ASEN5050 – STK Lab #4
Due Friday, 12/12/2014
Names: _________________________________________________________
Note: This lab has been developed in STK 9; there may still be a few issues with STK
10. Please let me know if you have problems anywhere.
Note 2: Don’t forget to save your scenario frequently. You will build four different
scenarios in this lab. Save each in its own directory! Remember that your files could be
deleted at midnight in any computer lab, so consider saving them on a Flash disk as well.
Getting Started
This lab consists of the development of four scenarios to demonstrate the patched-conic
method of interplanetary mission design. The first three are each a separate phase of the
patched-conic design; the fourth (which is worth bonus points) uses Astrogator’s
“Targeter” to combine all three phases into one. The mission is similar to that of the
Pioneer Venus Multiprobe, which launched in August of 1978.
Earth Departure
Open STK and create a new scenario called Earth_Depart. Set time period to start on 17
Aug 1978 00:00:00 UTCG and to stop on 1 Feb 1980 00:00:00 UTCG (if there’s an
option, set the epoch to be the same as the start time).
In the Scenario Properties menu (right-click the scenario’s name), under 2D Graphics:
Global Attributes: Planets, turn on ‘Show Orbits’, ‘Show Inertial Positions’, and ‘Show
Position Labels’; turn all other options off. Hit OK. Save the scenario.
Go to the Insert, Default Object… and select Planet to insert a new Planet. Right-click
the new planet and go to its Property Page. Under Basic Definitions, select Earth as the
Central Body. Go to the 2D Graphics: Attributes page in the Properties page. Select a
color that you like and notice that the Settings were inherited from the scenario (if you
forgot to set the scenario settings, then turn off “Inherit from Scenario” and select the
various options that were specified above). Hit OK. The Planet’s name should have
been renamed appropriately to Earth. Repeat this procedure to insert Venus as a second
new planet.
With the 2D map highlighted, hit the Properties button in the menu-bar (yellow button).
Under Projection, set the type to “Orthographic” and the Display Coordinate Frame to
“ECI.” Set the Display Height to 60,000 km, Center Lat to 90 deg, and Center Lon to 80
deg. The view will be above the North Pole, with the horizontal axis approximately
aligned with the velocity of the Earth. Click OK. If the screen gets distorted, hit the 2:1
Aspect Ratio button to realign it.
With the 3D map highlighted, hit the Properties button, go to Advanced, and set the Max
Visible Distance to something huge: say, 1e15 km. This way we can see trajectories
from a long way out, i.e., interplanetary! Note, if you change the 3D Graphics Central
Body (the blue globe) to the Sun or another body, you will probably have to re-set this.
Create a new satellite and rename it to Pioneer. In its Property Page, under Basic Orbit,
select the Propagator “Astrogator.” This creates a Mission Control Sequence. Set the
coordinate system of the Initial State segment to Earth J2000, and the element type to
Keplerian. Make the orbit epoch 17 Aug 1978 00:00:00.00, the semi-major axis 6878
km, and all the other elements zero.
1. What is the orbital period (in seconds)? ______________
Go to the Utilities menu at the top and select “Component Browser…”. This browser
shows all sorts of information about Astrogator’s components. Click the propagators
folder. Highlight Earth Point Mass, and click the Duplicate button. Change the name to
'Earth and Sun,' add any user comments you wish, and click on OK. Now you can see
that the new ‘Earth and Sun’ propagator is in green, hence it is user-defined and alterable.
Double click on 'Earth and Sun', click “Insert…”, the Third Bodies-> Sun. The Sun
should show up in the list of propagator functions. Press OK. You now have a new
propagator.
Highlight the Propagate segment after the initial state and select Earth Point Mass as the
propagator. Change the Trip duration to 6876 sec (one orbit period plus extra time
needed to orient the ΔV in the opposite direction of the Earth’s velocity vector).
