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Will the Martian Space Vehicle Return to Earth?
In a space exploration mission, you are preparing for a return
from Mars. You are designated designer of the route from Martian
launch to Martian orbit to Earth targeting and capture. In this
exercise, you will design that mission and use it to look at::
Model a Martian launch. Use STK/Astrogator to target various
stages of space flight. Use SOCRATES to identify satellites that
are at risk of collision. Usethe Vector Geometry Tool (VGT) to
construct various components from which you
can create customized planes and angles.
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Will the Martian Space Vehicle Return to Earth?
Problem StatementIn preparation for the manned missions to Mars,
the United States is planning a Martian mission that will fly to
Mars, land, and then return the sample to the international space
station in Earth orbit. After a successful landing on the surface
of Mars, the space vehicle is now ready to return. Before doing so,
you must model the Martian launch, orbit and return to Earth,
ending in a phasing orbit relative to the station.
BREAK IT DOWN
The mission plan is to wait to launch when the Mars velocity
vector is roughly aligned with the launch orbit plane to ensure the
spacecraft is targeted in the right direction.
The Mars mission will launch from the surface of Mars at the
location of the original Martian landing--Martian latitude 67
degrees, longitude 80 degrees and altitude 0 degrees around 21 Jun
2020 at 12:00:00 UTC.
The burnout will be at the fixed velocity of 3.299 km/sec. In
order to assist the targeting of the outgoing asymptotes, the
launch
should take place roughly when Mars heliocentric velocity vector
lies in the plane of the initial satellite orbit.
Using the Jaqar Swing-by Calculator
(http://www.jaqar.com/swingby.html), you estimated values that will
help you model the proper angles and energy.
A mid-course maneuver will correct the trajectory so it passes
Earth at the correct distance.
Aerobraking is used to capture into an earth orbit. A phasing
orbit relative to the station is targeted.
SOLUTIONBuild a STK Scenario that uses STK/Astroator to plan a
mission that will launch a spacecraft from the surface of Mars and
bring it back to Earth.
Model the World!To speed things up and allow you to focus on the
portion of this exercise that teaches you to design orbit maneuvers
and spacecraft trajectories in STK/Astrogator, a partially
developed scenario has been provided for you. Lets open PAGE 2
that now.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
1. Launch STK ( ).2. Click the Open a Scenario button when the
Welcome to STK window
appears.3. Browse to C:\Training\STK\SpaceExploration.4. Select
MarsReturn.vdf. 5. Click Open.6. Save the new scenario in your
student area (C:\My Documents\STK 9).
In doing so, create a unique folder and rename the new folder
and the scenario file (*.sc) MarsReturn.
When you open the scenario, you will find the following
objects:
The scenario also has the following three views already set
up:
Model a SpacecraftThe first thing we need to do is model the
spacecraft that will be making the trip back from Mars.
1. Open the Insert STK Object Tool ( ) if it is not already.2.
Use the Insert Default ( ) method to insert an satellite ( ) object
named
SampleReturn.
TABLE 1.
OBJECT DESCRIPTIONEarth Models various planets for geometries
and targeting.Mars
Sun
SpaceStation Satellite representing a nominal space station
orbit.
TABLE 2.
OBJECT DESCRIPTION3D Graphics - Mars View of the Martian
surface.3D Graphics - Sun View of the solar surface.3D Graphics -
Earth Traditional Earth view.Page 3
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Will the Martian Space Vehicle Return to Earth?
OBJECT GRAPHICSBefore you start configuring your spacecraft,
lets make some adjustments to its display in the visualization
windows.
1. Open SampleReturns ( ) properties ( ). 2. Select the 3D
Graphics - Pass page.3. Change the Lead Type for the Orbit Track to
All.4. Click Apply.5. Select the 3D Graphics - Model page.6. Move
the slider for Marker, Label; Marker; and Point all the way to the
right.
You will now see these things at a far distance.7. Click
Apply.
SELECT A PROPAGATOR
1. Select the Basic - Orbit page.2. Change the Propagator
selected to an Astrogator propagator.3. Click Apply.
What Is Astrogator?STK/Astrogator is an interactive orbit
maneuver and space mission planning tool for use by spacecraft
operations and mission analysis staff that offers wide flexibility
through the use of customized thrust models, finite and impulsive
maneuvers, and the ability to solve for solutions with a
differential corrector targeter. You can use Astrogator for a
variety of space mission analyses, such as:
Formation flying, rendezvous planning, constellation design,
space-based intercept.
Interplanetary, lunar, and libration point trajectories. GEO,
LEO, HEO, Sun-Sync orbit maintenance requirements. Automated
planning of event-driven maneuvers. Monte Carlo and other script
driven analyses. Incorporating fully customizeable force, engine,
and atmospheric models. High, low, and variable-thrust
trajectories. PAGE 4
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Mission Control Sequence
Mission Control Sequence (MCS) controls
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
MISSION CONTROL SEQUENCEOne of the first things that you will
notice on the Astrogator propagator is the Mission Control Sequence
(MCS). The MCS is the core of your space mission scenario. The MCS
functions as a graphical programming language, utilizing mission
segments that dictate how Astrogator will build the trajectory of
the spacecraft.
FIGURE 1.
By adding, removing, rearranging, and editing MCS Segments, you
can define a mission of any desired level of complexity. The MCS is
represented schematically by a tree structure appearing in the left
pane of the Orbit page of the satellite's basic properties.
MCS CONTROLSThe Astrogator propagator includes a full set of
controls that can be used for inserting, deleting, copying, and
editing segments.
FIGURE 2.
Model the Martian LaunchOur first goal is to launch from Mars by
leaving the surface and then coasting in a Martian orbit before
maneuvering and reaching an escape orbit. Well model each
piece--launch and propagate, then maneuver and propagate. That
being the case, we dont need the default initial state segment.
1. Select the default Initial State segment ( ) in the MCS
tree.2. Click the ( ) button.Page 5
3. When the delete warning appears, click OK.
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Will the Martian Space Vehicle Return to Earth?
4. Select the Propagate segment ( ).5. Click the ( ) button.6.
When the delete warning appears, click OK.
ADD A LAUNCH SEGMENTThe first steps for leaving Mars is to
target the launch from the surface and get the spacecraft heading
in the right direction. The mission plan is to wait to launch when
the Mars velocity vector is roughly aligned with the launch orbit
plane to ensure the spacecraft travels towards Earth.
1. Right-click the Return segment ( ) in the MCS tree.2. Select
Insert Segment ( ).3. When the segment selection dialog appears,
select Launch ( ).4. Click OK.5. Press F2.6. Rename the new segment
MarsLaunch.
LAUNCH PARAMETERSAccording to what you know, the Mars mission
will launch from the surface of Mars (zero altitude) at Martian
coordinates 67 degrees latitude by 80 degrees longitude around June
21, 2020 at 12:00:00. You need to set up the launch so that it
leaves Mars at the correct time from the correct location. Lets do
that now
1. Select MarsLaunch ( ) in the MCS tree. When you select a
segment in the MCS tree, its properties display in the panel to the
right.
2. Set the following Launch parameters:
TABLE 3. MarsLaunch Launch parameters
OPTION VALUECentral Body MarsLaunch GeodeticEpoch 21 Jun 2020
12:00:00 UTCGLatitude 67 degLongitude 80 degAltitude 0 kmPAGE 6
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MarsLaunch properties
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
BURNOUT VELOCITYThe default values for the Astrogator launch
segment yield a circular orbit at 300 km altitude for Earth. In
order to enter a 300 km circular orbit around Mars, the burnout
velocity should be changed to 3.299 km/sec. Let's let Astrogator
know that too.
