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Astrodynamics (AERO0024)
TP1: Introduction
2
Contact details
Space Structures and Systems Lab (S3L)
Structural Dynamics Research Group
Aerospace and Mechanical Engineering Department
Room: +2/418 (B52 building)
04 3669535
Teaching Assistant Amandine Denis
3
Today’s program
Objectives
Presentation of STK
Exercise 1: « What does STK do, anyway? »
Exercise 2: Do It Yourself!
4
Objectives of this session
Discover STK and its possibilities
Discover STK interface
Discover basic functions and options
Illustrate the first lesson
5
Objectives of this session
At the end of this session, you should be able to:
Create a new scenario
Handle graphics windows (2D and 3D, view from/to, …)
Use common options of the Properties Browser
Insert a satellite in three different ways (database, Orbit
Wizard, manually)
Insert a facility
Calculate a simple access
Generate simple reports
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Presentation of STK
Design, analyze, visualize, and optimize
land, sea, air, and space systems.
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Presentation of STK – interface
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9
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Presentation of STK
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Presentation of STK – basic elements
New scenario - Model the World!
Insert object - Populate the World!
Properties browser - Decide everything!
Animation
Reports
Tabs
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Exercise 1
First contact:
« What does STK do, anyway? »
Illustration of a Molniya orbit
Notion of scenario
Rules of thumb
Orbit Wizard
Insertion of a facility
Graphics windows
Calculation of a simple access
AGI tutorial
14
Exercise 1: what does STK do, anyway?
How many periods of access?
When does the first access occur?
What is the duration of the first access?
Remarks/questions ?
Are Molniya orbits really a great way to spy on the USA?
15
Exercise 2
Do It Yourself! :
Application to the satellites of
the first lesson
Insertion of satellites and definition of orbits:
• Using Orbit Wizard
• Importing from Data Base
• Manually
Illustration of differents satellites and orbits
Options of visualization
16
Exercise 2: application to the 1st lesson
To create a satellite:
Insert >>New… >> Satellite
Orbit wizard : cfr ex1
From Database
Define properties
Visualization:
Day/night limit ( 2D graphics Properties Browser >>
Lighting)
>> Represent in STK all the satellites named during the first lesson.
17
Debriefing:
Exercise 2: application to the 1st lesson
Astrodynamics(AERO0024)
TP2: Introduction (2)
2
Today’s program
Objectives
Exercise 1: A concrete problem
Exercise 2: Use in celestial mechanics
Exercise 3: Delfi-C3 operation
3
Objectives of this session
At the end of this session, you should be able to:
Use STK autonomously to solve simple problemsDefine and use constraintsCalculate accessImport and visualize planets
4
Exercise 1
A concrete problem:
« When could I see the ISS ? »
Outline to build a scenario
Constraints
AGI tutorial
5
Exercise 2
Use in celestial mechanics:
The Venus Transit of 2004
Planets and orbits
Insertion of sensors
Access calculation (Deck Access)
AGI tutorial
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7
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Exercise 3
Delfi-C3 operations
When does the Delfi-C3 team have access to their satellite?
When can they operate it?
How much does it help if the OUFTI-1 ground station is also used?
How long can the two teams communicate through Delfi-C3 transponder ?
Astrodynamics(AERO0024)
TP3: Orbital elements
2
Today’s program
Objectives
Exercises 1 & 2: SSO satellites
Exercise 3: XMM - RKF7 algorithm
3
Objectives of this session
At the end of this session, you should be able to:
Calculate orbital elements
Check your results with STK
Create customized reports
Export reports and use data in Matlab
4
Exercise 1 & 2: SSO satellites
Ex. 1:
Determine the altitude and the inclination of a sun-synchronous satellite for which T=100 min (circular orbit).Use STK to check your results.
5
Exercise 1 & 2: SSO satellites
Ex. 2:
Determine the perigee and apogee for the following satellite:
- SSO- Constant argument of perigee- T = 3h
Use STK to check your results.
6
Exercise 3 : XMM - RKF7 algorithm
Reproduce graph from Lecture 4, showing time-step of the RKF7(8) algorithm vs true anomaly for XMM satellite.
XMM data:Perigee = 7000 kmApogee = 114000 kmi = 40°
Astrodynamics(AERO0024)
TP4: Astrogator
2
Today’s program
Objectives
Introduction to Astrogator
Exercise 1: OUFTI-1
Exercise 2: Hohmann transfer
3
Today’s objectives
After this exercise session, you should be able to:
design missions involving orbital, impulsive maneuvers
This imply that you will be able to:
• Use Astrogator when appropriate
• Create a simple mission control sequence (MCS)
• Use the following segments: ‘initial state’, ‘propagate’, ‘impulsive maneuver’
• Create summaries
4
Today’s program
Introduction to Astrogator⇒ What is it ?⇒ Components of Astrogator:
• Mission Control Sequence• Segments• Stopping conditions
Ex.1: OUFTI-1
Ex.2: Hohmann transfer
5
What’s Astrogator?