Insert a maneuver after the propagate segment by highlighting the Propagate segment,
clicking on the Insert Segment button, and selecting Maneuver. Change the attitude
control of this maneuver to 'Thrust Vector', set the thrust axes to 'VNC(Earth)', and the
vector type to 'Cartesian.' Set X (velocity) to 3.45 km/s, and Y and Z to 0 km/s. Insert a
propagate segment after the impulse. Change the propagator to 'Earth and Sun', with a
duration of 365 days. Click Run (green arrow button) to propagate the Mission Control
Sequence (selecting Apply will propagate the sequence without closing it).
You should be able to see the orbit of the satellite in the 2D and 3D windows. If you do
not wish to see the ground track as well as the orbit, go to the Property Page of the
satellite, find the 2D Graphics options and click Pass. Change the Lead Type of the
Ground Track to None. Go to the 3D Graphics options, click Pass, and turn on “Inherit
from 2D Graphics” in the Leading/Trailing section. Press OK and the ground tracks will
be turned off. If the satellite’s name or model is not showing up, go to the Advanced
options in the 3D Property Page of the satellite and set the Maximum Viewing Distance
to a very large value. You can also play around with the Model settings in the Satellite’s
Properties page.
On the 3D map, click the “View From/To” button (on the toolbar on the left next to the
object browser), and select Pioneer as both the viewer position and the view direction.
View the Earth departure phase in both the 2D and 3D windows to get an idea of the
hyperbolic escape trajectory.
Now, change the 2D map’s Map Central Body (globe button on the toolbar) to the Sun to
get a heliocentric point of view (remember to add the 'Map Central Body' button to the
map toolbar if it doesn't already exist). Change the projection type to orthographic CBI
with a display height of 350 000 000 km, a center lat of 90 deg, and a center lon of 32
deg. Notice that Pioneer's trajectory is on course to rendezvous with Venus. This shows
that the patched conic method is a good approximation. Save this scenario.
Earth-Venus Heliocentric Transfer
Create a new scenario and rename it Earth_Venus. Set the same time period properties
and 2D visualization properties as for Earth_Depart. Save the scenario in a different
folder, so that the planets and satellites from the two scenarios don't overwrite. Create
the planets Earth and Venus with the same graphics properties as before.
Change the 2D map to a heliocentric view (Change the central body to the Sun using the
“Graphics Window Central Body” button). Change the projection type (in the properties
window) to orthographic CBI with a display height of 350 000 000 km, a center lat of 90
deg, and a center lon of 32 deg (so the x-axis will be along the first point of Aries).
We want to find the initial heliocentric orbital elements for our spacecraft. Right-click on
the Earth, and select Report Manager. Click on Time Properties, select Specify
Properties and change the step size to 1 day. Now use the report of the Earth’s initial
orbital elements to find the spacecraft’s initial elements.
2. What are the heliocentric orbital elements (Helio Classical Elements) for the Earth at
the start of the scenario?
a ___________________
ω _________________
e ____________________
ν _________________
i ____________________
M _________________
RAAN (Ω) ____________
Create a satellite named Pioneer. Use the Astrogator propagator to create a Mission
Control Sequence. With initial state highlighted, change the coordinate system to Sun
Inertial and the element type to Keplerian. Input the orbital elements you just wrote
down, but change the semi-major axis to 147 000 000 km. (Don’t forget to change the
orbit epoch.)
Add a maneuver after the Initial State. Change the attitude control to 'Thrust Vector', the
thrust axes to ‘VNC(SUN)', and the vector type to 'Cartesian.'
3. Use this space to calculate the ΔV necessary to depart from Earth’s orbit on a transfer
orbit to Venus. This ΔV should be in the heliocentric frame and should completely
ignore the gravity of Earth (i.e., it should begin in an orbit that looks exactly like Earth’s
orbit if Earth weren’t there – this is a first approximation).
4. Is the ΔV positive or negative relative to the velocity vector? _______________
Change the x-direction thrust vector to the value you have calculated, and the y- and zdirection vectors to 0. Add a propagate segment after the impulse, highlight it, and
change the propagator to heliocentric. Click the 'Advanced…' button, and turn off the
maximum propagation time. Change the trip time to 142 days.
