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Launch COLA
Dr. Salvatore Alfano
2
Outline
Problem Statement– Space Object Environment
Standard formulation– Description– Issues
JSPOC use case AGI’s patented solution method
– Re-formulate the problem
Questions and answers
Given– Launch trajectory
Designed in the Earth Fixed frame Motion characterized in MET (Mission Elapsed Time)
– MET = seconds past Launch time
– Satellite Catalog Given in the Earth Centered Inertial (ECI) frame Motion characterized in civil time
– Launch window Time interval in civil time (absolute time scale) Example: 12 Feb 09 05:00:00 to 12 Feb 09 11:00:00 UTC Launch may occur anytime during this window
3
Problem statement -Find permissible launch times
4
Problem Statement (Cont’d)
Concern: close approaches with space objects– Launching missile won’t be able to perform avoidance
maneuver
– Satellite object may not be able to move (debris)
– Satellite object unaware of launch
– Satellite object unwilling to move
Which time intervals in the launch window are NOT safe for launch?– These are the Launch Blackout intervals
5
Space object environment
12,000+ objects (publicly) cataloged by USSTRATCOM – Mostly debris with significant ephemeris uncertainty
(3-20km)
Object ephemeris modeling– SGP4 using a TLE
Analytic routine (fast) Accurate for short durations (days) Each object’s TLE is routinely updated every few days
– SP (Special Perturbations propagator) Numerically integrated trajectories
6
Definitions
Primary Designed launch trajectory Secondaries Other space objects Close Approach range < given threshold
Compute
All time intervals during the launch window for which the primary will have a close approach with some
secondary if launched during that interval
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Standard formulation
Identify the set of secondaries to consider– Use ephemeris generated near launch window time
– Filter out secondaries based upon apogee of launch trajectory
Choose a sampling of times within the launch window– Every 60 sec, 10 sec, 1 sec, etc.
For each sampled time– Transform launch trajectory to inertial frame
sampled time = launch time
– Perform close approach to secondaries
– If close approaches are detected, then sampled time is in Blackout interval
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Standard formulation (cont’d)
Do analysis in civil time– Convert MET incrementally for each launch time
Do analysis in ECI frame– Transform MET incrementally for each launch time
Will probably want to gather some further results – Close approach objects, minimum approach
distance
Assimilate all results
9
Issues
Sampling rate– Events occur over short durations (seconds)
Argues for using small time steps
– Launch Window is long (hours)
– May need to do many cases to assess entire window
Large number of cases– More cases means more computational time
– More cases means more results to process when determining the Blackout windows
10
Issues (cont’d)
Accuracy requires timely data– Ephemerides may not be valid for long times
– Argues for doing the analysis close to the time of launch window itself
Can all the cases be computed and assessed at a time close to the launch
window but before it starts?
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Still need to investigate
Planning– How to plan months in advance of the launch
window?
Launch trajectory design– How can one assess the impact of trajectory
changes knowing the computations may take a long time?
Resetting the Launch Window – Slips occur for lots of reasons
– How fast can a new assessment be made for the new window?
12
JSPOC Use Case
AGI In-House Hardware Configuration– Intel® Xeon® CPU – 8 cores @ 2.13 GHz– 24 GB RAM– All tests results obtained using only 1 core
Launch Window Example Configuration– 6 hour launch window– Primary trajectory MET duration ~ 15 min – Conjunction range threshold – 40 km
Example Catalog– ~12,000 secondaries using ephemeris files
generated from publicly available TLEs– Method not limited to TLEs
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Results
Launch Window
Sampling Strategy
Fixed at 60 sec
Fixed at 10 sec
Fixed at 1 sec
Fixed at 0.5 sec
AGI Launch COLA
Conjunctions Detected
< 1% 5.4 % 50 % >99 % 100 %
Compute Time
40 min 4 hrs 46.7 hrs 108.8 hrs
3.1 min
Found 573 conjunctions Shortest blackout interval ~ 0.2 sec Smallest minimum range ~ 22 m
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AGI Launch COLA papers
“Determination of Close Approaches for Earth Fixed Launch Trajectories” – Jim Woodburn, AAS 98-134, 1998.
