Space Mission Analysis and Design (SMAD): Orbit Design (Part 1 of 3)

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.

Additional installation - Analyzer capability. You can obtain the necessary install by visiting http://support.agi.com/downloads or calling AGI support.

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 Ansys Systems Tool Kit (STK®) digital mission engineering software capabilities:

  • STK Pro
  • STK Analyzer

Problem statement

Engineers and operators want to design and develop a satellite to characterize the steam, ash, and lava emissions of active volcanoes in the United States. The objective of the satellite, STKSat, is to image these volcanoes to provide early indications of volcanic eruption. The imaging camera on STKSat will take panchromatic and multispectral images of steam emissions, airborne ash, and lava flows on the volcanoes; these images will enhance current volcanic detection systems. They want to design an orbit for the satellite that maximizes the amount of time the imaging camera can view the volcanoes.

Solution

Use the STK Analyzer capability to perform Parametric and Carpet Plot trade studies to design a circular and an elliptical orbit for STKSat, identifying the best combination of orbital parameters that will provide the longest total observation time for the United States' active volcanoes.

What you will learn

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

  • Open and use the STK Analyzer capability.
  • Generate Parametric Studies using the STK Analyzer capability to narrow down ranges of orbital parameters.
  • Generate Carpet Plots using the STK Analyzer capability to identify the optimal combination of variables to design an orbit that best fits your mission requirements.

Video guidance

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

Using the starter scenario

You have the option of either using a starter scenario, which has a constellation of volcanoes already set up for use, or creating a new scenario and building out the constellation yourself. If you wish to manually build out your scenario, skip to the Building your scenario section.

Downloading the starter VDF

Download the starter VDF file and open it in the STK application.

If you are not already logged in, you will be prompted to log in to agi.com to download the file. If you do not have an agi.com account, you will need to create one. The user approval process can take up to three (3) business days. Please contact support@agi.com if you need access sooner.

  1. Download the starter VDF file, SatOrbitDesignStarter.vdf, here: https://support.agi.com/download/?type=training&dir=sdf/help&file=SatOrbitDesignStarter.vdf
  2. Launch the STK () application.
  3. Click Open a Scenario in the Welcome to STK dialog box.
  4. Browse to location of your extracted VDF file.
  5. Select SatOrbitDesignStarter.vdf.
  6. Click Open.

Saving the VDF as a Scenario File

When you save a scenario with the STK application, it will save in the from in which it originated. In other words, if you open a VDF, the default save format will be a VDF file (.vdf); the same is true for a scenario file (*.sc). If you want to save a VDF file as a SC file (or vice-versa), you must change the file format when you are performing the Save As procedure.

  1. Open the File menu.
  2. Select Save As.
  3. Select the STK User folder in the navigation pane when the Save As dialog box opens.
  4. Click the New Folder option in the selector bar.
  5. Name the folder SatOrbitDesign.
  6. Select the Enter key.
  7. Click Open.
  8. Select Scenario Files (*.sc) in the Save as type drop-down list.
  9. Enter SatOrbitDesign.sc as the File name.
  10. Click Save.

Save () often!

Building your scenario

Create a new scenario and model the United States' recently active volcanoes. If you are using the starter VDF, skip to the Setting up the Spacecraft section; the constellation of volcanoes you create in this section are already loaded into the starter scenario.

Creating a new scenario

  1. Launch the STK () application.
  2. Click Create a Scenario in the Welcome to STK window.
  3. Enter the following in the New Scenario Wizard:
    4. Option Value
    Name SatOrbitDesign
    Location Default
    Start 1 Jan 2024 00:00:00.000 UTCG
    Stop 15 Jan 2024 00:00:00.000 UTCG
  4. Click OK.
  5. Click Save () when the scenario loads. A folder with the same name as your scenario is created for you in the location specified above.
  6. Verify the scenario name and location.
  7. Click Save.

