Trajectory Design and Maneuver Planning with STK / Astrogator John Carrico Analytical Graphics, Inc.

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Agenda What is Astrogator? History Examples & Exercises Installation File Configuration Sharing Your Scenarios

Astrogator: What is it? “Astrogator” appears in Science Fiction; Follow-on to Navigator module. Interactive orbit maneuver and space mission planning tool For use by spacecraft operations and mission analysis staff Fully integrated within STK For Earth-orbiting, formation-flying, constellation, Geostationary, Lunar, Lagrange-point, and interplanetary missions

History: Swingby->Navigator->Astrogator Swingby developed at Goddard Space Flight Center/Flight Dynamics Division by Computer Sciences Corp. (CSC) in 1989 Swingby commercialized to become Navigator (CSC; 1994); purchased by AGI Astrogator developed to meet GSFC/Flight Dynamics Analysis Branch request for a COTS solution (Jan 1997) Requirements from Swingby, and other institutional software Swingby/Navigator algorithms, and some code, in Astrogator

Example: GTO to Mars From a Geostationary transfer orbit to Mars Arrive on 17 Dec, 2003 Lunar Swingby changes plane (look in VO) Mission Control Sequence (MCS) Colored Segments Trajectory draws while calculating Segment summary report Quick view of segment times

Exercise 1: The Mission Control Sequence Initial Modified Keplerian: Rp = 7000 km; inc = 28.5º; e = .01; Epoch = 4 July ‘00 Propagate orbit to 3rd perigee Generate Segment Summary Report Create new 2-D window ECI Orthographic Graphics Animation start time Show ‘All’ orbit pass Set scenario “as default”

Exercise 1 (Cont’d) Name and save scenario! AutoSave Good rules of thumb: Create new folder for each scenario Name folder the same as the scenario AutoSave Will save work every 5 minutes (by default) User can change save interval: Application Basic Properties

Example: Double Lunar Swingby (DLS) Two Gravity Assists (used for Wind and Geotail missions) Note MCS; Relationship of colors to trajectory Uses launch model (Simple Ascent) Use burnout information from launch vehicle Note use of maneuver segments Target on B-Plane for gravity assist Copy (with Ctrl-C) time of maneuver or of gravity assist off of MCS panel; Paste (Ctrl-V) into 2-D window and hit enter for visualization

Background: “Delta-V” Unique velocity at every point in orbit If you change the velocity at a given point on an orbit, you are on a new orbit A simple change in velocity is an impulsive “Delta-V” Firing an engine for a finite duration changes the velocity

Exercise 2: Maneuvers 1 km/s impulsive maneuver at perigee Local axes: VNC Propagate to 2nd apogee Change segment color Draw trajectory as calculated Turn off propagate on apply Adjust 2-D view with mouse

Exercise 2 (Cont’d) Graph Altitude and True Anomaly

Example: To The Moon Transfer from low-Earth orbit to the Lunar orbit Earth-centered trajectory Propagator Selection Definition in Astrogator Component Browser Moon-centered trajectory Segments may have different force models and even different central bodies Segment summary coordinate system choice Compare Blue Moon scenario Air Force Academy project Low Delta-V transfer to the Moon via “Weak Stability Boundary” (WSB)

Exercise 3: Propagators and Force Models Add 2nd maneuver at apogee Velocity = 1.0 km/s Normal = -2.0 km/s Propagate 1 day Type “1 day”; converted to units Use CisLunar Propagator Astrogator Component Browser Create & use new 12x12 gravity force model for last segment

Exercise 3 (cont’d) Graph semi-major axis and inclination Look at Initial State Segment Summary in Earth-Fixed coordinates

Example: 2-Maneuver Transfer Orbit transfer Propagate segments Type in Delta-Vs Repeat count for stopping conditions Let the targeter search for answer (Shows on 2-D window) Station contact: “Access”

Example: 2-Maneuver Transfer (cont’d) Help System: Uses HTML Browser “Explore STK” Main Page Module Help Context-Sensitive Help Math Exercises

Exercise 4: Targeting maneuvers Use ‘V’ component as control Select Radius of Apogee (Ra) as a result; observe value in Segment Summary Select Ra as a constraint (42165 km) Action = Run Targeter

Exercise 4 (Cont’d) Look at radius value at apogee These are not two- body orbits Lunar and Solar perturbations Move propagate into target sequence Target on Radius Magnitude (R Mag) at the real apogee Apply corrections

Exercise 5 Target second maneuver (2 x 2) Reasons for non- convergence Use Velocity and Normal components as controls Ecc = 0; Inc = 5º Reasons for non- convergence Max num iterations Max step on control No correlation Most problems are “square”; n controls and n constraints (n x n)

