Hohmann Transfer Using Targeter

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

Problem statement

Engineers and operators want to transfer a satellite from a low-Earth parking orbit with a radius of 6700 kilometers to an outer circular orbit with a radius of 42238 kilometers. They want to do this with a Hohmann Transfer. The Hohmann Transfer is, in terms of the velocity change (Delta-V) required, the most efficient two-burn method of transferring between two circular, coplanar orbits. As shown in the illustration, a Hohmann Transfer uses an elliptical transfer orbit with its periapsis at the inner orbit and its apoapsis at the outer orbit.

Solution

Use STK's Astrogator capability to design a Hohmann Transfer from a 6700 kilometers parking orbit to an outer circular orbit with a radius of 42238 kilometers. You will let Astrogator do the work of calculating the Delta-Vs, using its targeting capability called a Target Sequence.

This exercise and the preceding one are based on Example 3-6-1 in Hale, Francis J., Introduction to Space Flight, Englewood Cliffs, N.J.: Prentice-Hall (1994), pp. 43-44.

What you will learn

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

  • Design a Hohmann Transfer using Target Sequences
  • Set Control Parameters and Equality Constraints (Results) for a Differential Corrector
  • Set up and run the entire mission control 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, and then build from there.

  1. Launch the STK application ().
  2. Click Create a Scenario when the Welcome to STK dialog box opens.
  3. Enter the following in the STK: New Scenario Wizard:
    4. Option Value
    Name Hohmann_Sat_Targeter
    Start 1 Aug 2025 16:00:00.000 UTCG
    Stop + 3 days
  4. Click OK when you finish.
  5. Click Save () when the scenario loads. The STK software creates a folder with the same name as your scenario for you.
  6. Verify the scenario name and location in the Save As dialog box.
  7. Click Save.

Save () often during this scenario!

Cleaning up your workspace

The Timeline View and the 2D Graphics window aren't needed in this scenario.

  1. Close () the 2D Graphics window.
  2. Close () the Timeline View.

Inserting a Satellite object

Insert a Satellite object and name it Hohmann_Sat_Targeter.

  1. Bring the Insert STK Objects tool () to the front.
  2. Select Satellite () in the Select An Object To Be Inserted list.
  3. Select Insert Default () in the Select A Method list.
  4. Click Insert... .
  5. Right-click on Satellite1 () in the Object Browser.
  6. Select Rename in the shortcut menu.
  7. Rename Satellite1 () Hohmann_Sat_Targeter.

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.

  1. Right-click on Hohmann_Sat_Targeter () in the Object Browser.
  2. Select Properties () in the shortcut menu.
  3. Select the Basic - Orbit page when the Properties Browser opens.
  4. Open the Propagator drop-down list.
  5. Select Astrogator.

Setting up the Mission Control Sequence

The Mission Control Sequence (MCS) is the core of your space mission scenario. The MCS functions as a graphical programming language, in which mission segments dictate how Astrogator calculates the trajectory of the spacecraft based on the general settings that you specify for the MCS itself.

The MCS is defined by selecting and organizing MCS Segments in a manner that produces your desired trajectory. By default, an Astrogator satellite's MCS contains two segments: an Initial State segment and a Propagate segment.

The left side of the MCS is represented schematically by a tree structure, which lists the segments that make up the MCS and depicts their relationships to each other. Above the tree is the MCS toolbar, which contains buttons that perform various MCS and individual segment operations. By default, the MCS contains Initial State and Propagate segments that produce a low-Earth orbit. The right side of the window contains the parameters of the segment that is currently selected in the MCS Tree.

Defining the Initial State segment

Use the Initial State segment to define the initial conditions of your MCS or of a subsequence within the MCS.

  1. Select Initial State () in the MCS.
  2. Select the Elements tab.
  3. Open the Coordinate Type drop-down list.
  4. Select Keplerian.
  5. Open the Semi-major Axis drop-down list.
  6. Select Periapsis Radius.
  7. Set the following orbital parameters:
    8. Option Value
    Periapsis Radius 6700 km
    Eccentricity 0
    Inclination 0 deg
    Right Asc. of Asc. Node 0 deg
    Argument of Periapsis 0 deg
    True Anomaly 0 deg
  8. Click Apply to confirm your changes and to keep the Properties Browser open.