1. Click the Burnout Velocity button.2. Set the following
Burnout parameters:
3. Leave all other default values, and click OK.
FIGURE 3.
Model the Coast to the Martian Orbit
TABLE 4. MarsLaunch Burnout parameters
OPTION VALUEBurnout Options Use Fixed VelocityFixed Velocity
3.299 km/secPage 7
The first segment in the target sequence models the launch from
the surface of Mars. You want the spacecraft to coast to the
maneuver location. At the
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Will the Martian Space Vehicle Return to Earth?
maneuver location the engine will fire and put the spacecraft on
a path back to Earth. You need to add a propagate segment that
models the spacecraft coasting in Martian orbit. This will take the
spacecraft from the burnout state to the proper maneuver time. In
order to do this, we need to create a custom propagator to use in
modeling the propagate segment. Lets do that now.
The Component BrowserThe Astrogator Component Browser is a
powerful tool that enables you to redefine components of your space
mission analysis and create new ones. The components are organized
into groups listed in a tree structure.
1. Select the Component Browser ( ) option from SampleReturns
menu.
2. Select the Astrogator Components in the Show menu.3. Take a
look at the components in the Component Browser.
The components are organized into groups listed in a tree
structure in the left pane of the component browser. Individual
components in a given group or subgroup are displayed in the right
pane when you click the corresponding folder or subfolder in the
left pane.
CUSTOMIZE COMPONENTSIn order to correctly propagate a satellite
around Mars, youll need to create a customized propagator. We can
do that using the Component Browser.When you select Propagators in
the tree, all available components will display in the table on the
right.
4. Expand the Propagators in the Component Tree.5. Select
Previous Versions.6. Select Earth Full RKF.
The Componet Browser can also be found from the Utilities menu
in the STK Workspace.PAGE 8
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Propagator components
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
FIGURE 4.
7. Click the Duplicate button.8. Name the new propagator Mars
Full RKF.9. Click OK.
EDIT THE PROPAGATORIn order to correctly propagate a satellite
around Mars, we need to create a Mars-specific propagator that uses
a Mars gravity field, the Sun as a third body perturbation, and
solar radiation pressure as another perturbation. Lets do that
now.
1. Scroll down the components list to locate the new propagator
(Mars Full RKF) in the components list. It should be green.
2. Double-click Mars Full RKF ( ) in the components list.3. When
the Propagator definition window opens, ensure that the
Propagator
Function tab is selected.4. Change the Central Body to Mars.
When you change the central body, the
Gravitational Force is automatically updated with respect to the
selected
Components with Orange and Yellow icons cannot be edited. You
must duplicate the yellow component before you can customize it.
Components with green icons are customized by a user and can be
edited or removed. Page 9
body.
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Mars propagator definition
Will the Martian Space Vehicle Return to Earth?
5. Select Moon in the list of propagator functions. A Mars
propagator does not need to consider the Moon.
6. Click the Remove button.
FIGURE 5.
7. Click OK.8. Click OK to close the Components Browser.
Propagate Segment PropertiesNow, you can use the new propagator
in the propagate segment to model the spacecrafts coast into the
Martian orbit.
1. Right-click the Return segment ( ) in the MCS tree.2. Select
Insert Segment ( ).3. When the segment selection dialog appears,
select Propagate ( ).4. Click OK.5. Open the Propagate Segments
properties ( ).6. Enter the following:
TABLE 5. Mars coast segment properties
OPTION VALUEName MarsCoastPAGE 10
Color Select a color that isnt being used by any segment.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
7. Click OK.8. Select MarsCoast ( ) in the MCS tree.
Here well take an initial guess at the Trip value, which, in
this instance, represents the length of time that the spacecraft
will have to propagate to reach the next segment. Later, well
target that value and let Astrogator adjust it for us.
9. Click the button to change the Propagator.10. Expand the
Previous Versions directory.11. Set the Propagator to Mars Full
RKF.12. Click OK.13. Set the Trip to one (1) hr.
Add a Maneuver SegmentThus far, you have modeled the launch from
the surface and the coast into the Martian orbit. The next step is
to add the maneuver that will help you reach the escape orbit.
1. Use the same process to add a Maneuver segment ( ) after the
MarsCoast Propagate segment ( ).
2. Change the name of the Maneuver segment ( ) to
EscapeMnvr.
There is no need to change the color of the maneuver. You will
not be able to see it in the visualization windows.
THRUST VECTORThe term thrust vector is used to describe the
direction of acceleration applied to the satellite. This direction
is opposite to the exhaust of an engine. For example, for a single
chemical rocket engine mounted to a satellite, the thrust vector is
opposite to the direction of the flames.
If multiple engines are being used together in a thruster set,
the thrust vector is along the direction of the overall effective
acceleration. This is determined by calculating the acceleration
vector of each individual thruster, with both the direction and
magnitude. The thrust vector is then calculated along the direction
of the vector to be the sum of all the acting acceleration
vectors.Page 11
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Will the Martian Space Vehicle Return to Earth?
ATTITUDE PARAMETERSYou know you need to leave Martian gravity.
Burning in the velocity direction with respect to Mars is the most
efficient way to attempt to leave Martian gravity using an
impulsive maneuver with one burn. Well add a Delta-V maneuver that
is along the direction of the spacecraft velocity with respect to
Mars, which is the X direction of the VNC (Mars) frame.
Here, again, well take an initial guess at the X velocity value
needed to get us out of Martian gravity. Later, well target this
value and let Astrogator adjust it for us.
1. Select EscapeMnvr ( ) in the MCS tree.2. Ensure that the
Attitude tab is selected.3. Set the following:
Add a Second Propagate SegmentNow, you need to add a second
propagate segment that will take the spacecraft roughly to the Mars
sphere of influence (SOI) boundary which is where the midcourse
maneuver should occur.
1. Use the same process to add a second Propagate segment ( )
after the Maneuver ( ).
2. Double-click the new Propagate segment ( ).3. Enter the
following:
TABLE 6. Escape maneuver attitude definition
OPTION VALUEAltitude Control Thrust VectorThrust Axes VNC
(Mars)X(Velocity) 3 km/sec
TABLE 7. Leave Mars SOI segment properties
OPTION VALUEName LeaveMarsSOIColor Select a color that isnt
being used by any segment.PAGE 12
4. Click OK.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
DEFINE THE PROPERTIES OF THE SECOND PROPAGATORWell use our
customized Mars propagator, and a fifteen (15) day trip, as that is
a good estimate of the time that it will take to travel from launch
to the Mars SOI boundary. Later, well target this value, and let
Astrogator adjust it.
1. Select LeaveMarsSOI ( ) in the MCS tree.2. Change the
Propagator to Mars Full RKF.3. Click the Insert... button.4. Select
the R Magnitude item ( ).5. Click OK to add the new Stopping
Condition to the table.6. Set the following:
7. Select the Duration stopping condition in the table.8. Click
the Remove button.
Change Your PerspectiveYou can take a look at your mission so
far. Lets do that.
1. Click Run ( ).2. Bring the 3D Graphics - Mars window to the
front.3. Mouse around until you can clearly see the various
segments that make up
the portion of the orbit where the spacecraft is leaving
Mars.
