Astrodynamics (AERO0024) TP1: Introduction 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)

„ [email protected]

„ 04 3669535

2 Today’s program

ƒ Objectives ƒ Presentation of STK ƒ Exercise 1: « What does STK do, anyway? » ƒ Exercise 2: Do It Yourself!

3 Objectives of this session

ƒ Discover STK and its possibilities ƒ Discover STK interface ƒ Discover basic functions and options ƒ Illustrate the first lesson

4 Objectives of this session

At the end of this session, you should be able to: ƒ Create a new scenario ƒ Handle graphics windows (2D and 3D, view from/to, …) ƒ Use common options of the Properties Browser ƒ Insert a satellite in three different ways (database, Orbit Wizard, manually) ƒ Insert a facility ƒ Calculate a simple access ƒ Generate simple reports

5 Presentation of STK

Design, analyze, visualize, and optimize land, sea, air, and space systems.

6 Presentation of STK – interface

7 8 9 Presentation of STK

10 11 Presentation of STK – basic elements

New scenario - Model the World!

Insert object - Populate the World!

Properties browser - Decide everything!

Animation

Reports

Tabs 12 Exercise 1

First contact: « What does STK do, anyway? »

AGI tutorial

Illustration of a Molniya orbit Notion of scenario Rules of thumb Orbit Wizard Insertion of a facility Graphics windows Calculation of a simple access 13 Exercise 1: what does STK do, anyway?

Î Are Molniya orbits really a great way to spy on the USA?

How many periods of access? When does the first access occur? What is the duration of the first access?

Remarks/questions ?

14 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

15 Exercise 2: application to the 1st lesson

>> Represent in STK all the satellites named during the first lesson.

ƒ To create a satellite: ⇒ Insert >>New… >> Satellite Orbit wizard : cfr ex1 From Database Define properties

ƒ Visualization: ⇒ Day/night limit ( 2D graphics Properties Browser >> Lighting)

16 Exercise 2: application to the 1st lesson

Debriefing:

17 Astrodynamics (AERO0024) TP2: Introduction (2) Today’s program

ƒ Objectives ƒ Exercise 1: A concrete problem ƒ Exercise 2: Use in celestial mechanics ƒ Exercise 3: Delfi-C3 operation

2 Objectives of this session

At the end of this session, you should be able to:

ƒ Use STK autonomously to solve simple problems ƒ Define and use constraints ƒ Calculate access ƒ Import and visualize planets

3 Exercise 1

A concrete problem: « When could I see the ISS ? »

AGI tutorial

Outline to build a scenario Constraints

4 Exercise 2

Use in celestial mechanics: The Venus Transit of 2004

AGI tutorial

Planets and orbits Insertion of sensors Access calculation (Deck Access)

5 6 7 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 ?

8 Astrodynamics (AERO0024) TP3: Orbital elements Today’s program

ƒ Objectives ƒ Exercises 1 & 2: SSO satellites ƒ Exercise 3: XMM - RKF7 algorithm

2 Objectives of this session

At the end of this session, you should be able to: ƒ Calculate orbital elements ƒ Check your results with STK ƒ Create customized reports ƒ Export reports and use data in Matlab

3 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.

4 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.

5 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 km Apogee = 114000 km i = 40°

6 Astrodynamics (AERO0024) TP4: Astrogator Today’s program

ƒ Objectives ƒ Introduction to Astrogator ƒ Exercise 1: OUFTI-1 ƒ Exercise 2: Hohmann transfer

2 Today’s objectives

After this exercise session, you should be able to: ƒ 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

3 Today’s program

ƒ Introduction to Astrogator ⇒ What is it ? ⇒ Components of Astrogator: • Mission Control Sequence • Segments • Stopping conditions

ƒ Ex.1: OUFTI-1

ƒ Ex.2: Hohmann transfer

4 What’s Astrogator?

ƒ Astrogator is STK’s mission planning module ƒ Used for: ⇒ Trajectory design ⇒ Maneuver planning ⇒ Station keeping ⇒ Launch window analysis ⇒ Fuel use studies ƒ Derived from code used by NASA contractors ƒ Embedded into STK

