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 STK Capabilities:

  • 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. In this scenario, they will design a launch from an initial state to the Sun-Earth Lagrange 1 point.

Solution

Use STK’S Astrogator and Analysis Workbench capabilities to build and propagate the various sequences of launching a satellite to Sun-Earth L1. The goal of this tutorial is to model a mission to the vicinity of the Sun-Earth L1 point.

What You Will Learn

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

  • Create custom geometry and calculations for Lagrange points
  • Configure the magnitude of the injection thrust
  • Understand the effects of perturbations on the mission
  • Model station keeping at Sun-Earth L1

Video Guidance

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

Create a New Scenario

  1. Create a new scenario and call it Sun_Earth_L1.
  2. Set the analysis time to the following:
    3. Option Value
    Analysis Start Time 15 Jan 2018 10:00:00.000 UTCG
    Analysis End Time 15 Aug 2019 10:00:00.000 UTCG
  3. Create three Planet () objects, Sun, Earth, Moon.

This scenario interval covers the entire ballistic trip.

Configure the Graphics Windows

  1. Open Sun_Earth_L1's () properties ().
  2. Select the 2D Graphics - Global Attributes page.
  3. Set the following options:
    4. Option Value
    Show Orbits On
    Show Inertial Positions On
    Show Position Labels On
    Show Subplanet Points Off
    Show Subplanet Labels Off
  4. Click OK .

Configure 3D Graphics Window

Now that you have the 2D Graphics window setup for interplanetary travel, let's set up the 3D Graphics window.

  1. Open the 3D Graphics window properties ().
  2. Select the Advanced tab.
  3. Set the following options:
    4. Option Value
    Max Visible Distance 1e+012 km
    Field Of View 55 deg
  4. Click OK .

Configure 2D Graphics Window

  1. Open the 2D Graphics window properties ().
  2. Select the Projection page.
  3. Set the following options:
    4. Option Value
    Type Orthographic
    Display Coordinate Frame BBR
    Display Height 2e+006km
    Secondary Body Sun
    Show Axes On
  4. Click the Format... button.
  5. Set the following options:
    6. Option Value
    Coordinate Frame BBR
    +X Axis 250.00
    Color Yellow
    Secondary Body Sun
  6. Set the following options:
    7. Option Value
    Lat 90
    Lon 90
  7. Click OK .

Create the Geometry for the L1 Point

You'd like to create and display the proper geometry for the L1 point.

  1. Open the Analysis Workbench ().
  2. Select the Vector Geometry tab.
  3. Filter by Primary Central Bodies.
  4. Select Sun.

Create a Coordinate System

  1. Click the Create a new System () button.
  2. Set the following options:
    3. Option Value
    Type Assembled
    Name Syst_SEM_L1
    Origin Point Sun -> SEM_L1
    Reference Axes Sun -> SEM_L1

    Note the SEM acronym denotes Sun, Earth-Moon. The corresponding L1 point is the interior collinear libration point associated with the system comprised of the Sun and the Earth-Moon barycenter.

  3. Click OK .

Add a Plane in 3D

  1. Open the 3D Graphics Window properties ().
  2. Select the Vector page.
  3. Select the Planes tab.
  4. Click Add... .
  5. Select the Sun central body.
  6. Expand the Syst_SEM_L1 directory.
  7. Select XZ.
  8. Click OK .
  9. Follow the same steps to add the YZ plane.

Configure the Plane

  1. Set the color of the XZ plane to Gray.
  2. Clear the Draw at object check box.
  3. Select the Translucent plane check box.
  4. Repeat the same steps for the YZ Plane.
  5. Set the scale to 50 since the scenario deals with very large distances.

View in 3D

  1. Click Apply to apply the XZ and YZ planes.
  2. Bring the 3D Graphics window to the front.

You now see the two planes applied at the L1 point.

View the Geometry of the Defined LEO Orbit

The strategy you use is a ballistic transfer from the defined LEO Orbit. The first burn happens 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. To better understand the geometry, create a new Assembled System in the Analysis Workbench.