TABLE 8. Leave Mars SOI stopping conditions
OPTION VALUETrip 580,000 kmCoord System Mars J2000Page 13
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3D View: Martian launch sequence
Will the Martian Space Vehicle Return to Earth?
FIGURE 6.
The color of each segment in the orbit coincides with the color
of the segment in the MCS tree.
Create a Target SequenceOur first goal is to launch from Mars by
leaving the surface and then coasting in a Martian orbit before
maneuvering and reaching an escape orbit. Youve already modeled
each segment--launch and propagate, then maneuver and propagate.
Lets put them inside a target sequence that will target specific
goals, and let Astrogator solve for the control values to achieve
those goals.
In order to assist the targeting of the outgoing asymptotes, the
launch should take place roughly when Mars heliocentric velocity
vector lies in the plane of the initial satellite orbit. We'll use
Vector Geometry Tool to create three different geometric elements
that will help us model this relationship.
Vector Geometry ToolThe Vector Geometry Tool (VGT) enables you
to define elements used in constructing coordinate systems,
vectors, axes, and points, as well as angles and planes. These
structures and elements are then added to the standard PAGE 14
structure and elements available to display in the 3D Graphics
and 3D Attitude Graphics, and to use as Astrogator calculation
objects.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
CREATE THE ORBIT NORMAL VECTORFirst, well create the spacecrafts
orbit normal vector from the satellite.
1. Select SampleReturn ( ) in the STK Object Browser.2. Open on
the Vector Geometry Tool ( ).3. Ensure that SampleReturn ( ) is
selected in the tree.4. Click the Create New Vector... ( )
button.5. Set the following definition values:
6. Leave all other default values.7. Click OK to add the new
vector.
CREATE THE ORBITAL PLANEThe second element that we need to
create is the spacecrafts orbit plane with respect to Mars. The
orbital plane is defined as the plane perpendicular to normal to
the satellites orbital angular momentum; therefore, you will use
the Normal type for the plane that you create. We need to
1. Ensure that SampleReturn ( ) is selected in the tree.2. Click
the Create New Plane... ( ) button.3. Set the following
parameters:
TABLE 9. Mars orbit normal vector definition
OPTION VALUEName Orbit Normal (Mars)Description Spacecraft orbit
normal vector.Type Orbit NormalCentral Body Mars
TABLE 10. Mars orbit plane definition
OPTION VALUEName Orbit Plane (Mars)Description Satellite orbit
plane about Mars.Type NormalPage 15
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Will the Martian Space Vehicle Return to Earth?
Define the Normal Vector
1. Click the Select... button under Normal Vector.2. Expand the
tree as follows:
... SampleReturn... Orbit Normal (Mars)
3. Select the Orbit Normal (Mars) vector that you just
created.4. Click OK.
Define the Reference Vector
1. Click the Select... button under Reference Vector.2. Expand
the tree as follows:
... Mars... J2000
... X3. Select the Mars J2000 X vector. 4. Click OK.
Define the Reference Point
1. Click the Select... button under Reference Point.2. Expand
the tree as follows:
... Mars... Center
3. Select the Mars Center point.
4. Click OK.5. Click OK to add the new plane.
CREATE THE ANGLE BETWEEN
You can select Mars Center from either instance of Mars in the
elements tree.PAGE 16
Finally, create the angle between the velocity vector and the
orbital plane.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
1. Click the Create New Angle... ( ) button.2. Set the following
definition criteria:
The To Plane type is defined as the angle from a vector
(reference vector) to a plane (reference plane).
Select the Reference Vector
1. Click the Select... button under Reference Vector.2. Expand
the tree as follows:
... Mars... Velocity
3. Select the Mars Velocity vector. 4. Click OK.
Select the Reference Plane
1. Click the Select... button under Reference Plane.2. Expand
the tree as follows:
... SampleReturn... Orbit Plane (Mars)
3. Select the Mars Orbit Plane. 4. Click OK.5. When you return
to the Angle properties, enable the Signed Positive Toward
Plane Normal option.6. Click OK.7. Close the Vector Geometry
Tool ( ).
TABLE 11. Mars orbit plane angle definition
OPTION VALUEName Orbit Plane Angle (Mars)
DescriptionAngle between the Mars velocity vector and the
spacecrafts orbital plane.
Type To PlanePage 17
You have created the necessary targeting geometries for your
mission. Now, we can apply them to the segments in the target
sequence.
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Will the Martian Space Vehicle Return to Earth?
Target Sequence ProfilesThe default Target Sequence profile is
Differential Corrector which is what well be using here. The
Differential Corrector search profile targets specific values
defined as independent variables. The target sequence will change
the value of independent variables as needed to achieve the goal
defined by the dependent variables, utilizing a differential
correction algorithm. You can find more in depth information about
the differential correction algorithm in the Astrogator help
system.
1. Right-click the Return segment ( ) in the MCS tree.2. Select
Insert Segment ( ).3. When the segment selection dialog appears,
select Target Sequence ( ).4. Click OK.5. When you return to
Astrogator, the new target sequence will be listed in the
MCS tree.6. Click on the name of the Target Sequence ( ) to make
it editable.7. Change the name to MartianLaunch.
ADD THE SEGMENTS TO THE TARGET SEQUENCE
1. Expand ( ) the MartianLaunch target sequence ( ).2. When you
expand MartianLaunch ( ) you will see a Return segment ( ).3. Drag
the MarsLaunch segment ( ) and drop it inside the target
sequence ( ) before the Return segment ( ).4. Use the same
process to add the remaining segments to the target
sequence.5. Ensure that they are arranged in the following
order:
... MarsLaunch... MarsCoast
... EscapeMnvr... LeaveMarsSOI
Linking Independent VariablesAny element of a nested MCS segment
or linked component that is available for selection as an
independent variable will be identified by a target icon ( ) PAGE
18
appearing beside it. To select a given element as an independent
variable, simply click the associated target icon. Your selection
will be confirmed by the
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
appearance of a check mark over the icon ( ). Linking
independent variables allows the selected value to be changed by a
search profile to achieve targeting goals.
LAUNCH VARIABLESWell set the independent variables for the
launch segments so that we can use them in the search profile.
Allowing Astrogator to adjust these values for us will help ensure
that the spacecraft is headed in the correct direction.
1. Select MarsLaunch ( ) in the MCS tree to display its
properties.2. Click the target icon ( ) beside the Launch Epoch to
mark it as an
independent variable.
ResultsBeneath the MCS tree is a Results... button, which allows
you to specify calculation objects to be reported and targeted for
each segment. Clicking this button will open the User-Selected
Results window, in which you can select calculation objects to
include in the summary report for the currently selected segment,
and to target when defining a search profile for the target
sequence.
TARGET THE LAUNCHYou want to target the launch so the
spacecrafts orbital plane is aligned with Mars velocity vector. You
will add that angle now.
1. Select MarsLaunch ( ).2. Click the Results... button below
the MCS tree.3. Expand the component tree as follows:
... Vector... Angle
4. Double-click the Angle component ( ). When you double-click a
component in the tree, Astrogator will display information about
that component on the right hand side of the panel.
5. Change the name to Orbit Plane Angle (Mars).6. Double-click
the Angle value under Component Details.7. When the reference
selection dialog appears, expand the tree as follows:Page 19
... SampleReturn... Orbit Plane Angle (Mars)
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User selected results window
Will the Martian Space Vehicle Return to Earth?
