Determine a Global Positioning System Satellite Eclipse Period

STK Pro, STK Premium (Air), 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
  • Analysis Workbench

Problem Statement

When a Global Positioning System (GPS) satellite is in an eclipse season, it may not receive enough solar exposure on its solar panels. If it doesn't the satellite could lose power. The angle between the orbital plane of a GPS satellite and the Earth-Sun vector, or beta angle, indicates when a given orbital plane is entering or has entered an eclipse season.

For this scenario, only six months of time will be evaluated for a GPS satellite eclipse season. You need to analyze an orbital plane for which you are responsible and determine when the beta angle was less than five degrees.

Solution

Use STK's Analysis Workbench (AWB) capability, including the Vector Geometry Tool (VGT) and Calculation tool, to model the beta angle for a GPS orbital plane over a six month period. This will determine when the satellite was in an eclipse season.

What you will learn

Upon completion of this tutorial, you will understand the following:

  • Analysis Workbench
  • Vector Geometry Tool
  • Calculation Tool

Throughout this tutorial, unless otherwise specified, use default settings.

Creating a new scenario

You will create a new STK scenario and then build from there.

  1. Launch STK ().
  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: GPS_Eclipse
    Start: 1 Nov 2023 16:00:00.000 UTCG
    Stop: 30 Apr 2024 16:00:00.000 UTCG
  4. Click OK when you finish.
  5. Click Save () when the scenario loads. STK 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!

Inserting the GPS Satellite

Insert a Satellite () object which functions as the GPS satellite you are testing.

  1. Select Satellite () in the Insert STK Objects tool ().
  2. Select the From Standard Object Database () method.
  3. Click Insert... .
  4. Type GPS in the Name or ID: field when the Search Standard Object Data dialog box opens.
  5. Open the Operational Status: shortcut menu.
  6. Select Operational.
  7. Click Search.
  8. Select SVN-48 in the Results: list.
  9. Click Insert.
  10. Click Close to close the Search Standard Object Data dialog box after SVN-48 propagates.

SGP4 Propagator

The Simplified General Perturbations (SGP4) propagator is used with two-line mean element (TLE) sets. It considers secular and periodic variations due to Earth being oblate, as well as solar and lunar gravitational effects, gravitational resonance effects, and orbital decay using a drag model.

  1. Right-click on Svn48_32711 () in the Object Browser.
  2. Select Properties ().
  3. Select the Basic - Orbit page when the Properties Browser opens.
  4. Click Preview... in the TLE Source frame when the TLE Preview dialog box opens.

    5. STK queried the AGI Server to find the appropriate set of TLEs during the propagation interval for the specified SSC (in this case, 32711). Which TLEs are selected and how they are used is determined by the parameters on the Setup panel.

  5. Click Close to close the TLE Preview dialog box.
  6. Click Cancel to close the Properties Browser.

Eclipse Times Report

The Eclipse Times report takes into account the Earth and Moon as the central bodies for satellites orbiting the Earth. The report analyzes when the satellite enters umbra and penumbra of the central bodies.

  1. Right-click on Svn48_32711 () in the Object Browser.
  2. Select Report & Graph Manager... () in the shortcut menu.
  3. Select the Eclipse Times () report in the Styles list when the Report & Graph Manager opens.
  4. Click Generate....
  5. Scroll through the report.

    This report provides a wealth of information. However, you are interested in the display times based on a specific angle drawn between an orbital plane and the Earth Sun vector.

  6. Close the report.

Beta Angle Report

In the Beta Angle report, the beta angle defaults to measuring the angle between the satellite's orbital plane and the earth sun vector. This is exactly what you need to know for the 6-month period being analyzed in this scenario. Due to the length of the analysis period, generating this report can take a long time and STK will display a warning explaining this. Therefore, only generate the report if you want.

Neither report provides a graphical representation along with the analysis. This is where the Analysis Workbench comes into play.

  1. When finished, close any reports that are still open.
  2. Close the Report & Graph Manager.

Displaying the Earth Sun Vector

The angle between the orbital plane of a GPS satellite and the Earth-Sun Vector, or beta angle, alerts you when a given orbital plane in the GPS constellation is entering an eclipse season. A beta angle of five degrees or less can be considered an eclipse period. You need to add the Earth-Sun vector and the orbital plane for the GPS satellite to this scenario. The Earth-Sun vector is predefined. Since the Earth-Sun vector displays originating from the Earth, you will add this vector via your 3D Graphics window properties.

  1. Bring the 3D Graphics window to the front.
  2. Click Properties () in the 3D Window Defaults toolbar.
  3. Select the Vector page when the Properties Browser opens.
  4. Select the Vectors tab.
  5. Select the Earth Sun Vector - Show check box.
  6. Select the Show Label check box.
  7. Enter 4.0 in the Common Options - Component Size - Scale field.
  8. Click OK to accept your changes and to close the Properties Browser.

    9. Earth Sun Vector

The Earth-Sun vector is now clearly visible in the 3D Graphics window.

