Astrodynamics (AERO0024) TP1: Introduction

Transcription

1 Astrodynamics (AERO0024) TP1: Introduction

2 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)

3 Today s program Objectives Presentation of STK Exercise 1: «What does STK do, anyway?» Exercise 2: Do It Yourself! 3

4 Objectives of this session Discover STK and its possibilities Discover STK interface Discover basic functions and options Illustrate the first lesson 4

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 5

6 Presentation of STK Design, analyze, visualize, and optimize land, sea, air, and space systems. 6

7 Presentation of STK interface 7

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10 Presentation of STK 10

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12 Presentation of STK basic elements New scenario - Model the World! Insert object - Populate the World! Properties browser - Decide everything! Animation Reports Tabs 12

13 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

14 Exercise 1: what does STK do, anyway? 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

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 15

16 Exercise 2: application to the 1st lesson >> Represent in STK all the satellites named during the first 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) 16

17 Exercise 2: application to the 1st lesson Debriefing: 17

18 Astrodynamics (AERO0024) TP2: Introduction (2)

19 Today s program Objectives Exercise 1: A concrete problem Exercise 2: Use in celestial mechanics Exercise 3: Delfi-C 3 operation 2

20 Objectives of this session At the end of this session, you should be able to: Use STK autonomously to solve simple problems Define and use constraints Calculate access Import and visualize planets 3

21 Exercise 1 A concrete problem: «When could I see the ISS?» AGI tutorial Outline to build a scenario Constraints 4

22 Exercise 2 Use in celestial mechanics: The Venus Transit of 2004 AGI tutorial Planets and orbits Insertion of sensors Access calculation (Deck Access) 5

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25 Exercise 3 Delfi-C 3 operations When does the Delfi-C 3 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-C 3 transponder? 8

26 Astrodynamics (AERO0024) TP3: Orbital elements

27 Today s program Objectives Exercises 1 & 2: SSO satellites Exercise 3: XMM - RKF7 algorithm 2

28 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 3

29 Exercise 1 & 2: SSO satellites Ex. 1: Determine the altitude and the inclination of a sunsynchronous satellite for which T=100 min (circular orbit). Use STK to check your results. 4

30 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

31 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 = km i = 40 6

32 Astrodynamics (AERO0024) TP4: Astrogator

33 Today s program Objectives Introduction to Astrogator Exercise 1: OUFTI-1 Exercise 2: Hohmann transfer 2

34 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 3

35 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 4

36 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 5

37 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 Astrogator Browser 6

38 Astrogator Mission Control Control Sequence Configuration Astrogator Runs Mission Control Sequence Ephemeris Other Other Mission Data Data

39 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 8

40 The Mission Control Sequence State Segment 1 Ephemeris State Segment 2 Ephemeris State 9

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42 MCS tree 11

43 MCS toolbar 12

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47 Parameters of the segment currently selected 16

48 Segments Two types: That produce ephemeris That change the run flow 17

49 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 18

50 Initial state segment Specify spacecraft state at some epoch Choose any coordinate system Enter in Cartesian, Keplerian, etc. Enter spacecraft properties: mass, fuel, etc. 19

51 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 20

52 Propagate segment Numerically integrates using chosen propagator Propagator can be configured in Astrogator browser Propagation continues until stopping conditions are met 21

53 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 22

54 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 23

55 Stopping conditions Multiple conditions : «OR» Constraints : «AND» 24

56 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 25

57 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 26

58 Impulsive maneuver State Impulsive Maneuver Add delta-v to state State 27

59 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 28

60 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 29

61 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 30

62 Update segment State Update Update state parameters State 31

63 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 32

64 Auto-sequences Automatic sequence browser 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 33

65 Auto-sequences example Initial State Propagate Duration = 1 day Periapsis Burn In Plane Sequence Apoapsis Burn Out Of Plane Sequence Finite Maneuver In Plane Duration = 100 sec Finite Maneuver Out of Plane Duration = 100 sec 34

66 Target sequence Define maneuvers and propagations in terms of the goal they are intended to achieve Next week! 35

67 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 36

68 Questions 37

69 Today s program Introduction to Astrogator Ex.1: OUFTI-1 Ex.2: Hohmann transfer 38

70 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. r a = km, r p = km, e =

71 Today s program Introduction to Astrogator Ex.1: OUFTI-1 Ex.2: Hohmann transfer 40

72 Exercise 2: simple Hohmann transfer Represent Hohmann transfer (from 322km to GEO) using Astrogator. 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 41

73 Exercise 2: simple Hohmann transfer Δv 2 v circ = μ r v ellip 2 1 = μ r a r 2 r 1 2μr μ 2 Δ v1 = r ( ) 1 r1+ r2 r1 Δv 1 2μr μ 1 Δ v2 = + r ( ) 2 r1+ r2 r2 42

74 Exercise 2: simple Hohmann transfer Initial circular orbit: 322 km Δv 1 = km/s Transfer orbit Δv 2 = km/s Final circular orbit: GEO 43

75 Astrodynamics (AERO0024) TP5: Astrogator & Targeter

76 Today program Objectives Introduction to Astrogator Targeter Ex.1: Hohmann using target sequences Ex.2: Hohmann vs. bi-elliptic transfer 2

77 Today s objectives After this exercise session, you should be able to: Define and use target sequences Make videos of your scenarios 3

78 Introduction to Astrogator - Targeter Target sequence: 1. Add segments; 2. Define profiles; 3. Configure. 4

79 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 5

80 Ex.1: Hohmann transfer using target sequences Calculate the ΔV required for the following Hohmann transfer: Initial circular orbit: 322 km Δv 1 =? Transfer orbit Δv 2 =? Final circular orbit: GEO, km (r = 42165km) Capture a video of the final trajectory. 6

81 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 km radius. Let the apogee of the first ellipse be km. Compare the delta-v schedule and total time of flighttime with that of a single Hohmann transfer ellipse. Verify using STK. v circ v ellip μ = r 2 1 = μ r a 7

82 Ex.2: Hohmann vs. bi-elliptic transfer r A = 7000 km r B = km r C = km ΔV Hohmann =? ΔV bi-elliptic =? t Homann =? t bi-elliptic =? 8

83 Astrodynamics (AERO0024) TP6: Interplanetary trajectories

84 Today s program Objectives Ex.1: Mars Probe Ex.2: Moon mission with B-plane targeting 2

85 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 3

86 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: 4

87 Ex.2: Moon mission with B-Plane targeting Mission: Earth parking Trans-lunar injection Lunar orbit insertion ( Δ V ) ( circularization ) Targeting: Launch date? ΔV? When? Constraints: ΔRA & Δdecl. 5