiles panel and wait until the text is highlighted.
- Enter Anti-Sun Line in the Name cell.
- Select the Tab key.
If you double click quickly, it will open the profile's properties.
Setting the Differential Corrector properties
In order to match the anti-Sun line when crossing the L1_LEO X-Y plane, you need to null the RAAN in the Earth L1_LEO reference system.
- Click Properties... (
) on the toolbar in the Profiles panel. - Select the Use check box for InitialState.Keplerian.RAAN in the Control Parameters panel when the Anti-Sun Line dialog box opens.
- Select the Use check box for Right_Asc in the Equality Constraints (Results) panel.
- Click to confirm your selections and to close the Anti_Sun Line dialog box.
Earlier, when you selected the Initial State target, you set the RAAN as the control parameter. You want Astrogator to determine this value.
The is the result you selected for the Propagate segment.
Running the Mission Control Sequence
To calculate the trajectory of the spacecraft you must run the Mission Control Sequence. Astrogator will proceed through the MCS and run each segment, generating an ephemeris for the spacecraft. As it runs the MCS, Astrogator carries the trajectory and state of the spacecraft determined so far from one segment to the next.
- Open the Action drop-down list.
- Select Run active profiles.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Look at the Targeting Status window.
- Close (
) the Target Status window. - Click in the Profiles and Corrections panel.
- Click Clear Graphics (
) on the MCS toolbar. - Click to confirm your changes and to keep the Properties Browser open.
The Run Active profiles option runs the Mission Control Sequence, allowing the active profiles to operate.
targeting status window
It should say *CONVERGED* and also provide data on the run.
This applies the values of the search profile's controls and the changes specified by the segment configuration profiles to the segments within the target sequence.
Reviewing the changes to the Initial State segment
You previously had selected the RAAN as an independent variable. Review the changes to that value in the Initial State segment.
- Select Initial State (
) in the MCS. - Select the Elements tab.
- Look at the value of the Right Asc. of Asc. Node.
The default value was 0. After running the Mission Control Sequence and applying the changes, you should see the new RAAN value.
Viewing the orbit in the 3D Graphics window
You can view the orbit as it stops at the anti-sun line in the 3D Graphics window.
- Bring the 3D Graphics window to the front.
- Click Home View (
) on the 3D Graphics toolbar. - Use your mouse to obtain situational awareness of L1_Probe's (
) orbit and where it stops at the anti-sun line.
orbit crossing anti-sun line
The probe now crosses the X-Y L1_LEO plane exactly in the anti-Sun line direction. This gives you the opportunity to burn for the transfer orbit with the correct geometry.
Defining the Maneuver segment
Use an
- Return to L1_Probe's (
) Properties (
). - Select Coast (
) in the MCS. - Click Insert Segment After (
) on the MCS toolbar. - Select Maneuver (
) when the Segment Selection dialog box opens. - Click to confirm your selection and to close the Segment Selection dialog box.
- Click Segment Properties (
) on the MCS toolbar. - Enter L1 LEO Injection Thrust in the Name field when the Edit Segment dialog box opens.
- Open the Color drop-down list.
- Select white.
- Click to confirm your changes and to close the Edit Segment dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
An impulsive maneuver type can't be seen in the 2D and 3D Graphics windows. You can change the color to white in the MCS to make it stand out as an impulsive maneuver type.
Defining a second Propagate segment
You need to add another Propagate segment and set the stopping condition to model the probe's state after the burn.
- Select L1 LEO Injection Thrust (
) in the MCS. - Click Insert Segment After (
) on the MCS toolbar. - Select Propagate (
) when the Segment Selection dialog box opens. - Click to confirm your selection and to close the Segment Selection dialog box.
- Click Segment Properties (
) on the MCS toolbar. - Enter Z-X Plane Crossing in the Name field when the Edit Segment dialog box opens.
- Open the Color drop-down list.
- Select a color that is different from Coast (
). - Click to confirm your changes and to close the Edit Segment dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Unlike Impulsive Maneuver segments, Propagate segments can be seen in the 2D and 3D Graphics windows.