5 Astrogator in STK

ƒ Astrogator is one of 11 satellite propagators ƒ Propagator generates ephemeris ƒ Astrogator satellite acts like other STK satellites ⇒ Can run STK reports (including Access) ⇒ Can animate in 3D and 2D windows ƒ Generates ephemeris by running Mission Control Sequence (MCS) ƒ Components used in MCS configured in Astrogator Browser

6 Astrogator

MissionMission Control Control Sequence Sequence ConfigurationConfiguration

Astrogator EphemerisEphemeris Runs Mission Control Sequence OtherOther Mission Mission DataData The Mission Control Sequence

ƒ A series of segments that define the problem ƒ A graphical programming language ƒ Two types of segments ⇒ Segments that produce ephemeris ⇒ Segments that change the run flow of the MCS ƒ Segments pass their final state as the initial state to the next segment ⇒ Some segments create their own initial state

8 The Mission Control Sequence

State

Segment 1 Ephemeris

State

Segment 2 Ephemeris

State 9 10 MCS tree

11 MCS toolbar

12 13 14 15 Parameters of the segment currently selected 16 Segments

Two types: ƒ That produce ephemeris ƒ That change the run flow

17 Segments that produce ephemeris

ƒ Initial State – specifies initial conditions ƒ Launch – simulates launching ƒ Propagate – integrate numerically until some event ƒ Maneuver – impulsive or finite ƒ Follow – follows leader vehicle until some event ƒ Update – updates spacecraft parameters

18 Initial state segment

ƒ Specify spacecraft state at some epoch ƒ Choose any coordinate system ƒ Enter in Cartesian, Keplerian, etc. ƒ Enter spacecraft properties: mass, fuel, etc.

19 Launch segment

ƒ Specify launch and burnout location ƒ Specify time of flight ƒ Use any central body ƒ Connects launch and burnout points with an ellipse ƒ Creates its own initial state

20 Propagate segment

ƒ Numerically integrates using chosen propagator ƒ Propagator can be configured in Astrogator browser ƒ Propagation continues until stopping conditions are met

21 Stopping conditions

ƒ Define events on which to stop a segment ƒ 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

22 Stopping conditions

ƒ 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” ƒ Segments can have multiple stopping conditions ⇒ Stops when the first one is met ⇒ Behaves as a logical “Or”

23 Stopping conditions

Multiple conditions : «OR»

Constraints : « AND »

24 Maneuver segment

ƒ Maneuver segment owns two distinct segments: ⇒ Finite maneuver ⇒ Impulsive maneuver ƒ Combo box controls which one is run ƒ Finite maneuver created from impulsive maneuver with “Seed” button

25 Impulsive maneuver

ƒ Adds delta-V to the current state ƒ Can specify magnitude and direction of delta-V ƒ Computes estimated burn duration and fuel usage, based on chosen engine ƒ Can configure engine model in Astrogator browser

26 Impulsive maneuver

State

Impulsive Maneuver Add delta-V to state

State

27 Finite maneuver

ƒ Works like propagate segment, thrust added to force model ƒ Can specify the direction of the thrust vector ⇒ Can be specified in plug-in ƒ Magnitude of thrust comes from engine model

28 Follow segment

ƒ Choose leader to follow ƒ Specify offset from the leader ƒ Follow leader between “joining conditions” and “separation conditions” ⇒ Behave just like stopping conditions ƒ Creates its own initial state

29 Update segment

ƒ Used to update spacecraft properties ƒ Useful to simulate stage separation, docking, etc ƒ Set properties to a new value, or add or subtract from their current value

30 Update segment

State

Update Update state parameters

State

31 Segments that change run flow

ƒ Auto-Sequences – called by propagate segments ƒ Target Sequence – loops over segments, changing values until goals are met ƒ Backwards Sequence – changes direction of propagation ƒ Return – exits a sequence ƒ Stop – stops computation

32 Auto-sequences

Automatic sequence browser

ƒ Instead of stopping a segment, stopping conditions can trigger an auto-sequence ƒ An auto-sequence is another sequence of segments ⇒ Behaves like a subroutine ƒ After the auto-sequence is finished, control returns to the calling segment ƒ Auto-sequences can inherit stopping conditions from the calling segment

33 Auto-sequences example

Initial State

Propagate

Apoapsis Duration = 1 day Periapsis

Burn In Plane Burn Out Of Plane Sequence Sequence

Finite Maneuver Finite Maneuver In Plane Out of Plane

Duration = 100 sec Duration = 100 sec

34 Target sequence

ƒ Define maneuvers and propagations in terms of the goal they are intended to achieve

Î Next week !