Example: Ground Track Control LandSat-7 Repeating Ground Track (233) World Reference System (WRS) Reference Longitude (295.4°)

Example: Ground Track Control (cont’d) Drift to ground track error near 1.0 km Perform maneuver so turn-around within –1.0 km error Ground Track Error at Descending Node 1st Guess and Actual maneuvers plotted

Example: Formation Flying Model and Control Multiple Satellites Reference Satellite: Real Virtual Target on values relative to reference satellite(s)

Example: Ascent to Formation Plan maneuvers to obtain formation Plan maneuvers to maintain formation

Example: Constellation Multiple Satellites spread around a planet Control to reference satellite: In-plane reference Other-orbit-plane reference Phased ascent from single launch vehicle

Example: AutoBurn Capability to model repetitive sequences “Event Loop” philosophy Auto-burn capability using multiple stopping conditions Repeat count for stopping conditions

Example: Mars Climate Observer Uses auto-burn to simulate aero- braking

Exercise 6: AutoBurn Initial State: Modified Keplerian Elements: Radius of Periapsis = 7000 Eccentricity = 0.01 Create auxiliary sequence in Control Sequence Browser New Sequence: “Small Burn” Insert 1 segment: Impulsive Delta-V; 0.1 km/s along velocity In Main Sequence, add 2nd stopping condition Stop on periapsis. Run new sequence “Small Burn” Run and look at propagate summary for list

Example: Scripting Useful for parametric studies, Monte-Carlo analysis, automation, etc. Support for Perl, MATLAB®, and user programs (e.g., C, C++) Uses STK/Connect with TCP/IP socket Script can be run on same or separate computer User can write custom user interface

Example: Monte-Carlo Error Analysis Perl script to repeat same sequence with random perturbations of initial launch burnout values Script set control parameters Script retrieves STK calculated results Script calculates statistics Maneuvers can be automatically planned Results include all output data: Elements; Fuel-used; Delta-V; Access times and durations…

Example: Engine Modeling Integrate accelerations due to engine thrust model; Integrate mass loss based on Specific Impulse (Isp) Finite maneuver modeling setup Engine model setup: thrust and Isp Polynomial test utility Out of fuel message Blow-Down or Pressure-Regulated Effect of changing thrust Thrust efficiency Multiple thrusters Attitude input/output

Exercise 7: Engine Modeling MCS: Initial state Propagate to perigee Finite Maneuver: 2000 second duration along velocity Create new polynomial engine model Thrust: 400 (N) + 0.0001(N/Pa) x Pressure Isp: 150 (s) + 0.0001 (s/Pa) x Pressure Polynomial test utility: P = 1000 kPa; T = 293º K Run in Blow-Down mode Multiple thrusters: Use 2 Engines, half duration. Attitude input

Example: Low Thrust Super-synchronous transfer to geo-synchronous Multiple stopping conditions: stops on first satisfied Multiple stopping conditions is the “Logical OR” Stop propagation if ‘A = x’ OR ‘B = y’ Constraint on stopping conditions Finds stopping conditions and then checks constraints Multiple constraints allowed Constraints is the “Logical AND” Stop propagation if ‘A = x’ AND ‘B = y’ (within a tolerance) Stop propagation if ‘A = x’ AND ‘B < y’ Stop propagation if ‘A = x’ AND ‘B > y’

Example: Maneuver Calibration Calculate thruster efficiency based on orbit determination (OD) Use calibration factor to improve subsequent maneuvers Baseline trajectory Simulate OD Calibrate User must decide on mass flow rate

Example: Lagrange Point - MAP Microwave Anisotropy Probe Launch in spring 2001 Small-amplitude Lagrange point orbit Display in rotating coordinates Phasing loops before Lunar gravity assist Create Sun-Earth-SC angle graph Astrogator Browser

Example: NGST Next Generation Space Telescope Large Amplitude Libration Point Self-targeting for launch window calculations (+ 10 min) Can override trajectory segment colors (Turn off “Use Trajectory Segment Colors)

Installation Astrogator is part of regular STK Activated with license Full STK installation on each PC C:\Program Files\AGI\stk\… User Install Each user has own data area on each machine D:\stk\jcarrico

File Configuration Scenarios in a subdirectory share objects Rule of Thumb: One scenario per subdirectory (or very similar scenarios) Helps when zipping files for someone else Astrogator subdirectory holds user-defined objects Flag as Read-Only for configuration control User “config” subdirectory Styles Read-Only Astrogator components

Sharing Your Scenarios Using Winzip Recurse subfolders Make sure to include the “Astrogator” subfolder