– http://www.stk.com/downloads/resources/user-resources/downloads/whitepapers/CloseAppToEFLaunch.pdf
US Patent 6,102,334 Issued 15 Aug 2000– “METHOD AND APPARTATUS FOR
DETERMINING CLOSE APPROACHES FOR EARTH-FIXED LAUNCH TRAJECTORIES” by Jim Woodburn of AGI
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AGI-Patented solution strategy
Transform the analysis space– Use Earth-fixed frame rather than Inertial frame
– Use MET in addition to civil time
Each MET time value– Locates a single Earth-fixed position of launch
trajectory
– Corresponds to the considered interval (in civil time) Start: Launch window start + MET Stop: Launch window stop + MET
– The considered interval determines an arc of each secondary’s trajectory
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AGI-Patented solution strategy
Take advantage of conjunction metrics that are well behaved in MET in Earth-fixed frame– No need to sample at small steps to detect short
conjunctions
– Use small number of samples for determining functional trends
– Accurately identify extrema and threshold crossing events by iteratively sub-sampling as needed
Convert MET events into launch times (civil times)
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Minimum possible range
Launch vehicle positionat a given MET
MinimumPossible Range
Range Sample
Secondary TrajectoryLaunch Window Duration
Secondary positionat given civil time
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Solution strategy (cont’d)
Is secondary’s arc within range threshold at this position in the launch trajectory?– No: no close approach at this MET
– Yes: secondary does have close approach
If Yes:– Determine time interval within the considered interval
for which range < threshold (i.e., conjunction time interval)
– Convert this conjunction time interval into a time interval in the launch window when primary must have launched for the close approach to have occurred
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Conjunction time interval
Sample each secondary’s arc Use event detection routine to look for
threshold crossing– Identifies a conjunction time interval within
considered interval
time-into-considered-interval
Threshold
Range Range Sample
Conjunction time interval
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Computation Strategy
Filter out secondaries based upon perigee For each secondary not filtered out
– Judiciously sample launch trajectory in MET
– Compute conjunction intervals at each sample, where range < threshold This itself requires judicious sampling and iterative sub-
sampling
– Iteratively sub-sample in MET to precisely determine the envelope of all conjunction intervals for this secondary
– Convert envelope boundary time interval into time-into-launch-window interval (thus, blackout interval)
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Conjunction Timing
Laun
ch v
ehicl
e tra
jecto
ry
Secondary Trajectory
Just Touches
MET conjunctions
22
Shape of mapping is important
Latest end time
Earliest start time
Blackout start time
Blackout end time
23
Conjunction Timing
Laun
ch v
ehicl
e tra
jecto
ry
Secondary Trajectory
Touches twice
1 2
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MET conjunctions
Shape of mapping is important
Latest end time
Earliest start time
Blackout start time
Blackout end time
1
2
25
Conjunction Timing
Laun
ch v
ehicl
e tra
jecto
ry
Secondary Trajectory
Touches twice
12
26
MET conjunctions
Shape of mapping is important
Latest end time
Earliest start time
Blackout start time
Blackout end time
1
2
27
MET conjunctions
Shape of mapping is important
Latest end time
Earliest start time
Blackout start time
Blackout end time
Bla
ckou
t
win
dow
MET = 1.2 s
T =
1.6
s
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Concerns addressed
AGI Launch COLA:– Can make plans in advance and continually update
the results
– Can easily account for changes to launch trajectory design
– Can easily account for resetting the launch window
– Can be run very close to launch window start, using the best available data as of that time for best prediction accuracy
29
JSPOC Use Case Extended – Part 1
Which time intervals in the launch window are NOT safe for launch from any of the given launch sites?– These are the Launch Blackout intervals for the
entire set of multiple simultaneous launches
Extension from a single launch to
multiple simultaneous launches from nearby sites
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Problem Statement
Given– Launch trajectories and launch window as before
– Launch sites are close and trajectories remain in close proximity
Simultaneous launches from all launch sites may occur anytime during the launch window
AGI Solution - treat trajectories as a cluster– Generate single reference trajectory for the entire cluster