Selecting a new stopping condition
Apply a Z-X Plane Cross stopping condition, which stops the propagation when it crosses the X-Z plane that is located along the Sun-Earth direction.
- Click New... (
) on the toolbar in the Stopping Conditions panel. - Select Z-X Plane Cross (
) when the New Stopping Condition dialog box opens. - Click to confirm your selection and to close the New Stopping Condition dialog box.
- Select the Duration stopping condition.
- Click Delete (
) on the toolbar in the Stopping Conditions panel. - Click to confirm your changes and to keep the Properties Browser open.
Setting the Propagate segment’s propagator
The L1 Probe is operating in cislunar space, with motion governed by both the gravity of the Earth and of the Moon, each to relatively comparable effect. Change the Z-X Plane Crossing Propagate segment's
- Click the Propagator ellipsis (
). - Select Cislunar (
) when the Select Component dialog box opens. - Click to confirm your selection and to close the Select Component dialog box.
Setting the Propagate segment's advanced properties
Use the
- Click .
- Enter 864000 sec in the Minimum Propagation Time field when the Propagator Advanced dialog box opens.
- Click to confirm your change and to close the Propagator Advanced dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Updating the Coordinate System
Use the custom SEM_L1 coordinate system for the Propagate segment so that its stopping condition will take it into account.
- Click the Coord. System ellipsis (
). - Select Sun (
) in the object tree in the Select Reference dialog box. - Select Syst_SEM_L1 (
) in the Systems for: Sun list. - Click to confirm your selection and to close the Select Reference dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Guessing at a thrust vector velocity
You can apply a guess for the magnitude of the thrust needed to correctly put the probe in orbit around the L1 point. First, you'll try a value manually. Then, you'll use the Differential Corrector to find an exact value.
The following results were obtained using version 13.1 of the STK application and the Earth Default High Fidelity v13 Propagator for the Coast and L1 LEO Injection segments. The thrust needed to achieve these results may be different when using older versions of the STK application. You can use the steps below to iterate to find an approximate velocity that works, decreasing or increasing the velocity based on whether the probe overshoots the L1 point or falls back to Earth, respectively.
- Select L1 LEO Injection Thrust (
) in the MCS. - Select the Attitude tab.
- Open the Attitude Control drop-down list.
- Select Thrust Vector.
- Enter 3115.00 m/sec in the X (Velocity) field.
- Click to confirm your changes and to keep the Properties Browser open.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Close (
) the Target Status window. - Bring the 2D Graphics window to the front.
2D Graphics window first guess
This magnitude is not sufficient to reach L1_LEO. The L1_Probe is attracted back toward Earth.
Increasing the probe's velocity
Make another guess, this time, increasing the velocity to 3,120.00 m/sec.
- Return to L1_Probe's (
) Properties (
). - Enter 3125.00 m/sec in the X (Velocity) field.
- Click to confirm your change and to keep the Properties Browser open.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Bring the 2D Graphics window to the front.
2D Graphics window Second guess
This time you overshot and the L1_Probe moves away from the L1 point.
Making a third guess
You set the X (Velocity) to 3,115 m/sec first and didn't reach L1_LEO. Then you set the X (Velocity) to 3,125 m/sec and missed the L1 point completely. Try another guess. Try an X (Velocity) that gets you close to the L1 Point.
- Return to L1_Probe's (
) Properties (
). - Set the X (Velocity) to 3120 m/sec.
- Click to confirm your change and to keep the Properties Browser open.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Bring the 2D Graphics window to the front.
2D Graphics window third guess
This is a good guess for the Delta-V. Considering the target is the L1 region, you see how the final condition is very sensitive to changes in Delta-V.
Selecting a result
You can set up a second Differential Corrector to get a better burn magnitude estimate. For this purpose, you can use the built-in Cartesian SEM L1 X velocity (Vx) Calculation Object component for the constraint. You want to cross the X-Z plane with a SEM L1 Vx = 0 km/sec; that value should guarantee that you have another X-Z plane crossing.
- Return to L1_Probe's (
) Properties (
). - Select Z-X Plane Crossing (
) in the MCS. - Click .
- Expand (
) the Cartesian Elems (
) folder in the Available Components list when the User-Selected Results - Z-X Plane Crossing dialog box opens. - Select Vx (
). - Click Insert Component (
).