8. Select Orbit Plane Angle (Mars) ( ).9. Click OK.10. Click OK
to dismiss the Results window for MarsLaunch ( ).
FIGURE 7.
Search ProfilesSearch profiles define goals and modify variables
to achieve them. There are two types of search profiles you can use
in a target sequence--differential correctors and plugins. The
differential corrector profile targets specific values - defined as
independent variables. The target sequence will change the value of
independent variables as needed to achieve the goal defined by the
dependent variables, utilizing a differential correction
algorithm.
Dependent variables are defined in terms of Astrogator's
extensive repertoire of calculation objects. The selections that
appear here were selected in the User-Selected Results window for
that segment accessed via the Results... button. Calculation
objects are selected for dependent variable definition in the
User-PAGE 20
Selected Results window, but the manner in which they will be
used is specified here in the setup of the differential
corrector.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
ORBIT PLANE MATCHING DIFFERENTIAL CORRECTORThe first
differential corrector profile will change the launch epoch to
align the orbit plane with Mars velocity vector. This differential
corrector profile will use estimated values. This type of rough
guess will at least head us in the right direction.
1. Select the MartianLaunch ( ) target sequence. 2. Double-click
the Name value for the Differential Corrector in the Profiles
table
to make it editable.3. Rename it Orbit Plane Matching.4. Click
the Properties... button.5. Ensure that the Variables tab is
selected.6. Set the following:
7. Ensure that the Desired Value for the Orbit Plane Angle
(Mars) constraint is set to zero (0) degrees.
8. Click OK.
Run the Active ProfileYou can configure a Target Sequence to
execute in many different ways depending on the solution you are
trying to achieve.
Should converge in about 6 iterations
1. When you return to Astrogator, change the Action for the
target sequence to Run active profiles.
2. Click Run ( ). When the run finishes, a targeting status grid
will appear.
TABLE 12. Orbit plane matching properties
OPTION VALUELaunch Epoch OnPerturbation 5 minMax Step 1 hrOrbit
Plane Angle (Mars) On
If the differential corrector doesnt converge in one run, click
the green arrow to run it againPage 21
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3D View: Martian launch orbit plane matching
Orbit plane matching adjusted values
Will the Martian Space Vehicle Return to Earth?
FIGURE 8.
Did the profile converge? If so, what is the new launch date and
time?
3. When you finish, close the targeted status grid.4. Bring the
3D Graphics - Mars window to the front.
FIGURE 9.
Are all six (6) iterations visually represented?
INITIAL & FINAL DATE AND TIMEThe Initial and Final fields
beneath the segment parameters area are apparent for every segment
in the MCS and serve the same purpose for each; the Initial field
displays the scenario time and date at the beginning of the
currently selected segment, while the Final field displays the
scenario time and date at the end of that segment. If a segment has
not yet been run, these fields will be marked Not Set for that
segment - since these values are not determined until PAGE 22
the segment is run.
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3D View: Sample return at mars coast
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
The targeter will alter the launch epoch in order to force the
angle to zero. The initial and new values will display below the
Profiles panel.
What is the difference in the initial and final values?
LET ASTROGATOR CHANGE YOUR PERSPECTIVEOnce Astrogator updates
the Initial and Final values for each segment, you can select any
segment in the MCS tree and update the view in the visualization
window such that the SampleReturn spacecraft will be at that
position in time.
1. Select any segment in the MCS tree.2. Click on the unit
selector ( ) beside the Initial time.3. Select Set Animation
Time.4. Bring the 3D Graphics - Mars window to the front.
FIGURE 10.
In the picture above, we selected the EscapeMnvr segment and
updated the animation to the Initial time, so Astrogator positioned
the spacecraft at the beginning of the maneuver. Although the
maneuver doesnt have a visible portion of the orbit, you can see
where the spacecraft will be when it occurs. If we had done the
same thing using the Final time, Astrogator would have positioned
me at the end of the segment.Page 23
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Will the Martian Space Vehicle Return to Earth?
Asymptote Targeting ProfileLets create a second differential
corrector. Using this profile, well target the outgoing asymptote
properties and the energy of the transfer orbit to see if we can
obtain more accurate results.
PROPAGATE VARIABLESFirst, well define the independent variables
for the propagate segment. When we created the propagate segment,
we guessed at the approximate coast time before performing the
escape maneuver. Well mark that as an independent variable and let
Astrogator adjust the amount of time that the spacecraft should
coast.
1. Bring Astrogator to the front.2. Select MarsCoast ( ) in the
MCS tree.3. Click the beside Trip to mark it as an independent
variable ( ).
MANEUVER VARIABLESEarlier you took an initial guess at the X
velocity value needed to get out of Martian gravity in the maneuver
segment (EscapeMnvr). Now, we can mark that as an independent
variable so that Astrogator can adjust it if necessary.
1. Select EscapeMnvr ( ) in the MCS tree to display its
properties.2. Click the target icon ( ) beside the X(Velocity)
value to mark it as an
independent variable ( ).
Maneuver Targeting ComponentsThe second Differential Corrector
profile targets the outgoing asymptote properties and the energy of
the transfer orbit to chane the launch epoch, coast duration and
burn magnitude to match the outgoing asymptote and energy. First,
the proper components need to be added so that they can be selected
in the new Differential Corrector profile.
1. Select EscapeMnvr ( ) in the MCS tree.2. Click the Results...
button.PAGE 24
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
ADD C3 ENERGY
1. When the User-Selected Results dialog appears, expand the
tree as follows:... Target Vector
... C3 Energy2. Double-click the C3 Energy component ( ).3.
Select C3 Energy in the topmost table.4. Double-click the Value for
Central Body in the Components Details area.5. When the component
selection dialog appears, select Mars ( ).6. Click OK.
ADD OUTGOING ASYMPTOTE PARAMETERSThe outing asymptote parameters
will also need to be available to Astrogator for targeting
purposes.
1. Double-click the Outgoing Asymptote Dec component ( ) under
Target Vector ( ).
2. Select Outgoing Asymptote Dec in the topmost table.3.
Double-click the Value for Coord System in the Components Details
area.4. When the reference selection dialog appears, expand the
tree as follows:
... Mars... J2000
5. Select J2000 ( ).6. Click OK.7. Double-click the Outgoing
Asymptote RA component ( ).8. Repeat steps 2-6 to change the
coordinate system for Outgoing Asymptote
RA.9. Click OK.10. Click OK to dismiss the User-Selected Results
dialog.
Asymptote Targeting ProfileWell target the outgoing asymptote
properties and the energy of the transfer orbit using the values
from the Jaqar Swing-by Calculator.
1. Select the MartianLaunch ( ) target sequence. Page 25
2. Click the New... button in the profiles table.
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Will the Martian Space Vehicle Return to Earth?
3. Select Differential Corrector ( ).4. Click OK to add the new
profile to the target sequence.5. Rename the profile Asymptote
Targeting.
CONTROL PARAMETERSThe Control Parameters are independent
variables that you marked for inclusion while setting up the target
sequence. Well set the values for the control parameters and
equality constraints using values obtained using and external
Lambert problem solver.
1. Select the Targeting profile.2. Click the Properties...
button.3. Ensure that the Variables tab is selected.4. Enable the
following:
EQUALITY CONSTRAINTSEquality constraints in the search profile
outline dependant variables to be considered in your analysis. Here
well set the desired value based on the results from the Jaqar
Swing-by Calculator, and again, well let Astrogator adjust those
values as necessary.