Inserting the volcanoes

Add the volcanoes to your new scenario as Place () objects.

  1. Insert a Place () object using the Search by Address () method.
  2. Enter Mount St Helens, WA in the Enter an address or other search criteria below field when the STK: Insert by Address dialog box opens.

    3. The Insert by Address option requires an internet connection; if you do not have an internet connection, you can insert the volcanoes using the Define Properties () method and manually entering the latitude and longitude to 46.1912 deg and -122.194 deg, respectively, for Mount St Helens, WA.

  3. Click Insert.
  4. Repeat the steps above to insert the locations below as Place () objects in your scenario:
    5. Volcano Name Latitude (deg) Longitude (deg)
    Mount Hood, OR 45.3735 -121.696
    Mount Baker, WA 48.7766 -121.814
    Mount Rainier, WA 46.8529 -121.761
    Shishaldin Volcano, AK 54.7553 -163.971
    Mount Cleveland, AK 52.8250 -169.940
    Fourpeaked Mountain, AK 58.7682 -153.675
    Kasatochi Island, AK 52.1724 -175.510
    Middle Sister, OR 44.1485 -121.784
    Lassen Peak, CA 40.4882 -121.505

Creating a constellation of volcanoes

Group the volcanoes into a Constellation object for analysis. A Constellation () object in the STK application allows you to group objects together for use with other analysis tools available in the STK software, including the Chains capability. For this exercise, insert the Constellation () object using the Define Properties () method.

  1. Return to the Insert STK Objects dialog box.
  2. Select Constellation () in the Scenario Objects.
  3. Select Define Properties () in the Select a Method list.
  4. Click Insert....
  5. Select all of the volcanoes in the Available Objects list by selecting Ctrl and clicking on the individual Place () objects when the Properties Browser opens.
  6. Click Move () to move all of the volcanoes to the Assigned Objects list.
  7. Click OK to save your changes and to close the Properties Browser.
  8. Rename Constellation1 () Volcanoes.

Setting up the spacecraft

Now that your scenario is set up with the constellation of volcanoes, you can begin the orbit design for STKSat. Insert a new satellite, propagate it into circular orbit, and model its imaging camera.

Inserting a satellite object

Insert a new Satellite () object into your scenario.

  1. Insert a Satellite () object using the Define Properties () method.
  2. Rename Satellite1 () STKSat.

Propagating STKSat

Various properties of the satellite can be changed by navigating through different tabs in the Properties Browser. For this tutorial, you will simplify the complexity of the problem by choosing the propagator that accounts for first-order Earth oblateness effects while ignoring drag, solar pressure, lunar gravitational effects, and higher-order Earth oblateness effects.

  1. Select the Basic - Orbit page.
  2. Select J2Perturbation in the Propagator drop-down list.
  3. Enter 45 degrees in the Inclination field.
  4. Click OK.

    5. This is a good starting place for an initial guess of where the satellite’s orbit should be for when you perform trade studies using the STK Analyzer capability later in this lesson.

Adding STKSat’s imaging camera

Model STKSat's camera using a Sensor () object and simulate its field of view.

  1. Insert a Sensor () object using the Define Properties () method.
  2. Select STKSat () in the Select Object dialog box.
  3. Click OK.
  4. Select the Basic - Definition page.
  5. Set the following options:
    6. Option Value
    Sensor Type Rectangular
    Vertical Half Angle 16 deg
    Horizontal Half Angle 20 deg
  6. Click OK.
  7. Rename Sensor1 () Imager.

Modeling a Chain object

You will design your orbit in order to maximize the imaging time between the imaging camera and the constellation of volcanoes. You can analyze this property by computing the complete access duration between Imager and the Volcanoes constellation with a Chain () object .Grouping the volcanoes as a Constellation () object allows you to represent them as a single asset when computing the complete access duration. It is important to note that the chain you create will be between the constellation and the sensor object, not the constellation and the satellite. The satellite uses a direct line of sight for access calculations; you are interested in the imaging of the volcanoes that is possible within the sensor's field of view.