Propagating the parking orbit

Use the Propagate segment to model the movement of the spacecraft along its current trajectory until meeting specified stopping conditions. The segment uses the defined propagator and integrator to propagate the state, adding each point to the ephemeris as it goes.

  1. Select Propagate () in the MCS.
  2. Click Segment Properties () in the MCS toolbar.
  3. Type Parking Orbit in the Name field of the Edit Segment dialog box.
  4. Click OK to confirm your change and to close the Edit Segment dialog box.

Setting propagator components

A propagator component comprises a numerical integrator and a set of propagator functions. The numerical integrator defines the algorithm used to integrate the accelerations of the spacecraft and the constants that control the step size and accuracy of the propagation. Propagator functions define the external forces that will influence the spacecraft's trajectory. Use Earth Point Mass as the propagator. This will reduce the computational time while still providing useful results.

  1. Click the Propagator ellipsis ().
  2. Select Earth Point Mass () in the Select Component dialog box.
  3. Click OK to confirm your selection and to close the Select Component dialog box.

Setting the stopping condition

After each step, the segment checks to see if any stopping conditions were met during the step. If so, it then finds the exact point, within tolerance, where the stopping condition is satisfied. From that point, the segment either executes an automatic sequence or stops the propagation and passes the state at that point to the next segment. Astrogator also adds an ephemeris point at the time that the stopping condition is triggered.

  1. Look in the Stopping Conditions panel.
  2. Notice that the default stopping condition for Parking Orbit is Duration.
  3. Enter 7200 sec in the Trip field.

    4. 7200 seconds or 2 hours are more than enough time to have the satellite orbit one complete pass.

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

Using a target sequence to place the satellite into the transfer ellipse

In the Hohmann Transfer tutorial, you enter precalculated values for the two required Delta-Vs. In this scenario, use the targeter to calculate the Delta-V required to move the spacecraft from the parking orbit into the transfer orbit and finally the outer orbit. The goal of the targeter will be defined in terms of the radius of apoapsis of the transfer ellipse, coinciding with the radius of the desired final orbit.

Adding a Target Sequence

Add a Target Sequence to your MCS. A Target Sequence acts as a structural element to define maneuvers and propagations in terms of the goals they are intended to achieve.

  1. Select Parking Orbit () in the MCS.
  2. Click Insert Segment After () in the MCS toolbar.
  3. Select Target Sequence () in the Segment Selection dialog box.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.
  5. Right-click on Target Sequence () in the MCS.
  6. Select Rename in the shortcut menu.
  7. Rename Target Sequence () Start Transfer.
  8. Click Apply to confirm your changes and to keep the Properties Browser open.

Inserting an impulsive maneuver segment

For an Impulsive Maneuver, Astrogator calculates the new state of the spacecraft by adding a Delta-V vector to the final state velocity of the previous segment. This new state is then added to the ephemeris and passed to the next segment.

  1. Right-click on the Return () segment that's nested with Start Transfer().
  2. Select Insert Before... in the shortcut menu.
  3. Select Maneuver () in the Segment Selection dialog box.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.
  5. Notice that the default Maneuver Type is Impulsive.

Changing the segment properties

Change the name and color of the maneuver segment.

  1. Select Maneuver () in the MCS.
  2. Click Segment Properties () in the MCS toolbar.
  3. Type DV1 in the Name field of the Edit Segment dialog box.
  4. Open the Color drop-down list.
  5. Select white.
  6. Click OK to confirm your change and to close the Edit Segment dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Propagate segments can be viewed in the 3D Graphics window. By changing the color of each propagate segment (if you have multiple propagate segments), you can view them visually. Impulsive maneuver segments won't be seen in the 3D Graphics window. Changing their color to white in the MCS is just a way to make them stand out as impulsive maneuvers. This isn't required. It's the user's choice.

Setting the satellite's attitude

The Attitude Control field enables you to select the mode in which the maneuver pointing direction is prescribed. Using thrust vector, you specify the Delta-V vector in some reference frame using either Cartesian or spherical components. Astrogator then computes the attitude so that the total thrust vector in the body frame, as specified by the thruster set or engine model, aligns with this vector in the reference axes.

  1. Select the Attitude tab
  2. Open the Attitude Control drop-down list.
  3. Select Thrust Vector.

Selecting the control parameter

A Target Sequence's differential corrector profile uses a differential correction algorithm to achieve a goal value or set of values. The values that the profile targets are called independent variables. The values that define the goal of the profile are called dependent variables. When the target sequence runs, it will change the values of the independent variables to achieve the goal. You can use any element of a nested MCS segment or linked component as an independent variable. Select the Maneuver segment's X (Velocity) as the independent variable.