1. Select the C3 Energy Equality Constraint.2. Set the
following:
TABLE 13. Asymptote targeting control parameters
CONTROL PARAMETER STATE PERTURBATION MAX STEPLaunch Epoch On 15
min 1 hrStopping Condition Duration Trip On 60 sec 500 secImpulsive
Mnvr Cartesian X On 0.0001 (Default) 0.1 (Default)
TABLE 14. Asymptote targeting equality constraints
EQUALITY CONSTRAINT STATE DESIRED VALUEC3 Energy On 14.3572
km^2/sec^2Outgoing Asymptote Dec On 3.30596 degOutgoing Asymptote
RA On -131.622 degPAGE 26
3. Click OK.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
RUN THE ACTIVE PROFILE
3D View: Martian launch sequence
Now, you can run the selected profile and see what Astrogator
comes up with. Then well apply those changes. Doing this will apply
the values of search profiles' controls and the changes specified
by the segment configuration profiles to the segments within the
target sequence.
1. Ensure that the Action is set to Run active profiles.2. Click
Run ( ).
Did the profile converge? If so, did you achieve the desired
values?
3. Once converged, click the Apply Changes button.4. Change the
Action to Run nominal sequence.
CHANGE YOUR PERSPECTIVE
1. Bring the 3D Graphics - Mars window to the front.2. Mouse
around until you get a good look at the various iterations of
SampleReturns orbit.
FIGURE 11.Page 27
3. When you finish, close the status grid.4. Save ( ) the
scenario ( ).
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Will the Martian Space Vehicle Return to Earth?
Are We Headed In the Right Direction?
3D View:
Lets quickly test the Lambert solver, by propagating out one
year in heliocentric space and seeing if were going in the right
direction using the values that the Jaqar Swing-By Calculator gave
us.
1. Add a Propagate segment ( ) after the MartianLaunch target
sequence ( ).2. Select Propagate ( ) in the MCS tree.3. Change the
color of the segment so that you can clearly identify it in the
visualization windows.4. Change the Propagator to Heliocentric (
).5. Click the Advanced... button.6. Change the Maximum Propagation
Time to one (1) yr (year).7. Click OK.8. Change the Trip value
under Stopping Conditions to one (1) yr (year).9. Click Run (
).
CHANGE YOUR PERSPECTIVE
1. Bring the 3D Graphics - Sun window to the front.2. Mouse
around until you can clearly see where the spacecraft would be
headed.
FIGURE 12.PAGE 28
Is the spacecraft headed in the right direction? Would you
arrive at Earth?
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
The satellite is now headed roughly back toward Earth, but not
quite. A midcourse maneuver will assure the desired Earth arrival
in the orbit.
3. When you finish, delete ( ) the newly added Propagate segment
( ).
Earth ArrivalNow, lets create the midcourse maneuver that will
assure an Earth arrival. The first target sequence launched you
from the surface of Mars and took you to the Mars SOI boundary. The
one we create here will target a maneuver that sets the spacecraft
into a path which results in the desired orbit around Earth.
1. Add a new Target Sequence ( ) below the MartianLaunch ( )
sequence.2. Change the name to EarthArrival.
MODEL THE MID-COURSE MANEUVERThe first target sequence left you
at Mars SOI on a path towards Earth, but as we just demonstrated
that path isnt quite accurate enough. We can add a midcourse
maneuver here that will get us at the correct perigee altitude for
aerobraking and put us in the same orbital plane as the ISS, which
is where we want to be. A midcourse maneuver will assure an arrival
in the desired orbit geometry around the Earth.
1. Add a Maneuver segment ( ) to the EarthArrival ( )
sequence.2. Double-click the new Maneuver segment ( ).3. Change the
name of the Maneuver segment ( ) to MidCrsMnvr.
There is no need to adjust the color. The maneuver segment will
not be distinguishable in the visualization windows.
4. Select MidCrsMnvr ( ) in the MCS tree.5. Set the
following:
TABLE 15. Mid course maneuver stopping conditions
OPTION VALUEAltitude Control Thrust VectorThrust Axes VNC (Sun)X
(Velocity)Page 29
Independent variable ( )
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Will the Martian Space Vehicle Return to Earth?
Well use the velocity relative to the sun to define the thrust
axes because were now in heliocentric space. Astrogator will adjust
all three components of the maneuver to achieve the correct perigee
altitude and orbital plane.
PROPAGATE TO EARTH SOINow, well add the first of two propagate
segments after the maneuver. The first propagate segment takes the
satellite close to Earths SOI.
1. Add a Propagate segment ( ) after the maneuver.2.
Double-click the new Propagate segment ( ).3. Set the
following:
4. Change the Propagator to Heliocentric.5. Click the
Advanced... button.6. Change the Maximum Propagation Time to one
(1) yr.7. Click OK.
STOPPING CONDITIONS
1. Click the Insert... button.2. Select the R Magnitude item (
).3. Click OK to add the new Stopping Condition to the table.4.
Change the Trip value for R Magnitude to two million (2e+006) km.5.
Select the Duration stopping condition in the table.6. Click the
Remove button.
Y (Normal) Independent variable ( )Z (Co-normal) Independent
variable ( )
TABLE 16. To Earth SOI segment properties
OPTION VALUEName ToEarthSOIColor Any color not currently being
used.
TABLE 15. Mid course maneuver stopping conditions
OPTION VALUEPAGE 30
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
PROPAGATE TO EARTH PERIAPSISNow, add the second propagate
segment. The second propagate goes to Earth periapsis. This
periapsis will be targeted to 150 km altitude and in the same plane
as the space station.
1. Add a second Propagate segment ( ) after ToEarthSOI ( ).2.
Double-click the new Propagate segment ( ).3. Set the
following:
4. Click OK.
STOPPING CONDITIONS
1. Click the Insert... button.2. Select the Periapsis item (
).3. Click OK to add the new Stopping Condition to the table.4.
Select the Duration stopping condition in the table.5. Click the
Remove button.
TARGET THE B-PLANE Now we have an arrival trajectory, which is
close, but we want to return to Earth. The best way to do that is
to target the B-plane. The B-plane is a planar coordinate system
that allows targeting during a gravity assist or for planetary
orbit insertion. It can be thought of as a target attached to the
assisting body. If you have a trajectory that is close to the
encounter planet, the B-plane gives you targets that behave very
linearly, which is important with the differential corrector
targeting scheme in Astrogator. However, had we targeted the
B-plane before we had proper initial conditions (i.e. we were
pointing in some random direction this would not have worked since
we may never have crossed the plane. We first had to target to get
close to Earth, and only then were we close enough to Earth with
our trajectory to use B-plane targeting.
TABLE 17. To perigee segment properties
OPTION VALUEName ToPerigeeColor Any color not currently being
used.Page 31
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Will the Martian Space Vehicle Return to Earth?
FIGURE 13.
The B-plane is defined as the plane that contains the focus of
an idealized two-body trajectory (assumed to be a hyperbola) that
is perpendicular to the incoming asymptote of that hyperbola. The
incoming and outgoing asymptotes, and, the focus are contained in
the trajectory plane, which is perpendicular to the B-plane. The
intersection of the B-plane and the trajectory plane defines a line
in space. The B-vector is defined to lie alone this line, starting
on the focus and ending at the spot where the incoming asymptote
pierces the B-plane. The vectors and lie in the B-plane and are
used as axes.