Inserting a Chain object

Insert a Chain () object and define its connections.

  1. Insert a Chain () object using the Define Properties () method.
  2. Rename Chain1 () Observe.

Defining the start and end objects

Define your chain by choosing the start object and end objects.

  1. Select Observe's () Basic - Definition page.
  2. Click the Start Object ellipsis ().
  3. Select Imager () in the Select Object dialog box.
  4. Click OK to close the Select Object dialog box.
  5. Click the End Object ellipsis ().
  6. Select Volcanoes ().
  7. Click OK.

Building the Chain object's connections

After you choose the start and end objects in your chain, select the chain's connections.

  1. Click Add in the Connections panel.
  2. Click the From Object ellipsis ().
  3. Select Imager ().
  4. Click OK.
  5. Click the To Object ellipsis ().
  6. Select Volcanoes ().
  7. Click OK.
  8. Click OK to accept your changes and close the Properties Browser.

So far, the only active constraint applied to the Chain object is the imaging sensor's field of view, which was set up automatically by connecting the constellation of volcanoes to the imaging camera. If you recall, the imaging camera has a defined field of view. You could apply lighting constraints to your imaging camera to only take pictures during the day; this would be useful, if, for instance, your camera' s sensitivity was only in the visible light spectrum. For the larger goals of this scenario, you will leave additional constraints disabled.

Exploring circular orbit trade studies with Analyzer

You need to understand the orbital parameters you will be changing in this trade study. First, perform trade studies on a circular orbit, then a slightly eccentric orbit. You will also limit your satellite to a low Earth orbit; this will narrow down two variables for your trade study:

  • The altitude of perigee should aim to be greater than 250 km, due to drag effects.
  • The altitude of apogee should aim to be lower than 550 km to preserve imaging resolution.

Opening Analyzer

Open the STK Analyzer interface from the Analyzer toolbar.

  1. Select View in the STK application menu bar.
  2. Select Toolbars.
  3. Select Analyzer in the Toolbars submenu.
  4. Click Analyzer () in the Analyzer toolbar.

Selecting the input variables

By starting with a satellite in a circular but still low Earth orbit, you can focus on other orbital parameters to change, such as the inclination and semimajor axis, to see how they affect the amount of time the imaging camera is able to see the volcanoes in its field of view.

  1. Select STKSat () in the STK Variables tree when the Analyzer window opens.
  2. Expand () the Propagator (J2Perturbation) data provider in the STK Property Variables list in the General tab.
  3. Double-click on the following variables () in the STK Property Variables list to move them to the Analyzer Variables list as inputs:
    • SemiMajorAxis
    • Inclination

    Note that they have been added under the Inputs heading The direction that the aircraft is pointing. in the Analyzer Variables list.

Selecting the output variable

Evaluate the quality of your orbits using the total complete access duration variable, which is the time when the satellite's on-board camera can image the volcanoes.

  1. Select Observe () in the STK Variables list.
  2. Select the Show all Data Providers checkbox in the Data Providers Variables panel. This will display all possible data providers.
  3. Expand () Complete Access.
  4. Expand () Duration.
  5. Double-click on Total to move it to the Analyzer Variables list. Note that it was added under the Outputs heading in the Analyzer Variables list.

Performing a semimajor axis Parametric Study

Once all three variables are in the Analyzer Variables list, you can perform a Parametric Study using the Parametric Study Tool. This tool runs a model through a sweep of values for some input variable. The resulting data can be plotted to view trends.

  1. Click Parametric Study... () on the Analyzer toolbar to open the Parametric Study Tool.
  2. Drag SemiMajorAxis from the Component Tree on the left to the Design Variable field on the right.
  3. Set the following Design Variable parameters:
    4. Option Value
    starting value 6628
    ending value 6928
    number of samples 11

    Setting the number of samples to 11 will automatically set the step size to 30 km.