5. Use this space to calculate the ΔV necessary to drop into Venus’ heliocentric orbit
from the transfer orbit. Again, ignore the gravity effects of Venus and assume that the
spacecraft is going into a final circular heliocentric orbit that looks exactly like Venus’
orbit about the Sun.
6. Is the ΔV positive or negative relative to the velocity vector? _______________
Copy the impulsive maneuver and paste it after the propagate segment. Change the xdirection velocity to -2.57 km/s and the z-direction (co-normal) to 0.4 km/s. Copy the
propagate segment, and paste it below the second impulsive maneuver. Change the trip
time to 365 days. Click Run to propagate the Mission Control Sequence. Observe the
satellite motion on both map displays. Save the scenario.
Venus Approach
Create a new scenario called ‘Venus_Approach.’ Set the time period start to 5 Jan 1979
00:00:00.00, the stop to 10 Jan 1979 00:00:00.00, and the epoch to 5 Jan 1979
00:00:00.00. Save the scenario in its own folder.
For the 3D and 2D maps, change the Central Body to Venus. Make the 2D map
projection Orthographic CBI with a display height of 60 000 km, center lat = 90 deg and
center long = 140 deg (so the horizontal axis is along the velocity vector of Venus).
Create a new satellite (Pioneer). Create a new propagator for Astrogator as you did with
the Earth Departure phase. This time, name the new propagator ‘Venus and Sun’, select
Venus as the central body, and add the Sun 3rd body perturbation. Create a mission
control sequence. In the Initial State, change the coordinate system to Venus Inertial, and
the coordinate type to Target Vector Incoming Asymptote. Change the orbit epoch to 5
Jan 1979 00:00:00.00, the radius of periapsis to 7000 km, the C3 energy (which is just
V 2 ) to 7.344 km2/s2 , the RA of the incoming asymptote to 48 deg (this aligns the
incoming asymptote with the velocity vector of Venus), and the declination of the
incoming asymptote to 0. Set the velocity azimuth at periapse to 90 deg, and the true
anomaly to 215 deg.
∞
For the Propagate segment after the Initial State, use the ‘Venus and Sun’ propagator you
created with a duration of 81659 sec (which will bring the satellite to periapse).
Insert an impulsive maneuver after the propagate segment (thrust axes ‘VNC(Venus)’).
Set the X (velocity) to -3.1955 km/s, Y = 0, Z = 0. Copy the propagate segment, and
paste it after the impulse. Set the duration of this propagate segment to 5 days. Click
Run to propagate the Mission Control Sequence.
Set the camera in the 3D map to satellite/Pioneer (as described previously) and view the
approach in both the 2D and 3D screens.
Right-click on the last Propagate segment and change the coordinate system to ‘Venus
Inertial’ in the properties section.
7. Use the Summary tool to determine the Venus-centered orbital elements at the end of
the scenario:
a ___________________
ω _________________
e ____________________
ν _________________
i ____________________
M _________________
RAAN (Ω) ____________
Extra Credit: Full Mission Simulation (10 Points on Lab Grades)
Create a new scenario and rename it Pioneer_Mission. Set the same time period
properties and 2D visualization properties as for Earth_Depart (Aug 17, 1978 – Feb 1,
1980). Save the scenario in a different folder, so that the planets and satellites from the
previous scenarios don't overwrite. Create the planets Earth and Venus with the same
graphics properties as before.
Change the 2D map to a heliocentric view (Change the central body to the Sun using the
“Graphics Window Central Body” button). Change the projection type to orthographic
CBI with a display height of 350 000 000 km, a center lat of 90 deg, and a center lon of
32 deg (so the x-axis will be along the first point of Aries).
If you’d like to see the Earth in the 3D map, leave it as is. If you’d prefer to see the entire
trajectory in the 3D map, then follow these instructions. Change the Primary Central
Body to the Sun. Highlight the 3D Graphics window and hit the Properties button. Then
under Advanced change the Visible Distance option to 1e15 km (or something else
significantly large). Hit OK. Use the mouse to zoom out until you can see the orbits of
the planets (if the orbits don’t show up, check the orbit options in the planets’ properties
menus).
