astrodynamics · astrodynamics (aero0024) tp6: interplanetary trajectories. 2 today’s program
TRANSCRIPT
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Astrodynamics(AERO0024)
TP1: Introduction
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Teaching Assistant ⎯ Amandine Denis
Contact details
Space Structures and Systems Lab (S3L) Structural Dynamics Research Group Aerospace and Mechanical Engineering Department
Room: +2/516 (B52 building)
04 3669535
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Today’s program
Objectives
Presentation of STK
Exercise 1: « What does STK do, anyway? »
Exercise 2: Do It Yourself!
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Objectives of this session
Discover STK and its possibilities
Discover STK interface
Discover basic functions and options
Illustrate the first lesson
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Objectives of this session
At the end of this session, you should be able to:
Create a new scenarioHandle graphics windows (2D and 3D, view from/to, …)Use common options of the Properties BrowserInsert a satellite in three different ways (database, Orbit Wizard, manually)Insert a facilityCalculate a simple accessGenerate simple reports
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Presentation of STK
Design, analyze, visualize, and optimize land, sea, air, and spacespace systems.
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Presentation of STK – interface
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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
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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?
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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
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Exercise 2: application to the 1st lesson
To create a satellite: ⇒ Insert >>New… >> SatelliteOrbit wizard : cfr ex1From DatabaseDefine properties
Visualization:⇒ Day/night limit ( 2D graphics Properties Browser >>
Lighting)
>> Represent in STK all the satellites named during the first lesson.
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Debriefing:
Exercise 2: application to the 1st lesson
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Astrodynamics(AERO0024)
TP2: Introduction (2)
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Today’s program
Objectives
Exercise 1: A concrete problem
Exercise 2: Use in celestial mechanics
Exercise 3: Delfi-C3 operation
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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
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Exercise 1
A concrete problem:
« When could I see the ISS ? »
Outline to build a scenario
Constraints
AGI tutorial
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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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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 ?
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Astrodynamics(AERO0024)
TP3: Orbital elements
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Today’s program
Objectives
Exercises 1 & 2: SSO satellites
Exercise 3: XMM - RKF7 algorithm
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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
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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.
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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.
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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°
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Astrodynamics(AERO0024)
TP4: Astrogator
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Today’s program
Objectives
Introduction to Astrogator
Exercise 1: OUFTI-1
Exercise 2: Hohmann transfer
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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
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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
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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
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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
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Astrogator
Mission Control SequenceConfiguration
Mission Control SequenceConfiguration
Astrogator
Runs Mission ControlSequence
EphemerisEphemeris
Other MissionData
Other MissionData
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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
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The Mission Control Sequence
State
Segment 1
State
Segment 2
State
Ephemeris
Ephemeris
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MCS tree
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MCS toolbar
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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
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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
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Initial state segment
Specify spacecraft state at some epoch
Choose any coordinate system
Enter in Cartesian, Keplerian, etc.
Enter spacecraft properties: mass, fuel, etc.
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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
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Propagate segment
Numerically integrates using chosen propagator
Propagator can be configured in Astrogator browser
Propagation continues until stopping conditionsare met
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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
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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
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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
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Impulsive maneuver
State
Impulsive ManeuverAdd delta-V to state
State
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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
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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
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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
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Update segment
State
UpdateUpdate state parameters
State
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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
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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
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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
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Target sequence
Define maneuvers and propagations in terms of the goal they are intended to achieve
Next week !
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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
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Questions
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Today’s program
Introduction to Astrogator
Ex.1: OUFTI-1
Ex.2: Hohmann transfer
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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
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Today’s program
Introduction to Astrogator
Ex.1: OUFTI-1
Ex.2: Hohmann transfer
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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.
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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
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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
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Astrodynamics(AERO0024)
TP5: Astrogator & Targeter
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Today program
Objectives
Introduction to Astrogator – Targeter
Ex.1: Hohmann using target sequences
Ex.2: Hohmann vs. bi-elliptic transfer
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Today’s objectives
After this exercise session, you should be able to:
Define and use target sequences
Make videos of your scenarios
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Introduction to Astrogator - Targeter
Target sequence:
1. Add segments;
2. Define profiles;
3. Configure.
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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
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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.
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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 ⎛ ⎞= −⎜ ⎟⎝ ⎠
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Ex.2: Hohmann vs. bi-elliptic transfer
rA = 7000 km
rB = 210000 km
rC = 105000 km
ΔVHohmann = ?
ΔVbi-elliptic = ?
tHomann = ?
tbi-elliptic = ?
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Astrodynamics(AERO0024)
TP6: Interplanetary trajectories
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Today’s program
Objectives
Ex.1: Mars Probe
Ex.2: Moon mission with B-plane targeting
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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
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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
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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.