35 Backward sequence

ƒ Segments in backward sequences propagated backwards: ⇒ Propagate & finite maneuvers integrated with negative time step ⇒ Impulsive maneuvers’ delta-Vs are subtracted ƒ Can pass initial or final state of sequence to next segment

36 Questions

37 Today’s program

ƒ Introduction to Astrogator

ƒ Ex.1: OUFTI-1

ƒ Ex.2: Hohmann transfer

38 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

39 Today’s program

ƒ Introduction to Astrogator

ƒ Ex.1: OUFTI-1

ƒ Ex.2: Hohmann transfer

40 Exercise 2: ‘simple’ Hohmann transfer

Î Represent Hohmann transfer (from 322km to GEO) using Astrogator.

ƒ ‘Simple’: - coplanar maneuver - no use of ‘target sequence’ ƒ Most efficient 2-burn method (in terms of ΔV) ƒ Elliptical transfer orbit ⇒ periapsis at the inner orbit ⇒ apoapsis at the outer orbit

41 Exercise 2: ‘simple’ Hohmann transfer

Δv 2 μ ⎛⎞21 vcirc = vellip =−μ ⎜⎟ r ⎝⎠ra

r2 r1 2μr2 μ Δ=v1 − rr11()+ r 2 r 1

Δv1 2μr1 μ Δ=−v2 + rr21()+ r 2 r 2

42 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

43 Astrodynamics (AERO0024) TP5: Astrogator & Targeter Today program

ƒ Objectives ƒ Introduction to Astrogator – Targeter ƒ Ex.1: Hohmann using target sequences ƒ Ex.2: Hohmann vs. bi-elliptic transfer

2 Today’s objectives

After this exercise session, you should be able to: ƒ Define and use target sequences ƒ Make videos of your scenarios

3 Introduction to Astrogator - Targeter

Target sequence: 1. Add segments; 2. Define profiles; 3. Configure.

4 Introduction to Astrogator - Targeter

Profiles: ƒ Search ⇒ Differential corrector ⇒ Plugin ƒ Segment configuration ⇒ Change maneuver type (impulsive Æ finite) ⇒ Change propagator ⇒ Change return segment ⇒ Change stop segment ⇒ Change stopping condition state ⇒ Seed finite maneuvers

5 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.

6 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.

μ v = circ r ⎛⎞21 vellip =−μ ⎜⎟ ⎝⎠ra 7 Ex.2: Hohmann vs. bi-elliptic transfer

rA = 7000 km

rB = 210000 km

rC = 105000 km

Î ΔVHohmann = ?

Î ΔVbi-elliptic = ?

Î tHomann = ?

Î tbi-elliptic = ?

8 Astrodynamics (AERO0024) TP6: Interplanetary trajectories Today’s program

ƒ Objectives ƒ Ex.1: Mars Probe ƒ Ex.2: Moon mission with B-plane targeting

2 Today’s objectives

After this exercise session, you should be able to: ƒ Define interplanetary trajectories ƒ Construct your own point-mass propagator ƒ Take advantage of multiple 3D windows ƒ Create complex MCS and target sequences ƒ Use B-plane targeting

3 Ex.1: Mars probe

ƒ Based on orbital elements for the Math Pathfinder mission (Sojourner rover, 96-97) ƒ Two successive segments: - heliocentric - Mars point mass

«Spirit» 4 Source: www.xkcd.com Ex.2: Moon mission with B-Plane targeting

ƒ Mission: Earth parking Æ Trans-lunar injection Æ Lunar orbit insertion ( Δ V ) ( circularization )

ƒ Targeting: Launch date? ΔV? Constraints: ΔRA & Δdecl. When?

5