    These beginning and ending values come from the radius of the Earth, plus somewhere around the altitudes of perigee and apogee that were a part of your starting assumptions. The purpose of using these values is to help define an altitude which would be better, in preparation for the trade studies on an eccentric orbit.

  4. Drag Duration - Total from the Component Tree to the Responses field.
  5. Click Run... to collect your data.

Investigating the results with Data Explorer

The Data Explorer is a Trade Study tool used to display the data collected from your model. Create a 2D Line Plot to help you visualize the results of the semimajor axis Parametric Study.

  1. Click Add View in the Data Explorer toolbar.
  2. Select 2D Line Plot in the drop-down menu to create a new plot.
  3. Examine the results.

    4. Circular orbit Total vs. SemiMajor Axis 2D Line Plot

    You can see from your plot that there is a general trend of a longer total access duration with a higher altitude. Keep this in mind as you perform further trade studies.

Performing an inclination Parametric Study

Now that you understand the relationship between the semimajor axis and total duration, explore the inclination. How will orbits with different inclinations affect the total observation time (total complete access duration)?

  1. Return to the Parametric Study Tool.
  2. Clear the SemiMajorAxis variable from the Design Variable field.
  3. Drag Inclination from the Component Tree to the Design Variable field.
  4. Set the following Design Variable parameters:
    5. Option Value
    starting value 30
    ending value 90
    step size 10

    Later, you will perform another study with more refined values, but for now, use this range.

  5. Click Run....

Investigating the results with Data Explorer

Create a 2D Line Plot to help you visualize the results of the semimajor axis Parametric Study.

  1. Click Add View in the Data Explorer toolbar.
  2. Select 2D Line Plot in the drop-down menu.
  3. Examine the results.

    4. Circular orbit Total vs. Inclination 2D Line Plot

    You can see from your plot that there is a peak between 50 and 70 degrees. You'll examine this further in the next section.

Analyzing the results with Carpet Plots

Now that you have performed the two individual variable Parametric Studies, you have an idea for the general ranges where the duration is the greatest for each orbital parameter variable (semimajor axis and inclination). These two parameters can be efficiently plotted together using a Carpet Plot to find the best combination that maximizes the total observation time duration.

  1. Return to the Analyzer () window.
  2. Click Carpet Plot... () to open the Carpet Plot Tool.

Studying two variables with a Carpet Plot

Set Inclination and SemiMajorAxis as your Design Variables so you can perform a Carpet Plot study.

  1. Drag SemiMajorAxis from the Component Tree to the first Design Variable field.
  2. Drag Inclination from the Component Tree to the second Design Variable field.
  3. Set the following SemiMajorAxis Design Variable parameters:
    4. Option Value
    From 6828
    To 6928
    Num Steps 5

    These values reflect the best narrowed-down ranges from your semimajor axis Parametric Study.

  4. Set the following Inclination Design Variable parameters:
    5. Option From
    From 50
    To 70
    Num Steps 5

    These values reflect the best narrowed-down ranges from your inclination Parametric Study.

  5. Drag Total from the Component Tree to the Responses field.
  6. Click Run....

Investigating the results with Data Explorer

Create a Contour Plot to help you visualize the results of the Carpet Plot study.

  1. Click Add View in the Data Explorer toolbar.
  2. Select Contour Plot in the drop-down menu to create a new plot.
  3. Examine the results.

    4. Circular orbit Total Vs. Inclination vs. SemiMajor Axis Contour Plot

    Looking at the results from the Contour Plot, you can see that the ranges can be narrowed even further.

Refining your Carpet Plot

From the results of your Carpet Plot study, you can see that the bounds of your range can be narrowed down even further. Enter these new bounds and reperform your Carpet Plot study.