Selecting the calculation component's coordinate system
Update the coordinate system used with the Vx Calculation component.
- Double-click on the CoordSystem row in the Component Details list.
- Select Sun (
) in the object tree when the Select Reference dialog box opens. - Select Syst_SEM_L1 (
) in the Systems for: Sun list. - Click to confirm your selection and to close the Select Reference dialog box.
- Click to confirm your selections and to close the User-Selected Results - Z-X Plane Crossing dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Selecting L1 LEO Injection's X (Velocity) as a control parameter
With your result in place, select X (Velocity) as an additional independent variable.
- Select L1 LEO Injection Thrust (
) in the MCS. - Select the Attitude tab.
- Select the X (Velocity) target (
) to make it a control parameter.
Adding a new Differential Corrector
Add a second Differential Corrector to the Target Plane Crossing Target Sequence.
- Select Target Plane Crossing (
) in the MCS. - Click New... (
) on the toolbar in the Profiles panel. - Select Differential Corrector (
) when the New... dialog box opens. - Click to confirm your selection and to close the New... dialog box.
- Slowly click twice on the Differential Corrector cell in the Profiles panel and wait until the text is highlighted.
- Enter First Plane Crossing in the Name cell.
- Select the Tab key.
Updating First Plane Crossing's properties
Select the X (Velocity) control parameter and the Vx component as the result.
- Click Properties... (
) on the toolbar in the Profiles panel. - Select the Use check box for ImpulsiveMnvr.Pointing.Cartesian.X in the Control Parameters panel when the First Plane Crossing dialog box opens.
- Select the Use check box for Vx in the Equality Constraints (Results) panel.
- Click to confirm your selections and to close the First Plane Crossing dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Running the Mission Control Sequence
With your differential correctors set, re-run your Mission Control Sequence.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Close (
) the Target Status windows. - Click Clear Graphics (
) on the MCS toolbar. - Click to confirm your changes and to keep the Properties Browser open.
- Click the in the Profiles and Corrections panel.
- Select L1 LEO Injection (
) in the MCS. - Notice that the X (Velocity) value has changed since your last guess.
The converged Delta-V value should be very close to the guess you made.
Creating a Libration Point Orbit (LPO)
The SEM L1 region has a large degree of instability. The instability might mean the spacecraft requires only very small maneuvers to maintain its desired path.
Duplicating the Propagate segment
Copy the Z-X Plane Crossing Propagate segment to view the orbital instability.
- Select Z-X Plane Crossing (
) in the MCS. - Click Copy (
) on the MCS toolbar. - Right-click on the bottommost Return (
) segment in the MCS. - Select Paste Before in the shortcut menu to insert the duplicate Propagate segment below the Target Sequence.
- Click Segment Properties (
) on the MCS toolbar. - Enter LPO in the Name field when the Edit Segment dialog box opens.
- Open the Color drop-down list.
- Select a color that is different for the other Propagate segments.
- Click to confirm your changes and to close the Edit Segment dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Running the Mission Control Sequence
Re-run the entire Mission Control Sequence with your additional Propagate segment.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Close (
) the Target Status windows. - Click Clear Graphics (
) on the MCS toolbar. - Click to confirm your changes and to keep the Properties Browser open.
- Bring the 2D Graphics window to the front.
first libration point maneuver
Without a small injection maneuver, the probe returns to the Earth. It follows a somewhat symmetric path with respect to the Sun-Earth line.
Perturbing the trajectory into orbit
You would like to ensure the probe begins to orbit about the L1 point. To do this, modify the MCS to favorably perturb the trajectory toward orbital motion.
- Return to L1_Probe's (
) Properties (
). - Select Target Plane Crossing (
) in the MCS. - Select First Plane Crossing in the Profiles panel.
- Click Properties... (
) on the toolbar in the Profiles panel. - Double click on the Vx Desired Value cell in the Equality Constraints (Results) list when the First Plane Crossing dialog box opens.
- Enter -0.01 km/sec.
- Click to confirm your change and to close the First Plane Crossing dialog box.
You want this value to be negative.