Astrogator is STK’s mission planning module
Used for:⇒ Trajectory design⇒ Maneuver planning⇒ Station keeping⇒ Launch window analysis⇒ Fuel use studies
Derived from code used by NASA contractors
Embedded into STK
6
Astrogator in STK
Astrogator is one of 11 satellite propagators
Propagator generates ephemeris
Astrogator satellite acts like other STK satellites⇒ Can run STK reports (including Access) ⇒ Can animate in 3D and 2D windows
Generates ephemeris by running Mission Control Sequence (MCS)
Components used in MCS configured in AstrogatorBrowser
Astrogator
Mission Control SequenceConfiguration
Mission Control SequenceConfiguration
Astrogator
Runs Mission ControlSequence
EphemerisEphemeris
Other MissionData
Other MissionData
8
The Mission Control Sequence
A series of segments that define the problem
A graphical programming language
Two types of segments⇒ Segments that produce ephemeris⇒ Segments that change the run flow of the MCS
Segments pass their final state as the initial state to the next segment⇒ Some segments create their own initial state
9
The Mission Control Sequence
State
Segment 1
State
Segment 2
State
Ephemeris
Ephemeris
10
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MCS tree
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MCS toolbar
13
14
15
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Parameters of the segment currently selected
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Segments
Two types:
That produce ephemeris
That change the run flow
18
Segments that produce ephemeris
Initial State – specifies initial conditions
Launch – simulates launching
Propagate – integrate numerically until some event
Maneuver – impulsive or finite
Follow – follows leader vehicle until some event
Update – updates spacecraft parameters
19
Initial state segment
Specify spacecraft state at some epoch
Choose any coordinate system
Enter in Cartesian, Keplerian, etc.
Enter spacecraft properties: mass, fuel, etc.
20
Launch segment
Specify launch and burnout location
Specify time of flight
Use any central body
Connects launch and burnout points with an ellipse
Creates its own initial state
21
Propagate segment
Numerically integrates using chosen propagator
Propagator can be configured in Astrogator browser
Propagation continues until stopping conditionsare met
22
Stopping conditions
Define events on which to stop a segment
Stop when some “calc object” reaches a desired value ⇒ A calc object is any calculated value, such as an
orbital element ⇒ Calc objects can be user-defined
23
Stopping conditions
Can also specify constraints:⇒ Only stop if another calc object is =, <, >, some
value ⇒ Determines if exact point stopping condition is met,
then checks if constraints are satisfied ⇒ Multiple constraints behave as logical “And”
Segments can have multiple stopping conditions⇒ Stops when the first one is met ⇒ Behaves as a logical “Or”
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Stopping conditions
Multiple conditions :
« OR »
Constraints :
« AND »
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Maneuver segment
Maneuver segment owns two distinct segments:
⇒ Finite maneuver⇒ Impulsive maneuver
Combo box controls which one is run
Finite maneuver created from impulsive maneuver with “Seed” button
26
Impulsive maneuver
Adds delta-V to the current state
Can specify magnitude and direction of delta-V
Computes estimated burn duration and fuel usage, based on chosen engine
Can configure engine model in Astrogator browser
27
Impulsive maneuver
State
Impulsive ManeuverAdd delta-V to state
State
28
Finite maneuver
Works like propagate segment, thrust added to force model
Can specify the direction of the thrust vector
⇒ Can be specified in plug-in
Magnitude of thrust comes from engine model
29
Follow segment
Choose leader to follow
Specify offset from the leader
Follow leader between “joining conditions” and “separation conditions”
⇒ Behave just like stopping conditions
Creates its own initial state
30
Update segment
Used to update spacecraft properties
Useful to simulate stage separation, docking, etc
Set properties to a new value, or add or subtract from their current value
31
Update segment
State
UpdateUpdate state parameters
State
32
Segments that change run flow
Auto-Sequences – called by propagate segments
Target Sequence – loops over segments, changing values until goals are met
Backwards Sequence – changes direction of propagation
Return – exits a sequence
Stop – stops computation
33
Auto-sequences
Instead of stopping a segment, stopping conditions can trigger an auto-sequence
An auto-sequence is another sequence of segments ⇒ Behaves like a subroutine
After the auto-sequence is finished, control returns to the calling segment
Auto-sequences can inherit stopping conditions from the calling segment
Automatic sequence browser
34
Auto-sequences example
Initial State
Propagate
Burn In PlaneSequence
Burn Out Of PlaneSequence
Duration = 1 day Periapsis Apoapsis
Finite ManeuverIn Plane
Finite ManeuverOut of Plane
Duration = 100 sec Duration = 100 sec
35
Target sequence
Define maneuvers and propagations in terms of the goal they are intended to achieve
Next week !