  1. Click the X (Velocity) target ().

    2. Notice the target now has a check mark (). Selecting the target makes X (Velocity) an independent variable. This tells Astrogator to determine the Delta-V based on user determined results.

    X (velocity) targeted

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

Selecting the results variable

Dependent variables for a differential corrector profile are defined in terms of calculation objects.

  1. Click Results... at the bottom of the MCS.
  2. Expand () the Keplarian Elems () folder in the Available Components list when the User - Selected Results - DV1 dialog box opens.
  3. Select Radius Of Apoapsis ().
  4. Click Insert Component () to move Radius Of Apoapsis () to the selected components list.
  5. Click OK to close the User - Selected Results - DV1 dialog box.
  6. Click Apply to accept your changes and to keep the Properties Browser open.

Setting up the differential corrector profile

Set up the differential corrector profile to change the X (Velocity) to achieve a desired radius of apoapsis.

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

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

Setting the control parameter

Use X (Velocity) as the control parameter (independent variable).

  1. Select Differential Corrector in the Profiles panel.
  2. Click Properties... () in the Profiles toolbar.
  3. Select the Use check box for ImpulsiveMnvr.Pointing.Cartesian.X in the Control Parameters panel when the Differential Corrector dialog box opens.
  4. Enter 0.3 km/sec in the Max. Step field.

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

Setting the equality constraints (Results)

Set radius of apoapsis as the equality constraint (dependent variable) with a goal of 42238 kilometers. Astrogator will use radius of apoapsis to determine the required Delta-V.

  1. Select the Use check box for Radius_Of_Apoapsis in the Equality Constraints (Results) panel.
  2. Click the Desired Value cell.
  3. Enter 42238 km in the Desired Value cell.

    4. This is the value that you want to achieve.

    differential corrector settings

  4. Click OK to confirm your changes and to close the Differential Corrector dialog box.

Inserting a propagate segment

Insert a new propagate segment.

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

Changing the segment properties

Change the name and color of the propagate segment.

  1. Select Propagate () in the MCS.
  2. Click Segment Properties () in the MCS toolbar.
  3. Type Transfer Ellipse in the Name field of the Edit Segment dialog box.
  4. Open the Color drop-down list.
  5. Select a color that's different from Parking Orbit ().
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Setting the propagator component

  1. Click the Propagator ellipsis ().
  2. Select Earth Point Mass () in the Select Component dialog box.
  3. Click OK to confirm your selection and to close the Select Component dialog box.

Inserting an apoapsis stopping condition

Use the apoapsis stopping condition to stop at the farthest point from the origin.

  1. Click New... () in the Stopping Conditions panel toolbar.
  2. Select Apoapsis () in the New Stopping Condition dialog box.
  3. Click OK to confirm your selection and to close the New Stopping Condition dialog box.
  4. Select the Duration stopping condition.
  5. Click Delete () in the stopping conditions toolbar.
  6. Click Apply to confirm your changes and to keep the Properties Browser open.

Inserting a target sequence

Here you will use a second targeter to calculate the Delta-V required to move the spacecraft from the transfer orbit into the circular outer orbit. With the desired radius already achieved, the goal will be to circularize the orbit, i.e., change its eccentricity to zero.

  1. Select Transfer Ellipse () in the MCS.
  2. Click Insert Segment After () in the MCS toolbar.
  3. Select Target Sequence () in the Segment Selection dialog box.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.
  5. Right-click on Target Sequence () in the MCS.
  6. Select Rename in the shortcut menu.
  7. Rename Target Sequence () Finish Transfer.

Inserting an impulsive maneuver segment

  1. Right-click on the Return () segment that's nested with Finish Transfer().
  2. Select Insert Before... in the shortcut menu.
  3. Select Maneuver () in the Segment Selection dialog box.
  4. Click OK to confirm your selection and to close the Segment Selection dialog box.

Changing the segment properties

Change the name and color of the maneuver segment.