Running the Mission Control Sequence
Re-run your Mission Control Sequence to view the effects of the perturbation.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Close (
) the Target Status windows. - Click Clear Graphics (
) on the MCS toolbar. - Click to confirm your changes and to keep the Properties Browser open.
- Bring the 2D Graphics window to the front.
Second libration point maneuver
You should now see a sufficient amount of drift for the trajectory to start orbiting around the L1 point.
Adding a new stopping condition
Add a new stopping condition to the LPO Propagate segment.
- Return to L1_Probe's (
) Properties (
). - Select LPO (
) in the MCS. - Click New... (
) on the toolbar in the Stopping Conditions panel. - Select Duration (
) when the New Stopping Condition dialog box opens. - Click to confirm your selection and to close the New Stopping Condition dialog box.
Setting the propagation duration to one year
To further check what happens after a significant amount of time, you can add a stopping condition set to a year.
- Enter 1 yr in the Trip field.
- Clear the On check box for the Z-X Plane Cross stopping condition.
Running the Mission Control Sequence
Re-run the entire Mission Control Sequence to view the results of the longer propagation duration.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Close (
) the Target Status windows. - Click Clear Graphics (
) on the MCS toolbar. - Click to confirm your changes and to keep the Properties Browser open.
- Bring the 2D Graphics window to the front.
Third libration point maneuver
Modeling orbital station-keeping at the L1 point
Add an orbital station-keeping strategy to maintain the libration point orbit over time using an Automatic Sequence.
Creating a new Automatic Sequence
The Automatic Sequence Browser contains a list of all Automatic Sequences defined for an Astrogator satellite. Each Automatic Sequence appears in the list with an identifying Name and User Comment field.
- Return to L1_Probe's (
) Properties (
). - Click Automatic Sequence Browser (
) on the MCS toolbar. - Click when the Automatic Sequence Browser dialog box opens.
- Enter Station Keeping in the Name field when the Field Editor dialog box opens.
- Click to confirm your change and to close the Field Editor dialog box.
Editing the Station Keeping Automatic Sequence
Add a station-keeping strategy using a Target Sequence to maintain the libration point orbit over time.
- Select Station Keeping in the Automatic Sequence Browser dialog box.
- Click .
- Click Insert Segment After (
) on the MCS toolbar when the Automatic Sequence Properties dialog box opens. - Select Target Sequence (
) in the Segment Selection dialog box. - Click to confirm your selection and to close the Segment Selection dialog box.
- Right-click on Target Sequence (
) in the MCS. - Select Rename in the shortcut menu.
- Rename Target Sequence (
) Maintain LPO.
Inserting a Maneuver segment
Add a station-keeping Maneuver segment in the Maintain LPO Target Sequence.
- Click Insert Segment After (
) on the MCS toolbar. - Select Maneuver (
) in the Segment selection dialog box. - Click to confirm your selection and to close the Segment selection dialog box.
- Click and drag to nest Maneuver (
) in the Maintain LPO (
) Target Sequence. - Click Segment Properties (
) on the MCS toolbar. - Enter SK Burn in the Name field of the Edit Segment dialog box.
- Open the Color drop-down list.
- Select white.
- Click to confirm your changes and to close the Edit Segment dialog box.
Updating SK Burn's propagator
Use the Cislunar propagator for the station-keeping maneuver.
- Click the Finite Propagator and Force Model for Optimization ellipsis (
). - Select Cislunar (
) in the Select Component dialog box. - Click to confirm your selection and to close the Select Component dialog box.
Setting the attitude
Set the X (Velocity) as a control parameter and use the custom Sun Syst_SEM_L1 axes as the attitude control.
- Select the Attitude tab.
- Open the Attitude Control drop-down list.
- Select Thrust Vector.
- Select the X (Velocity) target (
) to set it as the control parameter. - Click the Thrust Axes ellipsis (
). - Select Sun (
) in the object tree when the Select Reference dialog box opens. - Expand (
) Syst_Sem_L1 (
) in the Axes for: Sun list. - Select Axes (
). - Click to confirm your selection and to close the Select Reference dialog box.
Inserting a Propagate segment
Insert a Propagate segment after SK Burn.