36
Backward sequence
Segments in backward sequences propagated backwards:
⇒ Propagate & finite maneuvers integrated with negative time step⇒ Impulsive maneuvers’ delta-Vs are subtracted
Can pass initial or final state of sequence to next segment
37
Questions
38
Today’s program
Introduction to Astrogator
Ex.1: OUFTI-1
Ex.2: Hohmann transfer
39
Exercise 1: OUFTI-1
Propagate the orbit of OUFTI-1 using classical two-body and Astrogator (Earth point mass and HPOP), compare the results.
OUFTI-1:354 x 1447 km, 71°i.e. ra = 7825.14 km, rp = 6732.14 km, e = 0.075
40
Today’s program
Introduction to Astrogator
Ex.1: OUFTI-1
Ex.2: Hohmann transfer
41
Exercise 2: ‘simple’ Hohmann transfer
‘Simple’:- coplanar maneuver
- no use of ‘target sequence’
Most efficient 2-burn method (in terms of ΔV)
Elliptical transfer orbit⇒ periapsis at the inner orbit⇒ apoapsis at the outer orbit
Represent Hohmann transfer (from 322km to GEO) using Astrogator.
42
1vΔ
2vΔ
1r2r
( )2
11 1 2 1
2v rr r r r
μ μΔ = −
+
( )1
22 1 2 2
2v rr r r r
μ μΔ = − +
+
circvrμ
=2 1
ellipvr a
μ ⎛ ⎞= −⎜ ⎟⎝ ⎠
Exercise 2: ‘simple’ Hohmann transfer
43
Exercise 2: ‘simple’ Hohmann transfer
• Initial circular orbit: 322 km
• Δv1=2.4195 km/s
• Transfer orbit
• Δv2=1.4646 km/s
• Final circular orbit: GEO
Astrodynamics(AERO0024)
TP5: Astrogator & Targeter
2
Today program
Objectives
Introduction to Astrogator – Targeter
Ex.1: Hohmann using target sequences
Ex.2: Hohmann vs. bi-elliptic transfer
3
Today’s objectives
After this exercise session, you should be able to:
Define and use target sequences
Make videos of your scenarios
4
Introduction to Astrogator - Targeter
Target sequence:
1. Add segments;
2. Define profiles;
3. Configure.
5
Introduction to Astrogator - Targeter
Profiles:
Search⇒ Differential corrector⇒ Plugin
Segment configuration⇒ Change maneuver type (impulsive finite)⇒ Change propagator⇒ Change return segment⇒ Change stop segment⇒ Change stopping condition state⇒ Seed finite maneuvers
6
Ex.1: Hohmann transfer using target sequences
Calculate the ΔV required for the following Hohmann transfer:
• Initial circular orbit: 322 km• Δv1= ?• Transfer orbit• Δv2= ?• Final circular orbit: GEO, 35787
km (r = 42165km)
Capture a video of the final trajectory.
7
Ex.2: Hohmann vs. bi-elliptic transfer
Find the total delta-v requirement for a bi-elliptic transfer from a geocentric circular orbit of 7000 km radius to one of 105000 km radius.
Let the apogee of the first ellipse be 210000 km.
Compare the delta-v schedule and total time of flighttime with that of a single Hohmann transfer ellipse.
Verify using STK.
circvrμ
=
2 1ellipv
r aμ ⎛ ⎞= −⎜ ⎟⎝ ⎠
8
Ex.2: Hohmann vs. bi-elliptic transfer
rA = 7000 km
rB = 210000 km
rC = 105000 km
ΔVHohmann = ?
ΔVbi-elliptic = ?
tHomann = ?
tbi-elliptic = ?
Astrodynamics(AERO0024)
TP6: Interplanetary trajectories
2
Today’s program
Objectives
Ex.1: Mars Probe
Ex.2: Moon mission with B-plane targeting
3
Today’s objectives
After this exercise session, you should be able to:
Define interplanetary trajectories
Construct your own point-mass propagator
Take advantage of multiple 3D windows
Create complex MCS and target sequences
Use B-plane targeting
4
Ex.1: Mars probe
Based on orbital elements for the Math Pathfinder mission (Sojourner rover, 96-97)
Two successive segments: - heliocentric- Mars point mass
« Spirit »Source: www.xkcd.com
5
Ex.2: Moon mission with B-Plane targeting
Mission:Earth parking Trans-lunar injection Lunar orbit insertion
Targeting:
Launch date?ΔV?When?
( Δ V ) ( circularization )
Constraints: ΔRA & Δdecl.