  1. Open the Analysis Workbench ().
  2. Select the Vector Geometry tab.
  3. Select Earth as the Primary Central Bodies option.
  4. Create a new System ().
  5. Set the following options:
    6. Option Value
    Type Assembled
    Name L1_LEO
    Origin Point Earth -> Center
    Reference Axes Sun -> SEM_L1
  6. Click OK .

Add an Axes in 3D

  1. Open the 3D Graphics Window properties ().
  2. Select the Vector page.
  3. Select the Axes tab.
  4. Click the Add... button.
  5. Select the Earth central body.
  6. Extend () the L1_LEO system directory.
  7. Select Axes.
  8. Click OK .

Add the Plane in 3D

  1. Bring the 3D Graphics Window properties () to the front.
  2. Select the Plane page.
  3. Click the Add... button.
  4. Select the Earth central body.
  5. Expand () the L1_LEO system directory.
  6. Select XY plane.
  7. Click OK .

Display the Plane in 3D

  1. Set the color of the XY plane to yellow.
  2. Clear the Draw at object option.
  3. Select the Translucent plane option.

The newly added plane is the reference and the stopping condition for the initial (coasting) spacecraft propagation.

Add a New Satellite

  1. Create a new satellite () using the Define Properties () method.
  2. Rename the satellite L1_Probe.
  3. Open the 2D Graphics - Pass page.
  4. Set the Orbit Track - Lead Type to All.
  5. Open the 3D Graphics - Pass page.
  6. Set the Orbit Track - Lead Type to All.

Create a New BBR Frame

  1. Select the Orbit System page.
  2. Select 3D Graphics 1 - Earth in the 3D Windows field.
  3. Click Add BBR System... .
  4. Set the Primary Central Body to Earth.
  5. Set the Secondary Central Body to Sun.
  6. Disable the Inertial by Window option.

Target Plane Crossing

You want to get to the L1 vicinity first. Once you reach L1, you can see how unstable a trajectory around L1 becomes without station keeping.

  1. Select the Basic - Orbit page.
  2. Change the Propagator to Astrogator.
  3. Remove the default segments from the MCS.
  4. Add a new Target Sequence () named Target Plane Crossing.

Define the Initial State

  1. Add an Initial State () segment within Target_Plane_Crossing.
  2. Set the following parameters for the Initial State.
    3. Option Value
    Coordinate Type Keplerian
    Orbit Epoch 15 Jan 2018 10:00:00.000 UTCG
    Semimajor Axis 6678.14
    Eccentricity 0
    Inclination 28.5
    RAAN 0
    Argument of Perigee 0
    True Anomaly 0
  3. Set the RAAN () to be an independent variable.

Add a Propagate Segment

  1. Add a Propagate segment named Coast.
  2. Add a new X-Y Plane Cross stopping condition.
  3. Remove the Duration stopping condition.
  4. Set the Coord. System to Earth > L1_LEO.
  5. Set the Criterion field to Cross Decreasing.

Add a Right Ascension Result

  1. Click Results... .
  2. Move () the Right Asc result from the Spherical Elems directory.
  3. Set the CoordSystem to Earth > L1_LEO.
  4. Click OK .

In order to match the anti-Sun line when crossing the L1_LEO XY plane, you need to null the RAAN in Earth L1_LEO reference system.

Define the Anti-Sun Line

  1. Select the Target Plane Crossing () target sequence segment.
  2. Rename the Differential Corrector to Anti-Sun Line.
  3. Open Anti-Sun Line's properties ().
  4. Select RAAN as a Control Parameter.
  5. Select Right_Asc as a Result.
  6. Click OK .

Run the MCS

  1. Set the Action field to Run active profiles.
  2. Run () the MCS.
  3. Ensure the MCS has converged.

  4. Clear () the Graphics.

Run the MCS to See the Final Trajectory

  1. Click Apply Changes in the Profiles and Corrections section.
  2. Verify the Action field is set to Run active profiles.
  3. Run () the MCS.

The probe now crosses the XY 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.

Configure the Burn to L1

You need to guess the magnitude of the thrust to correctly put the probe in orbit around L1. You'll try some values manually and then use the Differential Corrector to find the exact value.