USER SELECTED RESULTS
1. Select the ToPerigee propagate segment ( ).2. Click the
Results... button.3. Expand the component tree as follows:
... MultiBody
... BDotR
... BDotT4. Double-click the BDotR component ( ) to add it to
the list.5. Select BDotR in the topmost table.6. Double-click the
Value for Reference Vector in the Components Details area.7. When
the reference selection dialog appears, expand the tree as
follows:PAGE 32
... Earth
... Orbit Normal
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
8. Select Orbit Normal ( ).9. Click OK.10. Double-click the
Value for Target Body in the Components Details area.11. Select
Earth ( ).12. Click OK.13. Double-click the BDotT component ( ) to
add it to the list.14. Repeat steps 4-11 for BDotT.15. Click
OK.
Earth Arrival Differential CorrectorsUsing an initial rough
estimate of the geometry of the orbit were trying to enter, well
target the B-Plane.
1. Select EarthArrival ( ) in the MCS tree.2. Select the
Differential Corrector.3. Rename it BPlane.4. Click the
Properties... button.5. Enable the maneuvers as active
controls:
6. Enable the equality constraints as active controls:
7. Click OK.
TABLE 18. B-plane targeting control parameters
CONTROL PARAMETERS STATEImpulsive Mnvr.Cartesian X OnImpulsive
Mnvr.Cartesian Y OnImpulsive Mnvr.Cartesian Z On
TABLE 19. B-plane targeting equality constraints
EQUALITY CONSTRAINTS STATE DESIRED VALUEBDotR On 10,000 kmBDotT
On 20,000 kmPage 33
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3D View: B-plane targeting
Will the Martian Space Vehicle Return to Earth?
RUN THE ACTIVE PROFILENow, you can run the selected BPlane
profile and let Astrogator adjust the BDot values. Then well apply
those changes. Doing this will apply the values of search profiles'
controls and the changes specified by the segment configuration
profiles to the segments within the target sequence.
1. Ensure that the Action is set to Run active profiles.2. Click
Run ( ).
Did the profile converge? If so, did you achieve the desired
values?
3. When you finish, close the status grid.4. Bring the 3D
Graphics - Sun window to the front.
FIGURE 14.
Did targeting the B-Plane get you closer to Earth?
Lets see how close.
LET ASTROGATOR CHANGE YOUR PERSPECTIVEPAGE 34
1. Bring Astrogator to the front.2. Click on the unit selector (
) beside the Final time.
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3D View (Earth): B-plane targeting
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
3. Select Set Animation Time.4. Bring the 3D Graphics - Earth
window to the front.
FIGURE 15.
Target Keplerian ElementsWe can use another differential
corrector to achieve the desired perigee altitude for aerobraking
and to match the plane of the space stations orbit.
ALTITUDE OF PERIAPSIS
1. Select the ToPerigee propagate segment ( ).2. Click the
Results... button.3. Expand the component tree as follows:
... Keplerian Elems
... Altitude of Periapsis4. Double-click the Altitude of
Periapsis component ( ) to add it to the list.
RELATIVE INCLINATIONPage 35
1. Expand the component tree as follows:... Formation
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... RelativeValue2. Double-click the RelativeValue component ( )
to add it to the list.3. Select RelativeValue in the topmost
table.4. Set the following:
RELATIVE RAAN
1. Expand the component tree as follows:... Formation...
RelativeValue
2. Double-click the RelativeValue component ( ) to add it to the
list.3. Select RelativeValue in the topmost table.4. Set the
following:
5. Click OK.
KEPLERIAN ELEMENTS DIFFERENTIAL CORRECTORLets create a second
differential corrector to target Keplerian elements.
1. Select EarthArrival ( ) in the MCS tree.2. Click the New...
button above the profiles table.
TABLE 20. Relative inclination values
OPTION VALUECalcObject Keplerian Elems/InclinationComponentName
RelativeInclinatinReference Selection
UserSpecifiedReferenceReference Satellite/SpaceStation
TABLE 21. Relative RAAN values
OPTION VALUECalcObject Keplerian Elems/RAANComponentName
RelativeRAANReference Selection UserSpecifiedRefreenceReference
Satellite/SpaceStationPAGE 36
3. Select Differential Corrector ( ).
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4. Click OK to add the new profile to the target sequence.5.
Rename the profile KeplerianElems.6. Click Properties...7. Enable
the maneuvers as active controls:
8. Enable the equality constraints as active controls:
Well set the desired relative values to zero since were
targeting the space station.
9. Click OK.
RUN THE ACTIVE PROFILENow, you can run the selected
KeplerianElems profile.
1. Ensure that the Action is set to Run active profiles.2. Click
Run ( ).
Did the profile converge? If so, did you achieve the desired
values?
3. Once converged, click the Apply Changes button.4. Change the
Action to Run nominal sequence.
TABLE 22. Keplerian element targeting control parameters
CONTROL PARAMETERS STATE PERTURBATIONImpulsive Mnvr.Cartesian X
On 0.00001 km/secImpulsive Mnvr.Cartesian Y On 0.00001
km/secImpulsive Mnvr.Cartesian Z On 0.00001 km/sec
TABLE 23. Keplerian element targeting equality constraints
EQUALITY CONSTRAINTS STATE DESIRED VALUEAltitude of Periapsis On
150 kmRelative Inclination On 0.0Relative RAAN On 0.0Page 37
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3D View: Keplerian element targeting
Will the Martian Space Vehicle Return to Earth?
LET ASTROGATOR CHANGE YOUR PERSPECTIVE
1. Click on the unit selector ( ) beside the Final time.2.
Select Set Animation Time.3. Bring the 3D Graphics - Earth window
to the front.
FIGURE 16.
4. When you finish, close the status grid.5. Save ( ) the
scenario ( ).
Earth CaptureThe satellite is now arriving at Earth in the
proper orbit.
1. Add a new Target Sequence ( ) below the EarthArrival ( )
sequence.2. Change the name to EarthCapture.
MANEUVERLets add a maneuver that will put the spacecraft in the
initial capture orbit.
1. Add a Maneuver segment ( ) to the EarthCapture ( )
sequence.PAGE 38
2. Rename the segment CaptureMnvr.3. Change the name of the
Maneuver segment ( ) to CaptureMnvr.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
4. Select CaptureMnvr ( ) in the MCS tree.5. Set the
following:
RESULTS
1. Click the Results... button.2. Expand the component tree as
follows:
... Keplerian Elems
... Eccentricity3. Double-click the Eccentricity component ( )
to add it to the list.4. Click OK.
PROPAGATE
1. Add a Propagate segment ( ) after the maneuver.2. Select the
new Propagate segment ( ).3. Set the following:
4. Click OK.
STOPPING CONDITIONSNow, well add a stopping condition to
1. Click the Insert... button.
TABLE 24.
OPTION VALUEAltitude Control Antivelocity Vector
Delta V Magnitude2 km/secMark as independent variable ( )
TABLE 25. To apoasis segment properties
OPTION VALUEName ToApoapsisColor Any color not currently being
used.Page 39
2. Select the Apoapsis item ( ).3. Click OK to add the new
Stopping Condition to the table.
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Will the Martian Space Vehicle Return to Earth?
4. Select the Duration stopping condition in the table.5. Click
the Remove button.
Earth Capture Differential CorrectorThe space station is in a
circular orbit. The eccentricity of that orbit is zero. Although we
want to match that value well target a larger value and see if we
can get to an elliptical orbit. Then we can simulate
aerobraking.
