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 6,700 km to an outer circular orbit with a radius of 42,238 km. 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.

In the other Hohmann Transfer lesson, you enter precalculated values for the two required Delta-Vs. For this case, you will determine the Delta-V values.

Solution

Use STK's Astrogator capability to design a Hohmann Transfer from a 6,700 km parking orbit to an outer circular orbit with a radius of 42238 km. 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.

The values used here for the radii of the inner and outer orbits are for illustration purposes only. For further practice after completing this exercise, try substituting different values, such as a radius of 42164.197 km (geosynchronous) for the outer orbit.

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 Target Sequences

Video guidance

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

Setup

  1. Start STK and create a new scenario; name it Target_Hohmann_Transfer.
  2. Set the analysis period to the following:
    OptionValue
    Analysis Start Time1 Jul 2016 16:00:00.000 UTCG
    Analysis End Time3 Jul 2016 16:00:00.000 UTCG
  3. Insert a satellite and name it Hohmann_Sat_Targeter.
  4. On the Orbit page of the satellite's Basic properties, select the Astrogator propagator. You may need to expand the properties window to see all of the controls.

Constructing the MCS

To design a Hohmann transfer from a 6700 km parking orbit to a 42238 km outer orbit, you will use the following MCS segments:

  • An Initial State defining a parking orbit with a radius of 6700 km
  • A segment to Propagate the parking orbit
  • A Target Sequence containing an Impulsive Maneuver to enter the elliptical transfer orbit
  • A segment to Propagate the transfer orbit to apogee
  • A Target Sequence containing an Impulsive Maneuver to enter the outer circular orbit
  • A segment to Propagate the outer orbit

Here are the steps to accomplish that.

Defining the Initial State

  1. The default MCS that appears when you display the satellite's Orbit page probably already begins with an Initial State segment. If not, insert one at the beginning of the MCS.
  2. Name the segment "Inner Orbit".
  3. Select Keplerian as the Coordinate Type.
  4. Change Semimajor Axis to Periapsis Radius with a value of 6700 km.

    5.  All other elements should be set to zero. Your set up should match the following:

    Field Value
    Periapsis Radius 6700 km
    Eccentricity 0
    Inclination 0
    Right Asc. of Asc. Node 0
    Argument of Periapsis 0
    True Anomaly 0

Propagating the parking orbit

  1. If the second segment of the MCS is not already a Propagate segment, insert one in that position.
  2. Click ... to select Earth Point Mass as the Propagator.
  3. If you wish, select a different color for the segment.
  4. Set the Duration (Trip value) to 2 hours (7200 sec), more than enough to have the satellite orbit one complete pass.

Creating a maneuver into the transfer ellipse

Now use the targeter to calculate the Delta-V required to move the spacecraft from the parking orbit into the transfer 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.

Defining a Target Sequence

  1. Insert a Target Sequence segment.
  2. Rename the Target Sequence segment "Start Transfer".
  3. Nest a Maneuver in the Target Sequence.
  4. Rename the nested Maneuver segment "DV1".

Selecting Variables

  1. Highlight the nested Maneuver and make certain that the Maneuver Type is set to Impulsive.
  2. Select Thrust Vector in the Attitude Control field.
  3. Select VNC(Earth) Thrust Axes.
  4. Select the Cartesian option.
  5. Select the X (Velocity) component as the sole independent variable by clicking the target to the right of the text field.

  6. Click Results... and move () Radius of Apoapsis from the Keplerian Elements folder as the only dependent variable.

Setting up the Targeter

  1. Select Start_Transfer ().
  2. Highlight the default Profile (Differential Corrector) and open its page by clicking Properties...().
  3. Select the Use check boxes under Control Parameters and Equality Constraints.
  4. Set the Desired Value for the Radius of Apoapsis to 42238 km.
  5. Set Max. Step (under Control Parameters) to 0.3 km/sec and set Tolerance (under Equality Constraints) to 0.1 km.

  6. Select the Convergence tab.
  7. Set the Maximum Iterations amount to 50 and select the Display Status check box.
  8. Click OK to close the Properties window for the Profile.
  9. Set the Mode field of the Profile to Iterate.
  10. Select Run active profiles in the Action field.

Propagating the transfer orbit to apogee

  1. Insert another Propagate segment after the Target Sequence.
  2. Rename the segment "Transfer Ellipse" and change its color to a different color than that used for the first Propagate segment.
  3. Click ... to select Earth Point Mass as the Propagator.
  4. Insert an Apoapsis Stopping Condition and remove Duration.

Designing a maneuver to get to the outer orbit

Here you will use the 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.

Defining a Target Sequence

  1. Insert another Target Sequence segment.
  2. Name the Target Sequence segment "Finish Transfer".
  3. Nest a Maneuver in the Target Sequence.
  4. Name the nested Maneuver segment "DV2".

Selecting Variables

  1. Highlight the nested Maneuver and make certain that the Maneuver Type is set to Impulsive.
  2. Select Thrust Vector in the Attitude Control field.
  3. Select VNC(Earth) Thrust Axes.
  4. Select the Cartesian option.
  5. Select the X (Velocity) component as the sole independent variable.
  6. Click Results... and move () Eccentricity from the Keplerian Elements folder as the only dependent variable.
  7. Click OK .

Setting up the Targeter

  1. Select Finish_Transfer ().
  2. Highlight the default Profile (Differential Corrector) and open its Variables page by clicking Properties...().
  3. Select the Use check boxes under Control Parameters and Equality Constraints.
  4. Set Max. Step (under Control Parameters) to 0.3 km/sec.

    5. Leave the Desired Value for Eccentricity at its default value of zero.

  5. Click the Convergence tab and select the Display Status check box.
  6. Click OK to close the Properties window for the Profile.
  7. Set the Mode field of the Profile to Iterate.
  8. Select Run active profiles in the Action field.

Propagating the outer orbit

  1. Insert a Propagate segment after the target sequence.
  2. Rename the segment "Outer Orbit" and change its color to a different color than that used for the other two Propagate segments.
  3. Click ... to select Earth Point Mass as the Propagator.
  4. Set the Duration to 24 hours (86400 sec), so that the satellite will make a complete orbit pass that you can see in the 3D Graphics window.

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

Running and analyzing the MCS

Run the MCS and observe the targeting process as displayed in the Status window. When the process is finished, the 3D Graphics window display should be similar to the illustration.