  1. Return to the Carpet Plot Tool and update the From and To values:
    2. Name From To Num Steps
    SemiMajorAxis 6900 6928 5
    Inclination 50 60 5
  2. Click Run....
  3. Bring the Table page to the front when all runs are completed.
  4. Click Add View in the Data Explorer toolbar.
  5. Select Contour Plot in the drop-down menu.

    6. Updated circular orbit Total Vs. Inclination vs. SemiMajor Axis Contour Plot

    From the plot, you can determine the best range of values for a circular orbit. Next, you will perform studies on an elliptical orbit.

Adjusting the satellite’s initial orbit

Using the defined upper and lower orbital limits, 550 km and 250 km, the most eccentric orbit you could possibly have is e=0.0221. This comes from this formula:

Where rA and rP are the radii of Apogee and Perigee (6,928.14 km and 6,628.14 km). These values come from the radius of the Earth plus the minimum altitude of perigee and the maximum altitude of apogee, respectively.

  1. Open STKSat’s Properties ().
  2. Select the Basic - Orbit page.
  3. Enter 0.0221 in the Eccentricity field.

    4. When the eccentricity is changed, the semimajor axis must be calculated from the formula:

    To remain consistent with the perigee and apogee altitudes, the semimajor axis must also be adjusted.

  4. Enter 6778 km in the Semimajor Axis field.
  5. Click OK.

Recomputing Chain Access

With the new satellite orbital parameters entered in, recompute the chain access before continuing the trade study portion of the analysis.

  1. Right-click on Observe () in the Object Browser.
  2. Select Chain in the shortcut menu.
  3. Select Compute Accesses in the Chain submenu.

Exploring eccentric orbit trade studies

Now that you've adjusted STKSat to have an elliptical orbit, reperform your trade studies to account for the eccentricity.

Performing an inclination Parametric Study

Perform another Parametric Study to study the effects of the new orbital eccentricity.

  1. Bring the Analyzer () window to the front.
  2. Select SemiMajorAxis in the Analyzer Variables list.

    3. Notice that by selecting SemiMajorAxis, STKSat's () Propagator (J2Perturbation) data provider is now displayed, expanded, in the STK Property Variables list.

  3. Drag SemiMajorAxis from the Analyzer Variables list to the STK Property Variables list to remove it as an input variable.
  4. Drag ArgOfPerigee into the Analyzer Variables list.
  5. Click Parametric Study... () on the Analyzer Toolbar.
  6. Drag Inclination from the Component Tree to the Design Variable field.
  7. Set the following Design Variable parameters:
    8. Option Value
    starting value 45
    ending value 90
    number of samples 11
  8. Drag Total from the Component Tree to the Responses field.
  9. Click Run....

Investigating the results with Data Explorer

Create a 2D Line Plot to help you visualize the results of the inclination Parametric Study.

  1. Click Add View in the Data Explorer toolbar.
  2. Select 2D Line Plot in the drop-down menu.
  3. Examine the results.

    4. Elliptical orbit Total vs. Inclination 2D Line Plot

    From these results, you can conclude an appropriate inclination range is 50 to 65 degrees.

Performing an argument of perigee Parametric Study

Examine the affects of changing the argument of perigee on the total duration.

  1. Return to the Parametric Study ().
  2. Clear the Inclination variable from the Design Variable field.
  3. Drag and drop ArgOfPerigee from the Component Tree to the Design Variable field.
  4. Set the following Design Variable parameters:
    5. Option Value
    starting value 0
    ending value 360
    number of samples 10
  5. Click Run....

Investigating the results with Data Explorer

Create a 2D Line Plot to help you visualize the results of the argument of perigee Parametric Study.

  1. Click Add View in the Data Explorer toolbar.
  2. Select 2D Line Plot in the drop-down menu.
  3. Examine the results.

    Elliptical orbit Total vs. Argument of perigee 2D Line Plot

    You can see that a good range for the argument of perigee from this study is 200 to 300 degrees.