  1. Select Maneuver () in the MCS.
  2. Click Segment Properties () in the MCS toolbar.
  3. Type DV2 in the Name field of the Edit Segment dialog box.
  4. Open the Color drop-down list.
  5. Select white.
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Setting the satellite's attitude

  1. Select the Attitude tab
  2. Open the Attitude Control drop-down list.
  3. Select Thrust Vector.

Selecting the control parameter

  1. Click the X (Velocity) target ().
  2. Click Apply to confirm your changes and to keep the Properties Browser open.

Selecting the results variable

  1. Click Results... at the bottom of the MCS.
  2. Expand () the Keplarian Elems () folder in the Available Components list when the User - Selected Results - DV2 dialog box opens.
  3. Select Eccentricity ().
  4. Click Insert Component () to move Eccentricity () to the selected components list.
  5. Click OK to confirm your selection and to close the User - Selected Results - DV2 dialog box.
  6. Click Apply to accept your changes and to keep the Properties Browser open.

Setting up the differential corrector profile

Set up the differential corrector profile to change the X (Velocity) to achieve a desired eccentricity.

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

Setting the control parameter

Use X (Velocity) as the control parameter (independent variable).

  1. Select Differential Corrector in the Profiles panel.
  2. Click Properties... () in the Profiles toolbar.
  3. Select the Use check box for ImpulsiveMnvr.Pointing.Cartesian.X in the Control Parameters panel when the Differential Corrector dialog box opens.
  4. Enter 0.3 km/sec in the Max. Step field.

Setting the equality constraints (Results)

Set eccentricity as the equality constraint (dependent variable) with a goal of zero. Astrogator will use eccentricity to determine the required Delta-V.

  1. Select the Use check box for Eccentricity in the Equality Constraints (Results) panel.
  2. Notice that the default value in the Desired Value cell is 0.

    3. differential corrector settings

  3. Click OK to confirm you changes and to close the Differential Corrector dialog box.
  4. Click Apply to accept your changes and to keep the Properties Browser open.

Inserting a propagate segment

Insert a new propagate segment.

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

Changing the segment properties

Change the name and color of the propagate segment.

  1. Select Propagate () in the MCS.
  2. Click Segment Properties () in the MCS toolbar.
  3. Type Outer Orbit in the Name field of the Edit Segment dialog box.
  4. Open the Color drop-down list.
  5. Select a color that's different from the other Propagate () segments.
  6. Click OK to confirm your changes and to close the Edit Segment dialog box.
  7. Click Apply to confirm your changes and to keep the Properties Browser open.

Setting the propagator component

  1. Click the Propagator ellipsis ().
  2. Select Earth Point Mass () in the Select Component dialog box.
  3. Click OK to confirm your selection and to close the Select Component dialog box.

Setting the duration stopping condition

Use the duration stopping condition.

  1. Insert 3 day in the Trip Field in the Stopping Conditions panel.
  2. Click Apply to confirm your changes and to keep the Properties Browser open.

    3. The MCS tree should appear as follows when you are finished:

    final mcs view

Running the entire 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.

  1. Click Run Entire Mission Control Sequence () in the MCS toolbar.
  2. You can view the data in the Targeting Status Windows.
  3. Close the Targeting Status Windows when finished.
  4. Click OK to close the Properties Browser.

Viewing the orbit in the 3D Graphics window

You can view the orbit in the 3D Graphics window.

  1. Bring the 3D Graphics window to the front.
  2. Use your mouse to obtain a good view of Hohmann_Sat () as it transfers from a low Earth orbit to the outer orbit.

    3. hohmann transfer

Creating a Maneuver Summary report

Now that you have modeled the satellite's orbit and visualized its behavior, examine the results in a Maneuver Summary report to get an overview about the engine's performance.

  1. Right-click on Hohmann_Sat_Targeter () in the Object Browser.
  2. Select Report & Graph Manager... () in the shortcut menu.
  3. Select the Maneuver Summary () report in the Installed Styles () folder in the Styles panel.
  4. Click Generate....
  5. Scroll through the Maneuver Summary report.

    6. You targeted the X (Velocity) for both the maneuver segments. If you look at the Delta V (m/sec) column, you can see the values that Astrogator determined are required to place your satellite into the proper orbit.

  6. Close the report and the Report & Graph Manager when finished viewing the data.

Saving your work

Clean up your workspace and save your work.

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

Summary

Using Astrogator, you transferred a satellite from a low-Earth parking orbit with a radius of 6700 kilometers to an outer circular orbit with a radius of 42238 kilometers using a Hohmann Transfer. You determined the required Delta-V by targeting the X (Velocity) Delta-V vectors in the reference axes.