- Click Insert After (
) on the MCS toolbar. - Select Propagate (
) in the Segment Selection dialog box. - Click to confirm your selection and to close the Segment Selection dialog box.
- Click Segment Properties (
) on the MCS toolbar. - Enter Prop to Plane Cross in the Name field when the Edit Segment dialog box opens.
- Open the Color drop-down list.
- Select a color that's different than all the other Propagate (
) segments in the scenario. - Click to confirm your changes and to close the Edit Segment dialog box.
Updating Prop to Plane Cross' propagator
Use the Cislunar propagator to model the station-keeping orbit.
- Click the Propagator ellipsis (
). - Select Cislunar (
) in the Select Component dialog box. - Click to confirm your selection and to close the Select Component dialog box.
Setting a stopping condition
Insert a Z-X Plane Cross stopping condition for the Prop to Plane Cross propagate segment.
- Click New... (
) on the toolbar in the Stopping Conditions panel. - Select Z-X Plane Cross (
) when the New Stopping Condition dialog box opens. - Click to confirm your selection and to close the New Stopping Condition dialog box.
- Select the Duration stopping condition.
- Click Delete (
) on the toolbar in the Stopping Conditions panel.
Setting the minimum propagation time and tolerance
You want to propagate the orbit for a total of 10 days before Astrogator will begin checking if the Z-X Plane Cross stopping condition has been satisfied.
- Click .
- Enter 864000 sec in the Minimum Propagation Time field when the Propagator Advanced dialog box opens.
- Click to confirm your change and to close the Propagator Advanced dialog box.
- Enter 1e-06 km in the Tolerance field.
Updating Prop to Plane Cross' coordinate system
Use the SEM L1 coordinate system for the Propagate segment's stopping condition.
- Click the Coord. System ellipsis (
). - Select Sun (
) in the object tree of the Select Reference dialog box. - Select Syst_SEM_L1 (
) in the Systems for: Sun list. - Click to confirm your selection and to close the Select Reference dialog box.
Selecting as the result
You want the X component of the velocity to be nearly zero at the Rotating Libration Point (RLP) X-Z plane crossing. Use the Vx component as the result for the Propagate segment.
- Click .
- Expand (
) the Cartesian Elems (
) folder in the Available Components list when the User-Selected Results - Prop to Plane Cross dialog box opens. - Select Vx (
). - Click Insert Component (
).
Selecting the calculation component's coordinate system
Update the coordinate system used with the Vx Calculation component.
- Double-click on the CoordSystem row in the Component Details list.
- Select Sun (
) in the object tree when the Select Reference dialog box opens. - Select Syst_SEM_L1 (
) in the Systems for: Sun list. - Click to confirm your selection and to close the Select Reference dialog box.
- Click to confirm your selections and to close the User-Selected Results - Prop to Plane Cross dialog box.
Information about RLP coordinate system can be found in the Astrogator
Adding a Return segment
Use a Return segment to control the execution of the Mission Control Sequence by returning control to its parent segment. If the MCS encounters an active Return segment, it will not run any segments after it in the MCS (or subsequence, if it belongs to one).
- Select SK Burn (
) in the MCS. - Click Insert Segment After (
) on the MCS toolbar. - Select return (
) when the Segment Selection dialog box opens. - Click to confirm your selection and to close the Segment Selection dialog box.
- Select the Enable (except Profiles bypass) option.
The Return segment is active except when run from a Target Sequence profile (for example, a Differential Corrector), which will ignore it. When it converges, the SK Burn segment is executed once again (with the right Delta-V value) and the control is passed back to the main sequence.
Setting the Differential Corrector's control parameter
Update the control parameter's perturbation and maximum step (Max Step). Perturbation is the value that you want the profile to use in calculating numerical derivatives. Max Step is the maximum increment to the value of the parameter in a step.
- Select Maintain LPO (
) in the MCS. - Click Properties... (
) on the toolbar in the Profiles panel. - Select the Use check box for ImpulsiveMnvr.Pointing.Cartesian.X in the Control Parameters panel when the Differential Corrector dialog box opens.