Generating a Carpet Plot

Now that you have performed Parametric Studies on each parameter, you have an idea for the general ranges where the duration is the greatest for each orbital parameter variable (semimajor axis and inclination). These two parameters can be plotted together efficiently to find the best combination that maximizes.

  1. Return to the Analyzer () window.
  2. Click Carpet Plot... ().
  3. Drag ArgOfPerigee from the Component Tree to the first Design Variable field.
  4. Drag and Inclination from the Component Tree to the second Design Variable field.
  5. Enter the following parameters, as concluded from your Parametric Studies:
    6. Name From To Num Steps
    ArgOfPerigee 200 300 6
    Inclination 50 65 6
  6. Drag Total from the Component Tree into the Responses field.
  7. Click Run....

Investigating the results with Data Explorer

Create a Contour Plot to help you visualize the results of the Carpet Plot study.

  1. Click Add View in the Data Explorer toolbar.
  2. Select Contour Plot in the drop-down menu.
  3. Examine the results.

    Elliptical orbit Total vs. Inclination vs. Argument of perigee 2D Line Plot

    The Contour Plot shown above has had its Max # X bins increased from the default of 15 to 20 for clarity.

    You can see from your plot that you can further narrow your ranges of values.

Refining your Carpet Plot

From the results of your previous Carpet Plot study, you can see that your range can be narrowed down even further. Enter these new bounds and reperform your Carpet Plot study.

  1. Return to the Carpet Plot tool and update the From and To values:
    2. Name From To Num Steps
    ArgOfPerigee 220 280 6
    Inclination 50 60 6
  2. Click Run....
  3. Bring the Table page to the front when all runs are completed.
  4. Click Add View in the Table Page toolbar.
  5. Select Contour Plot in the drop-down menu.

    6. Updated Elliptical orbit Total vs. Inclination vs. Argument of perigee 2D Line Plot

    The Contour Plot shown above has had its Max # X bins increased from the default of 15 to 20 for clarity.

    From these results, the orbit with the greatest total coverage duration with an eccentricity of 0.0221 and a semimajor axis of 6778 km would have an inclination of 54 degrees and an argument of perigee of about 255 degrees.

Updating STKSat's orbit

Now that you have determined the optimal elliptical orbital for your scenario, update STKSat's orbital parameters with these new values.

  1. Open STKSat’s Properties ().
  2. Select the Basic - Orbit page.
  3. Enter the optimal values you determined by performing your trade studies:
    4. Parameter Value
    Semimajor Axis 6778 km
    Eccentricity 0.0221
    Inclination 54 deg
    Argument of Perigee 255 deg
  4. Click OK.

Viewing STKSat's orbit

Once you have updated the orbital parameters, examine your changes in the 3D Graphics window.

  1. Bring the 3D Graphics window to the front.
  2. Right-click on STKSat () in the object browser.
  3. Select Zoom To in the shortcut menu.
  4. Use your mouse to get a good view of STKSat's orbit.

Propagated elliptical orbit of STKSat

Saving your work

Clean up your workspace and close out your scenario to prepare for the next lesson in the Space Mission Analysis and Design series.

  1. Close all reports and windows except the 2D and 3D Graphics windows.
  2. Save () your work.
  3. Close the scenario when finished.

Summary

In this tutorial you created an access between a Satellite’s imaging camera and a constellation of volcanoes. Using the STK Analyzer capability, you optimized the orbit. First, using parametric trade studies, you determined that a higher altitude resulted in longer access periods. With that in mind, you then conducted trade studies for an eccentric orbit to find the optimal orbital parameters for the maximum complete access duration.

Space Mission Analysis and Design Part 2: Solar and Power Design

The next lesson in the Space Mission Analysis and Design series focuses on solar and power design. You will use the Solar Panel tool and the Analysis Workbench capability to determine what solar panel and battery combination will best satisfy your mission requirements.