Astrodynamics · Astrodynamics (AERO0024) TP6: Interplanetary trajectories. 2 Today’s program

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)

[email protected]

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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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


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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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 ?


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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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°


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

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


Ex.1: OUFTI-1


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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


Ex.1: OUFTI-1


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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 ⎛ ⎞= −⎜ ⎟⎝ ⎠


http://upload.wikimedia.org/wikipedia/commons/d/df/Hohmann_transfer_orbit.svg

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• Initial circular orbit: 322 km

• Δv1=2.4195 km/s

• Transfer orbit

• Δv2=1.4646 km/s

• Final circular orbit: GEO



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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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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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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rA = 7000 km

rB = 210000 km

rC = 105000 km

ΔVHohmann = ?

ΔVbi-elliptic = ?

tHomann = ?

tbi-elliptic = ?


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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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.

Astrodynamics · Astrodynamics (AERO0024) TP6: Interplanetary trajectories. 2 Today’s program

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