- Set the following options:
| Option | Value |
|---|---|
| Perturbation | 0.05 m/sec |
| Max Step | 10 m/sec |
Setting the Equality Constraints (Results) parameters
Update Vx's tolerance. The profile will stop when it achieves a value within this range of the Desired Value.
- Select the Use check box for Vx in the Equality Constraints (Results) panel.
- Enter 0.05 m/sec in the Tolerance field.
- Click to confirm your changes and to close the Differential Corrector dialog box.
Setting the action to run active profiles
Set the Mission Control sequence to allow the active profiles to operate.
- Open the Action drop-down list.
- Select Run active profiles.
- Click to confirm your changes and to close the Automatic Sequence Properties dialog box.
- Click to close the Automatic Sequence Browser dialog box.
- Click to confirm your changes and to keep the Properties Browser open.
Using the automatic sequence
Apply the automatic sequence to the Z-X Plane Cross stopping condition. Astrogator will run it and, when finished, the LPO Propagate segment will continue to run until the automatic sequence is triggered once again, and so on until it reaches the end of its Duration stopping condition.
- Select LPO (
) in the MCS. - Select the On check box for Z-X Plane Cross in the Stopping Conditions panel.
- Click the Sequence ellipsis (
). - Select Station Keeping (
) when the Select Component dialog box opens. - Click to confirm your selection and to close the Select Component dialog box.
Running the Mission Control Sequence
Rerun the entire Mission Control Sequence with the station-keeping Automatic Sequence enabled.
- Click Run Entire Mission Control Sequence (
) on the MCS toolbar. - Close (
) the Target Status windows. - Click Clear Graphics (
) on the MCS toolbar. - Click to confirm your changes and to close the Properties Browser.
Viewing the changes in the 3D Graphics window
View the results of implementing the station-keeping Automatic Sequence.
- Bring the 3D Graphics window to the front.
- Use your mouse to set the view so that you can see the L1_Probe's (
) entire orbit.
orbital station-keeping at L1
If you're going to perform further analysis, remember to reset all target sequences including the Automatic Sequence. A useful way to reset all active target sequence priorities at once is by clicking MCS Options (
) on the MCS toolbar, selecting the Targeting tab in the MCS Options dialog box and clicking in the Active Profiles panel.
Creating a Maneuver Summary report
Now that you have modeled the probe's orbit and visualized its behavior, examine the results with a Maneuver Summary report that provides a summary of L1_Probe's maneuvers. The probe is propagated ahead in time by the LPO segment until it reaches the Duration condition (365 days) that stops the execution. In the meantime, each time there is a plane crossing, the Station Keeping Automatic Sequence is fired, bringing back the needed Delta-V for orbit maintenance.
- Right-click on L1_Probe (
) in the Object Browser. - Select Report & Graph Manager... (
) in the shortcut menu. - Select the Maneuver Summary (
) report in the Installed Styles (
) folder in the Styles panel. - Click .
- Scroll through the Maneuver Summary report.
You can see that the first maneuver was the LEO Injection thrust. This burn had the largest estimated finite burn duration, Delta-V, and fuel used. This is because the probe is lifting away from Earth, which requires the most energy. Afterward, you can see the reported number of times the Station Keeping Automatic sequence was fired. By scrolling through the report you can review the estimated finite burn duration, Delta-V, and fuel used, which are all much smaller than the initial burn. The L1 point is unstable, and while you don't need as much fuel or Delta-V to maintain the probe's orbit for the specified mission time, it is still an important component to know when modeling a mission.
- Close the report and the Report & Graph Manager when finished.
Saving your work
Clean up your workspace and save your work.
- Close any open reports, properties and tools.
- Save (
) your work.
Summary
This scenario showed you how to configure your 2D and 3D Graphics windows for space operations and situational awareness. You learned how to create multiple assembled systems using the Vector Geometry tool. Using the custom components you created, you made best guesses to inject a Satellite object modeling a probe in a libration point orbit around the Sun-Earth libration point, L1. Using a control parameter, your Satellite object came very close to establishing an orbit. Finally, you created an Automatic Sequence, which enabled you to use station-keeping maneuvers to keep the probe in orbit around the L1 point.