  1. Insert a new Maneuver () segment in Target Plane Crossing after the Coast propagate segment.
  2. Rename the Maneuver segment L1 LEO Injection Thrust.
  3. Set the Attitude Control field to Thrust Vector.

Add a Propagate Segment

  1. Create a new Propagate () segment.
  2. Rename the segment Z-X Plane Crossing.
  3. Add a Z-X Plane Cross stopping condition.
  4. Delete the Default stopping condition.
  5. Set the Coord. System field to Sun > Syst_SEM_L1.
  6. Click Advanced... .
  7. Set the Minimum Propagation Time to 864000 sec.
  8. Click OK .
  9. Click ... in the Propagator field and set it to CisLunar.

The propagation is stopped when the probe reaches the XZ plane that is located along the Sun-Earth direction.

Set the L1 LEO Injection Thrust

The magnitude of the thrust is unknown, but you can make guesses about it. Try to set the X(Velocity) to 3.16 km/sec and see how that works.

  1. Select the L1 LEO Injection Thrust () in the MCS.
  2. Set the X(Velocity) to 3160.00 m/sec.
  3. Set X(Velocity) () as a control parameter.
  4. Run () the MCS.

This magnitude is not sufficient to reach L1_LEO. Also the probe is attracted back toward Earth.

Set a Burn Magnitude

  1. Select the L1 LEO Injection Thrust () segment to begin making changes.
  2. Set the X(Velocity) to 3170.00 m/sec (ten (10) m/sec more than the previous case).
  3. Run () the MCS.

This time you overshoot and the probe moves away from the L1 point.

Try a Middle Ground

You set the X(Velocity) to 3160 m/sec first and didn't reach L1_LEO. Then you set the X(Velocity) to 3170 m/sec and missed the L1 point completely. Let's try something in the middle, like 3165 m/sec.

  1. Bring the L1 LEO Injection Thrust () segment to the front.
  2. Set the X(Velocity) to 3165 m/sec.
  3. Run () the MCS.

This is a good first guess for the Delta-V. Considering the target is the L1 region, you see how the final condition is very sensitive to the Delta-V changes. You can set up a second Differential Corrector to get a better burn magnitude estimate. For this purpose, you can use the Cartesian SEM L1 Vx as the constraint. You want to cross the ZX plane with a SEM L1 Vx=0 km/sec. That value should guarantee that you have another ZX plane crossing.

Create a Calculation Object

The calculation object you want to use does not exist in the Component Browser by default. You will create it.

  1. Extend the Utilities menu.
  2. Select the Component Browser.
  3. Expand () the Calculation Objects.
  4. Select the Cartesian Elems directory.
  5. Duplicate () the Vx component.
  6. Rename it VxL1.
  7. Double-click on VxL1 to begin making changes.
  8. Set the Coordinate System to Sun -> Syst_SEM_L1.

    9. To ensure the spacecraft remains near the L1 point, the X component of the velocity needs to be nearly zero at the Rotating Libration Point (RLP) XZ plane crossing.

  9. Click OK when done and close the Component Browser.

Set VxL1 as a Result

  1. Select the ZX Plane Crossing () propagate segment.
  2. Click the Results... button.
  3. Expand () the Cartesian Elems directory.
  4. Move () the VxL1 result.
  5. Click OK.

Target a Plane Crossing Near L1

  1. Create a new Target Sequence ().
  2. Rename the differential corrector to First Plane Crossing.
  3. Add the L1 LEO Injection Thrust and Z-X Plane Crossing segments to this target sequence.
  4. Verify that the Z-X Plane Crossing's Results has the VxL1 results selected.
  5. In the First Plane Crossing target sequence, open the Differential Corrector Properties.
  6. Enable the Cartesian X Velocity as a Control Parameter.
  7. Enable VxL1 as a Result.

Run the MCS

  1. Set the action to Run active profiles.
  2. Run () the MCS.
  3. Click the Apply Changes button.
  4. View the result in the 3D Graphics window.

The converged Delta-V is very close to the guess you made.