1. Select EarthCapture ( ) in the MCS tree.2. Select the
Differential Corrector.3. Rename it Target Capture.4. Click the
Properties... button.5. Enable ImpulsiveMnvr.SphericalMagnitude.6.
Enable the Eccentricity equality constraint.7. Set the Desired
Value for Eccentricity to 0.6.8. Set the Tolerance value to 1e-5.9.
Click OK.
RUN!
1. Ensure that the Action is set to Run active profiles.2. Click
Run ( ).
Did the profile converge? If so, did you achieve the desired
values?
3. Once converged, click the Apply Changes button.4. Change the
Action to Run nominal sequence.5. When you finish, close the status
grid.
LET ASTROGATOR CHANGE YOUR PERSPECTIVE
1. Click on the unit selector ( ) beside the Final time.2.
Select Set Animation Time.3. Bring the 3D Graphics - Earth window
to the front.PAGE 40
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3D View: Target capture
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
FIGURE 17.
AerobrakingThe satellite is captured in an elliptical orbit.
Now, we need to work our way down to a circular orbit like the one
that the space station is in.
1. Add a Propagate segment ( ) after the EarthCapture target
sequence ( ).2. Double-click the new Propagate segment ( ).3. Set
the following:
4. Click OK.
STOPPING CONDITIONS
1. Select Aerobraking ( ) in the MCS tree.2. Click the Insert...
button.
TABLE 26. Aerobraking segment properties
OPTION VALUEName AerobrakingColor Any color not currently being
used.Page 41
3. Select the Periapsis item ( ).
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4. Click OK to add the new Stopping Condition to the table.5.
Repeat steps 3-5 to add a second Periapsis Stopping Condition.6.
Select the Duration stopping condition in the table.7. Click the
Remove button.
Automatic SequencesAutomatic Sequences are MCS elements that are
structurally similar to Sequence segments, but are not MCS
segments, properly. Rather, Automatic Sequences can be assigned to
Propagate and Maneuver (Finite) segments, and function as
subroutines by executing in response to specified stopping
conditions of those segments.
THE AUTOMATIC SEQUENCE BROWSERThe Automatic Sequence Browser
contains a list of all Automatic Sequences defined for the
Astrogator satellite. You define or edit Automatic Sequences, in
the Automatic Sequence Browser window.
1. Click the Automatic Sequence Browser button ( ) on the MCS
Controls.2. Click the New Button.3. Rename it SmallBurn.4. Click
OK.
EDIT THE AUTOMATIC SEQUENCETo simulate aerobraking the apoapsis
altitude is decreased by firing a thruster at every periapsis in
the antivelocity direction.
1. Click the Edit button.2. Add a Maneuver segment ( ) to the
Automatic Sequence.3. Set the following:
TABLE 27. Small burn sequence values
OPTION VALUEAttitude Control Antivelocity VectorDelta V
Magnitude 0.25 km/secPAGE 42
4. Click OK.5. Click OK to dismiss the Automatic Sequence
Browser.
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
The Automatic Sequence for this propagate segment will run for
seven periapsides and the propagate segment will stop on the eight
periapsis.
EDIT STOPPING CONDITIONSNow we can use the automatic sequence in
the stopping condition to simulate the aerobraking.
1. Select the first Periapsis entry in the Stopping Condition
table.2. Set the following:
3. Select the second Periapsis entry in the Stopping Condition
table.4. Chane the repeat count to 8.
RUN!
1. Select EarthCapture ( ) in the MCS tree.2. Ensure that the
Action is set to Run active profiles.3. Click Run ( ).
Did the profile converge? If so, did you achieve the desired
values?
LET ASTROGATOR CHANGE YOUR PERSPECTIVE
1. Click on the unit selector ( ) beside the Final time.2.
Select Set Animation Time.3. Bring the 3D Graphics - Earth window
to the front.
TABLE 28.
OPTION VALUESequence SmallBurnMax Trip Times 7Page 43
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3D View: Aerobraking
Will the Martian Space Vehicle Return to Earth?
FIGURE 18.
4. When you finish, close the status grid.5. Save ( ) the
scenario ( ).
Circular Phasing OrbitWell add another target sequence will
result in a phasing orbit. Two Hohmann transfers will be utilized
to circularize the orbit at an altitude of 800 km.
1. Add a new Target Sequence ( ) below the EarthCapture ( )
sequence.2. Change the name to CircularPhasingOrbit.
Add a Propagate SegmentFirst, well add a propagate segment that
will get us to apogee.
1. Use the same process to add a Propagate segment ( ).2.
Double-click the new Propagate segment ( ).3. Enter the
following:PAGE 44
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WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
4. Click OK.
STOPPING CONDITIONS
1. Click the Insert... button.2. Select the Apoasis stopping
condition ( ).3. Click OK to add the new Stopping Condition to the
table.4. Select the Duration stopping condition in the table.5.
Click the Remove button.
Add a Maneuver Segment1. Use the same process to add a Maneuver
segment ( ) after ToApogee ( ).2. Rename the new Maneuver segment (
) BurnOne.3. Select BurnOne ( ) in the MCS tree.4. Ensure that the
Attitude tab is selected.5. Set the following:
6. Click the ( ) beside X(Velocity) to mark it as an independent
variable ( ).
CREATE A NEW CALCULATION OBJECTThe second maneuver should be a
half-revolution after the first maneuver. The first maneuver was at
apogee, but the maneuver may have pushed the orbit higher so the
current location is now perigee. Therefore, we cant use a
TABLE 29.
OPTION VALUEName ToApogeeColor Select a color that isnt being
used by any segment.
TABLE 30.
OPTION VALUEAltitude Control Thrust VectorX(Velocity) 0
km/secPage 45
perigee stopping condition to find the location of the second
maneuver.
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Will the Martian Space Vehicle Return to Earth?
Instead, well use a mean anomaly difference of 180 degrees. But
first, we have to define a calculation object that gives us the
difference in mean anomaly.
1. Select the Astrogator Browser option from the View menu in
the STK Workspace to open the component browser.
2. Expand the component tree as follows:...
CalculationObjects... Math
3. Select Math.4. Select Difference ( ) components table.5.
Click the Duplicate button.6. Rename it MeanAnomalyDifference.7.
Click OK.8. When the new component (Mean Anomaly Difference)
appears in the table,
double-click it.9. Double-click the CalcObject value.10. Expand
the component tree as follows:
... Keplerian Elems
... MeanAnomaly11. Select MeanAnomaly ( ).12. Click OK.13. Click
OK to dismiss the component editing window.14. Click OK to dismiss
the Astrogator Browser.
Add a Second Propagate SegmentSince the maneuver (BurnOne) could
have flipped apogee and perigee, we dont know to which apsis were
propagating, but we do know that we want to propagate to the next
apsis.
1. Use the same process to add a Propagate segment ( ) after
BurnOne ( ).2. Double-click the new Propagate segment ( ).3. Enter
the following:
TABLE 31. Half around properties
OPTION VALUEPAGE 46
Name HalfAroundColor Select a color that isnt being used by any
segment.
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4. Click OK.
STOPPING CONDITIONSWell add the same stopping condition to the
second propagate segment that we used for the first to ensure that
we stop at the next apsis.
1. Click the Insert... button.2. Select the UserSelect stopping
condition ( ).3. Click OK to add the new Stopping Condition to the
table.4. Set the User Calc Object to Mean Anomaly Difference.5.
Click OK.6. Set the Trip value to zero (0) deg.7. Select the
Duration stopping condition in the table.8. Click the Remove
button.