Create a satellite and call it Pioneer. Change the propagator to Astrogator and create a
mission control sequence. We will be using a lot of the information from the previous
scenarios to outline this scenario; however, since STK models quite a lot more than our
simple equations do, we will be required to implement STK’s targeting capabilities to
complete this scenario.
Set the coordinate system of the Initial State segment to Earth Centered Mean J2000, and
the element type to Keplerian. Make the orbit epoch 17 Aug 1978 00:00:00.00, the semimajor axis 6878 km, and all the other elements zero. This is our initial parking orbit.
We will now target exactly when and where we will perform the ΔV to reach Venus and
how large the ΔV will be.
Insert a Target Sequence between the Initial State and the Propagate segments. This
sequence is a subsequence of the mission control sequence. Press the (+) to its left to
explode the subsequence. Insert a Propagate segment and an Impulsive Maneuver
segment in the Targeting Sequence, in that order. Rename the propagate segment to
‘Parking Orbit’ and the Impulsive Maneuver to ‘Delta V1.’ Highlight the Parking Orbit
segment and change the trip time to 6876 sec (the initial approximation we used in the
first scenario). Check the bull’s-eye to the right of the trip duration. Highlight the Delta
V1 segment. Make sure the attitude control is set to Thrust Vector, the thrust axes are
VNC and then change the magnitude of X to 3.45 km/s (the initial approx. used
previously). Now check all three bull’s-eyes to the right (X, Y, and Z).
Add another propagate segment after the Delta V1 segment in the target sequence and
rename it ‘Cruise to Venus.’ Highlight it and change the propagator to Heliocentric.
Click on the ‘Advanced…’ button and de-select the Maximum Propagation time (don’t
check any bull’s-eyes). Now hit ‘Insert…’ and select Periapsis. This adds a new
propagation stopping condition. Change the Central Body of the periapsis condition to
Venus. Remove the Duration stopping condition by highlighting it and clicking Remove.
Finally, with the Cruise to Venus segment highlighted, hit the ‘Results…’ button (below
the mission control sequence). Go to the Spherical Elems and select ‘R Mag.’ Hit the
blue right-arrow button to move it to the right-hand box. With R Mag highlighted on the
right, look down and double-click Value and change it to Venus J2000. Then go to the
MultiBody folder and select both Delta Dec and Delta RA. As you did with R Mag,
change both of their ‘Value’s to Venus. Then hit OK.
Now click on the Target Sequence. Change the Targeter Mode to ‘Run Active Profiles’
(the Profiles are shown below – there should be one called ‘Differential Corrector’).
Under Mode there should be a box that says ‘Run Once’ – click on that box and you’ll
see that you can change it to other options. Change it to ‘Iterate.’ Now with that profile
highlighted, click on the button ‘Properties…’ This is where you designate the controls
and constraints for the targeter profile. The top portion shows the Control Parameters.
You should see four selections in that box (Cartesian.X, Cartesian.Y, Cartesian.Z, and
StoppingConditions.Duration.TripValue). Check the Use box next to all four of those.
Highlight the one called StoppingConditions…. and change the Max. Step to 7 sec and
the Perturbation to 10 sec. Now, look further down and you can see the box of Equality
Constraints. There should be three of these; check the Use box next to all of them. With
the R Mag option highlighted, change the Desired Value to 1e5 km and the tolerance to
1e4 km. Press OK.
If you now hit the green arrow ‘Run Sequence’ button above the Mission Control
Sequence STK will propagate this mission and run the targeter. You’ll see a targeter box
pop up showing the status of all of the control variables and how close the targeter has
come to each of the constraint parameters. It should eventually converge on a solution
(but it might take a while). You can increase the maximum number of iterations under
the convergence tab of the previous differential corrector properties.