Creating an orbital plane

You can create the orbital plane for the GPS satellite using the Vector Geometry Tool inside the Analysis Workbench. You want the plane that you are going to create to be a child of the Earth rather than the satellite. Having Earth as the parent object allows you to duplicate and modify the orbital plane in the future to represent the other orbital planes in the GPS constellation.

The orbital plane is defined as the plane perpendicular to (or "normal to") the satellite’s orbital angular momentum; therefore, you can use the Normal type for the plane that you create. In order to properly construct this plane, you need to define two vectors and a reference point.

  1. Click Analysis Workbench... () icon in the STK Tools toolbar.
  2. Select the Vector Geometry tab when Analysis Workbench opens.
  3. Open the Filter by: shortcut menu.
  4. Select All Objects.
  5. In the Objects list, select Earth () in the Objects list.
  6. Click Create new Plane () in the Vector Geometry toolbar.

Adding a Vector Geometry component

The Vector Geometry Tool includes multiple components.

  1. Click Select... for Type:.
  2. Select Normal () in the Select Component Type dialog box.
  3. Click OK to close the Select Component Type dialog box.
  4. Type Plane_Svn 48 in the Name: field.

Defining a Normal Vector

The Normal Vector is a unit vector perpendicular to the plane of an elliptical orbit created from the motion of the specified point with respect to the center of the specified central body. At any time, the orbit is fit to the current motion of the specified point according to the specified type orbital elements. Available types are:

  • Osculating
  • Brouwer-Lyddane long
  • Brouwer-Lyddane short
  • Kozai

The unit vector is directed along the current orbit angular momentum of the specified point with respect to the specified central body.

  1. Click the Normal Vector: ellipses ().
  2. Select Svn48_32711 () in the Objects list when the Select Reference Vector dialog box opens.
  3. Select Orbit_Normal () in the Vectors for: Svn48_32711 list.
  4. Click OK to close the Select Reference Vector dialog box.

Defining the Reference Vector

The Reference Vector determines where the axes of the plane are positioned, and sets up how the X and Y axes of the plane are oriented. Align the X axis with the satellite’s ascending node.

  1. Click the Reference Vector: ellipses ().
  2. Select Svn48_32711 () in the Objects list when the Select Reference Vector dialog box opens.
  3. Select LineOfNodes () in the Vectors for: Svn48_32711 list.
  4. Click OK to close the Select Reference Vector dialog box.
  5. Click OK to close the Add Geometry Component dialog box.

    6. Since the orbital plane will pass through the Earth, you can keep the Earth Center as the reference point.

Displaying the Orbital Plane

You can display the Orbital Plane in the 3D Graphics window.

  1. Bring the 3D Graphics window to the front.
  2. Click Properties () in the 3D Window Defaults toolbar.
  3. Select the Vector page when the Properties Browser opens.
  4. Select the Planes tab.
  5. Click Add... .
  6. Select Earth () in the Objects list when the Add Components dialog box opens.
  7. Select Plane_Svn48 () in the Components for: Earth list. It is located in My Components ().
  8. Click OK to close the Add Components dialog box.
  9. Select the Translucent plane check box.
  10. Click Apply to accept your changes and to keep the Properties Browser open.

Displaying the Line of Nodes Vector

You used the line of nodes vector as the reference axis for the plane that you created. It should line up along the x-axis of Plane_Svn43 when displayed.

  1. Select the Vectors tab.
  2. Click Add... .
  3. Select Svn48_32711 () in the Objects list when the Add Components dialog box opens.
  4. Select LineOfNodes () in the Components for: Svn48_32711 list.
  5. Click OK to close the Add Components dialog box.
  6. Click OK to accept your changes and to close the Properties Browser.
  7. Bring the 3D Graphics window to the front.

Orbital Plane and Line Of Nodes

Defining the Beta Angle

For the purposes of this tutorial, the beta angle is defined as the angle between the orbital plane of the satellite and the vector to the sun. The beta angle is the smaller angle (there are two angles) between the Sun vector and the plane of the satellite's orbit.

  1. Return to the Vector Geometry tool.
  2. Select Earth () in the objects list.
  3. Click Create New Angle () in the Vector Geometry toolbar.
  4. Set the following in the Add Geometry Component dialog box:
    5. Option Value
    Type: To Plane
    Name: Beta Angle
    Reference Vector: Sun
    Reference Plane: Plane_Svn48
    Signed Selcted
    Toward plane normal: Positive

    If Signed is selected, the angle can be measured as either Positive or Negative when the reference Vector is directed toward the plane’s normal. Otherwise, the angle is measured as positive regardless of on which side of the plane the reference vector is located.

  5. Click OK to close the Add Geometry Component dialog box.

Displaying the Beta Angle in 3D

You can display Beta_Angle () in the 3D Graphics window.