Create the Libration Point Orbit (LPO)

  1. Copy the Z-X Plane Crossing () segment.
  2. Paste the Z-X Plane Crossing () segment outside of both target sequences.
  3. Rename the new Propagate segment LPO.
  4. Change LPO's () color.
  5. Run () the MCS.

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. Without a small injection maneuver, the probe returns to the Earth. It follows a somewhat symmetric path with respect to the Sun-Earth line.

Perturb the Trajectory into Orbit

You would like to ensure the probe begins to orbit about the L1 point. To do this, you will modify the MCS to favorably perturb the trajectory toward orbital motion.

  1. Reopen the First Plane Crossing Differential Corrector.
  2. Set the VxL1 Desired Value to -0.01 km/sec.
  3. Run () the MCS.

You should now see a sufficient amount of drift for the trajectory to start orbiting around the L1 point.

Set the Trip to 365 Days

To further check what happens after a significant amount of time, you can add a stopping condition set to a year.

  1. Add a Duration Stopping Condition to LPO.
  2. Set the Trip value to 365 days.
  3. Disable the Z-X Plane Crossing condition. Do not delete this condition.
  4. Run () the MCS.

The probe trajectory departs from the L1 region after just one orbit. You will add a station keeping strategy to maintain the libration point orbit over time using an Autosequence.

Maintain LPO

  1. Open the Automatic Sequence Browser ().
  2. Create a new sequence and name it Station Keeping.
  3. Double-click on Station Keeping to begin editing.
  4. In the Station Keeping's MCS, add a Target Sequence () named Maintain LPO.
  5. Add a Maneuver () named SK Burn inside the Target Sequence.
  6. Set the Attitude Control to Thrust Vector.
  7. Set the Thrust Axes to Sun -> Syst_SEM_L1.Axes.
  8. Set X () as an independent variable.
  9. Set the X to -20 m/sec.

Add a Propagate Segment

  1. Add a Propagate () segment named Prop to Plane Cross.
  2. Set the Stopping Condition to Z-X Plane Cross.
  3. Set the Coordinate System to Sun -> Syst_SEM_L1.
  4. Set CisLunar as the Propagator.
  5. Set the Tolerance to 1e-006 km.
  6. Delete the default stopping condition.
  7. Click the Advanced... button.
  8. Set the Minimum Propagation Time to 864000 sec.

Set VxL1 as a Result

  1. Ensure the Prop to Plane Cross segment is selected.
  2. Click the Results... button.
  3. Expand () the Cartesian Elems directory.
  4. Move () the Vx L1 result.

Add a Return Segment

  1. Add a Return () segment between the SK Burn () and the Prop to Plane Cross () segments.
  2. Set the state to Enable (except Profiles bypass).

    3. The Return segment allows the Differential Corrector to run until the last Propagate segment. When it converges, the SK Burn segment is executed again once (with the right Delta-V value) and the control is passed back to the main sequence.

  3. Open the Differential Corrector inside of the Maintain LPO target sequence.
  4. Enable the X Velocity component as a Control Parameter.
  5. Set the following options:
    6. Option Value
    Perturbation .05 m/sec
    Max Step 10 m/sec
  6. Enable the VxL1 as a Result. This is the condition you'd like to achieve.
  7. Set the Tolerance to .05 m/sec.
  8. Set the Action to Run active profiles.
  9. Close the Autosequence properties.

Define the Station Keeping

  1. Bring the satellite's Basic - Orbit page to the front.
  2. Select the LPO segment in the MCS.
  3. Enable the Z-X Plane Cross condition.
  4. Set the Sequence to Station Keeping.

Run the MCS

  1. Run () the MCS.
  2. Bring the 3D Graphics window to the front to view the orbit.

The probe is propagated ahead in time by the LPO segment until it reaches the Duration condition (one (1) year) that stops the execution. In the meantime, each time there is a plane crossing, the Station Keeping Autosequence is fired, bringing back the needed Delta-V for orbit maintenance.

Remember to reset the target sequence in the autosequence if you rerun the analysis. A useful way to reset all active target sequence priorities at once is through the MCS Options (). Click MCS Options, then select the Targeting tab, and click Reset All.