Add a Second Maneuver Segment1. Use the same process to add a
Maneuver segment ( ) after
HalfAround ( ).2. Rename the new Maneuver segment ( ) BurnTwo.3.
Select BurnTwo ( ) in the MCS tree.4. Ensure that the Attitude tab
is selected.5. Set the following:
6. Click the ( ) beside X(Velocity) to mark it as an independent
variable ( ).
RESULTS
1. Click the Results... button.2. Expand the component tree as
follows:
TABLE 32.
OPTION VALUEAltitude Control Thrust VectorX(Velocity) 0Page
47
... Geodetic
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... Altitude3. Double-click the Altitude component ( ) to add it
to the list.4. Expand the component tree as follows:
... Keplerian Elems
... Eccentricity5. Double-click the Eccentricity component ( )
to add it to the list.6. Click OK.
Phasing Orbit Differential CorrectorsWell now use the target
sequence to enter an 800 km altitude circular phasing orbit above
the space stations orbit. Well see the desired values for this run
to reflect that.
1. Select CircularPhasingOrbit ( ) in the MCS tree.2. Select the
Differential Corrector.3. Rename it TargetPhasing.4. Click the
Properties... button.5. Enable the two maneuvers as active
controls:
6. Enable the equality constraints as active controls:
7. Set the Tolerance for Eccentricity value to 1e-5.8. Click
OK.
RUN!
TABLE 33. Target phasing control parameters
CONTROL PARAMETERS STATEImpulsive Mnvr.Cartesian X OnImpulsive
Mnvr.Cartesian X On
TABLE 34. Target phasing equality constraints
EQUALITY CONSTRAINTS STATE DESIRED VALUEAltitude On 800
kmEccentricity On 0PAGE 48
1. Select CircularPhasingOrbit ( ) in the MCS tree.
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3D View: Circular phasing orbit
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
2. Ensure that the Action is set to Run active profiles.3. Click
Run ( ).
Did the profile converge? If so, did you achieve the desired
values?
4. Once converged, click the Apply Changes button.5. Change the
Action to Run nominal sequence.
LET ASTROGATOR CHANGE YOUR PERSPECTIVE
1. Click on the unit selector ( ) beside the Final time.2.
Select Set Animation Time.3. Bring the 3D Graphics - Earth window
to the front.
FIGURE 19.
Final OrbitNow that the targeter has put us in the final phasing
orbit, we need to propagate to see the orbit. Well propagate for
five days in the final orbit.Page 49
1. Add a Propagate segment ( ) after the CircularPhasingOrbit
target sequence ( ).
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Will the Martian Space Vehicle Return to Earth?
2. Double-click the new Propagate segment ( ).3. Enter the
following:
4. Set the Trip value under the Stopping Conditions to 5
days.
RUN!
1. Select CircularPhasingOrbit ( ) in the MCS tree.2. Ensure
that the Action is set to Run active profiles.3. Click Run ( ).
Did the profile converge? If so, did you achieve the desired
values?
LET ASTROGATOR CHANGE YOUR PERSPECTIVE
1. Select the Final Propagate ( ) segement in the MCS tree.2.
Click on the unit selector ( ) beside the Final time.3. Select Set
Animation Time.4. Bring the 3D Graphics - Earth window to the
front.
TABLE 35. Half around properties
OPTION VALUEName Final OrbitColor Select a color that isnt being
used by any segment.PAGE 50
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3D View: Final prop to station
WILL THE MARTIAN SPACE VEHICLE RETURN TO EARTH?
FIGURE 20.
Data ReportingMCS ephemeris segments just give a listing of the
segments run. It will show the autosequences and MCS segments and
is good for getting an idea of how the run progressed.
The Maneuver Summary report style is available only to
Astrogator satellites. This report shows a summary of the maneuver
segments in the MCS that have been run.
1. Select SampleReturn( ) in the Object Browser.2. Open the
Report & Graph Manager ( ).3. Select the Maneuver Summary
Report style ( ).4. Click Generate...
How much Delta-V does this mission require? What is the
estimated fuel usage based on the engine models selected for
the maneuvers?
The MCS Ephemeris Segments report style shows which Astrogator
segment produced each interval of ephemeris.
1. Bring the Report & Graph Manager ( ) to the front.2.
Select the MCS Ephemeris Segments Report style ( ).3. Click
Generate...Page 51
4. Take a moment to discuss the report contents with your
instructor.
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Will the Martian Space Vehicle Return to Earth?
When You Finish1. Close all open status grids.2. Close any open
reports.3. Close the Report & Graph Manager ( ).4. Click OK to
dismiss SampleReturns ( ) properties ( ) and save your
changes.5. Save ( ) the scenario ( ).PAGE 52
Will the Martian Space Vehicle Return to Earth?Problem
StatementBreak It DownSolution
Model the World!Model a SpacecraftObject GraphicsSelect a
Propagator
What Is Astrogator?Mission Control SequenceMCS Controls
Model the Martian LaunchAdd a Launch SegmentLaunch
ParametersBurnout Velocity
Model the Coast to the Martian OrbitThe Component
BrowserCustomize ComponentsEdit the Propagator
Propagate Segment PropertiesAdd a Maneuver SegmentThrust
VectorAttitude Parameters
Add a Second Propagate SegmentDefine the Properties of the
Second Propagator
Change Your PerspectiveCreate a Target SequenceVector Geometry
ToolCreate the Orbit Normal VectorCreate the Orbital PlaneCreate
the Angle Between
Target Sequence ProfilesAdd the Segments to the Target
Sequence
Linking Independent VariablesLaunch Variables
ResultsTarget the Launch
Search ProfilesOrbit Plane Matching Differential Corrector
Run the Active ProfileInitial & Final Date and TimeLet
Astrogator Change Your Perspective
Asymptote Targeting ProfilePropagate VariablesManeuver
Variables
Maneuver Targeting ComponentsAdd C3 EnergyAdd Outgoing Asymptote
Parameters
Asymptote Targeting ProfileControl ParametersEquality
ConstraintsRun the Active ProfileChange Your Perspective
Are We Headed In the Right Direction?Change Your Perspective
Earth ArrivalModel the Mid-Course ManeuverPropagate to Earth
SOIStopping ConditionsPropagate to Earth PeriapsisStopping
ConditionsTarget the B-PlaneUser Selected Results
Earth Arrival Differential CorrectorsRun the Active ProfileLet
Astrogator Change Your Perspective
Target Keplerian ElementsAltitude of PeriapsisRelative
InclinationRelative RAANKeplerian Elements Differential
CorrectorRun the Active ProfileLet Astrogator Change Your
Perspective
Earth CaptureManeuverResultsPropagateStopping Conditions
Earth Capture Differential CorrectorRun!Let Astrogator Change
Your Perspective
AerobrakingStopping Conditions
Automatic SequencesThe Automatic Sequence BrowserEdit the
Automatic SequenceEdit Stopping ConditionsRun!Let Astrogator Change
Your Perspective
Circular Phasing OrbitAdd a Propagate SegmentStopping
Conditions
Add a Maneuver SegmentCreate a New Calculation Object
Add a Second Propagate SegmentStopping Conditions
Add a Second Maneuver SegmentResults
Phasing Orbit Differential CorrectorsRun!Let Astrogator Change
Your Perspective
Final OrbitRun!Let Astrogator Change Your Perspective
Data ReportingWhen You Finish
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