  1. Bring the 3D Graphics window to the front.
  2. Click Properties () in the 3D Window Defaults toolbar.
  3. Select the Vector page when the Properties Browser opens.
  4. Select the Angles tab.
  5. Click Add... .
  6. Select Earth () in the Objects list when the Add Components dialog box opens.
  7. Select Beta_Angle () in the Components for: Earth list.
  8. Click OK to close the Add Components dialog box.
  9. Clear the Show label check box.
  10. Select the Show angle value check box.
  11. Click OK to accept your changes and to close the Properties Browser.

Beta Angle

Animate the Scenario

Animate your scenario to visualize the change in your beta angle.

  1. Click Increase Time Step () in the Animation toolbar and set the Time Step: to 7200.00 sec.
  2. Click Start () to animate the scenario.

    3. You can see the angle change over the six month analysis period.

  3. Click Reset () when finished.

Calculation Tool

For this problem, you want to know when the beta angle is between -5 degrees and 5 degrees. This can be accomplished quickly using the Calculation tool. You can use the Calculation tool to combine system data with algebraic, functional, and calculus operations to extend models and define new data providers with custom algorithms from 20 mathematical operations.

Defining a Scalar Calculation

Scalars define components that produce scalar time-varying calculations.

  1. Return to the Analysis Workbench.
  2. Select the Calculation tab.
  3. Select Earth () in the Objects list.
  4. Click Create new Scalar Calculation () in the Calculation toolbar.
  5. Set the following in the Add Calculation Component dialog box:
    6. Option Value
    Type: Angle
    Name: Beta Angle Angle
    Input Angle: Beta_Angle
  6. Click OK to close the Add Calculation Component dialog box.

Defining a Condition

Conditions define a scalar calculation which is considered to be satisfied when it is positive and not satisfied when it is negative.

  1. Select Earth () in the Objects List.
  2. Click Create new Condition () in the Calculation toolbar.
  3. Set the following in the Add Calculation Component dialog box:
    4. Option Value
    Type: Scalar Bounds
    Name: Eclipse Season
    Scalar: Beta_Angle_Angle
    Operation: Between Minimum and Maximum
    Minimum: -5 deg
    Maximum: 5 deg
  4. Click OK to close the Add Calculation Component dialog box.

Setting report units

You want to set report units that appear in your analysis.

  1. Expand () Eclipse_Season () in the Components for: Earth list.
  2. Right-click on SatisfactionIntervals ().
  3. Select Report... in the shortcut menu.
  4. In the report's toolbar, select Report Units ().
  5. Select the Time Dimension in the Units: Eclipse_Season.SatisfactionIntervals dialog box.
  6. Select Days (day) in the New Unit Value list.
  7. Click OK to close the Units: Eclipse_Season.SatisfactionIntervals dialog box.

    8. The report gives you the exact dates and times, during the 6-month test period, that Svn48_32711 entered and exited the eclipse season based on the conditions set for the beta angle.

    Eclipse Season Report

Viewing the start of the eclipse season

You can use the report to jump to the beginning of the satellite's eclipse season.

  1. Right-click on the Start Time in the report.
  2. Select Start Time in the first shortcut menu.
  3. Select Set Animation Time in the second shortcut menu.
  4. Close the report.
  5. Bring the 3D Graphics window to the front to view the beginning of the eclipse season.

Data Display

You can display dynamic data in the 3D Graphics window showing the beta angle. This feature is useful when presenting information that requires both visual and textual data.

  1. Open Svn48_32711's () properties ().
  2. Select the 3D Graphics - Data Display page when the Properties Browser opens.
  3. Click Add... .
  4. Select Beta Angle in the Add a Data Display dialog box.
  5. Click OK to close the Add a Data Display dialog box.
  6. Adjust any Position and/or Appearance settings that you desire.
  7. Click OK to accept your changes and to close the Properties Browser.

Beta Angle and Data Display

You now have a report with the eclipse dates based on the beta angle and beta angle data in the 3D Graphics window. If required, this makes good use of STK to build a briefing on the satellite that requires both analysis and graphics.

Animate the Scenario

You can visualize the beta angle display.

  1. Click Start () in the Animation toolbar to animate your scenario.
  2. Click Reset () when you are finished.

Summary

The purpose of this tutorial focused on determining a GPS satellite eclipse season during a 6-month analysis period. You began by inserting a selected GPS satellite. Then you displayed the Earth Sun vector in the 3D Graphics window. You turned on the Analysis Workbench and selected the Vector Geometry Tool. You built a Normal orbital plane using the satellite's normal vector and line of nodes reference vector. You displa

yed the orbital plane and the line of nodes in the 3D Graphics window. You created a beta angle between Sun vector and the satellite's orbital plane and visualized the beta angle in the 3D Graphics window. You switched to the Calculation Tool. You created a scalar calculation using the beta angle and created a condition that focused on the beta angle when it fell between -5 and 5 degrees. You created a report that showed when the eclipse season would begin and end during your 6-month analysis period based on the condition. Finally, you displayed the beta angle data in your 3D Graphics window.

Save Your Work

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