8. Enter the final values that the targeter converged on:
ΔV X (km/s) ___________________________________
ΔV Y (km/s) ___________________________________
ΔV Z (km/s) ___________________________________
Propagation time (sec) ___________________________
Go back to the Target Sequence, hit apply changes and change the Targeter Mode to Run
Nominal Sequence (otherwise, every time you run this mission the targeter will redo its
targeting).
Look at the current orbit in each of the views and notice that the trajectory has been
targeted to fly very near Venus.
We will now add a trajectory correction maneuver to target the final parking orbit about
Venus that we wish to reach. This is an example, but you could modify this to go into
any orbit about Venus that you wish. We’ll keep it simple.
Go into the Target Sequence and delete the last propagate segment. Then insert a new
propagate segment after the Target Sequence. Change the propagator to Heliocentric and
set the trip length to 100 days. Go to Advanced and deselect the maximum propagation
length.
Add a new Target Sequence and add an impulsive maneuver. Change its name to TCM.
Change the Attitude Control to Thrust Vector and check each of the three bull’s-eyes on
the right. Now add a propagate segment after the TCM. Change the propagator to
Heliocentric, deselect the max prop time, and then hit ‘Insert…’ Insert a Periapsis
stopping condition and change the Central Body to Venus. Now remove the first
stopping condition.
With the propagate segment highlighted, hit the Results button. From the Keplerian
Elements folder, select the Radius of Periapsis component. Change its Value from Earth
to Venus.
Now go back to the Target Sequence, change the Targeter Mode to Run Active Profiles,
change the Mode to Iterate, and hit Properties… Check all of the ‘Use’ boxes. Change
the desired value of the Radius of Periapsis to 7000 km (from Scenario 3).
When you now hit the green ‘Run Sequence’ button, the first targeter will run the current
sequence and the new, second targeter will target a radius of periapsis around Venus of
7000 km.
9. Enter the final TCM values that the targeter converged on (they should be pretty
small):
ΔV X (km/s) ___________________________________
ΔV Y (km/s) ___________________________________
ΔV Z (km/s) ___________________________________
Click “Apply Changes” and change the Targeter’s targeter mode back to Run Nominal
Sequence so that it won’t re-run the next time we run the simulation.
We will use STK’s targeter once more to determine exactly what ΔV we need in order to
circularize our orbit about Venus.
10. Highlight the last propagate segment in the second Target Sequence. Right-click on
it and hit Properties. Change the Coord. System to Venus Centered Inertial. Hit OK and
now press the Summary button. This will output all of the Spacecraft’s parameters at the
end of this segment using the Venus Inertial coordinates. Enter the spacecraft’s velocity
magnitude at this point (it should be about 11 km/s):
|V| (km/s) ______________________________________
11. Use this space to calculate the velocity the spacecraft will need to have to be in a
circular orbit about Venus with a radius of 7000 km. Use that value to determine the
approximate ΔV that the spacecraft will need to perform to enter that orbit.
12. Should that ΔV be in the spacecraft’s velocity direction or in the anti-velocity
direction?__________________________________________
Insert one final Target Sequence at the end of the current Mission Control Sequence. In
the Target Sequence, insert an Impulsive Maneuver. Change its name to ‘Venus Orbit
Insertion’ (or VOI). Now select the Attitude Control that you wrote down in Question 12
and enter the value you calculated in Question 11 in the Magnitude. Check the Bull’seye. Hit the Results… button and select Eccentricity from the Keplerian Elems folder.
Change the Value from Earth to Venus. Hit OK. Go to the Target Sequence, change the
Targeter Mode to Run Active Profiles, the Mode to Iterate, and press Properties. Check
the Use box for the single Control Parameter and the single Constraint we have. Leave
the desired value for the eccentricity at 0. Hit OK. Now run the whole sequence.
13. Enter the final ΔV magnitude that the targeter converged on:
ΔV (km/s) ___________________________________
Change the targeter mode back to Run Nominal Sequence. Add a propagate segment
after this final targeter to see the final orbit about Venus. Congratulations! You
completed a full mission design to Venus using the Patched-Conic method as a first
approximation.