– Create new conservative range threshold for the entire cluster
– Compute conservative blackout intervals for reference trajectory using conservative range threshold
– Refine blackout intervals for individual trajectories
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Reference for multiple launches
Define single reference launch site and trajectory, e.g. average of all launch trajectories in Earth-fixed frame in MET
Launch sites Reference launch site
Reference trajectory
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Max dispersion distance
Determine maximum distance of any launch vehicle from the reference position at any time in MET
Positions at some MET
Maximum dispersion
distance at METPositions at
MET=0
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Filter using reference trajectory
Original range threshold sphere
Conservative range threshold
sphere
Additional “pad”
Compute conservative blackout intervals using reference launch trajectory with range threshold set to
max dispersion distance + original range threshold + additional “pad”
34
Individual trajectory processing
Filtered conservative blackout intervals are refined using launch window analysis of actual individual trajectories– Computational savings result from using filtered
blackout intervals which are typically much shorter than the overall launch window
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JSPOC Use Case Extended – Part 2
Which time intervals in the launch window are NOT safe for launch from anywhere within given area?– These are the Launch Blackout intervals for the
entire area
Extension from a finite set of launch sites to launches from anywhere within a continuous area
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Problem Statement
Given– Launch trajectory and launch window as before
– Method for changing Earth-fixed MET trajectory from one launch site to another within specified area
Launch may occur anytime during the launch window and anywhere within the specified area
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Area Launch Definition
Rectangular area in lat-lon space Earth-fixed MET trajectory is defined for
some launch site within the area (e.g. its center)
Trajectory is modified when moved to a different launch site within the area, e.g.– Same trajectory in local topocentric frame
– Same Earth-fixed MET burnout point
– Other methods are possible
38
Area Launch – Same Trajectory
Trajectories are fixed in MET in local topocentric frame for each launch site
A lot of samples to cover the area
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Area Launch – Same Burnout Point
Burnout point fixed in MET in Earth-fixed frame is the same for any launch site
A lot of samples to cover the area
40
Standard formulation
Sample launch area at some acceptable resolution
For each sample launch site– Perform launch window analysis
– Accumulate results
Report accumulated results from all sampled sites
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Issues
How to determine acceptable area resolution? Fine resolution over large area = many launch
sites = many analyses to run– 100 km x 100 km at 10 km resolution = 100 launches
It may be difficult to obtain answers that are both timely and accurate
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Primary Trajectory Surface at MET
Launch Area (MET = 0)
Primary Trajectory Surface at a given MET
At a given MET, positions of all possible primary trajectories starting within specified launch area make up primary trajectory surface
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Minimum possible range to surface
Minimum Possible Range for entire
surface at a given MET
Sample on secondary trajectory
Secondary TrajectoryLaunch Window Duration
Corresponding Min Range point on Primary trajectory surface
Primary trajectory surfaceat a given MET
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AGI Solution
Start using approach similar to clustered trajectories case– Generate reference trajectory for the area
– Create conservative padded range threshold
– Compute conservative blackout intervals
Refine blackout intervals– Replace range computation to a single position at MET with
range computation to the nearest point on the surface at MET
– Nearest point is found using judicious sampling and iterative sub-sampling of surface points
– Clearing any and all points on the surface means clearing the nearest point
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Judicious Area Sampling
Judicious sampling works well for areas of various size
Initial samples
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Results Extended
Launch Window
Sampling Strategy
AGI Launch COLA
AGI Launch COLA
for 18 trajectories
AGI Clustered Launch COLA
for 18 trajectories
AGI Area Launch COLA
Rectangular Area 100 x
100 km
Compute Time
3.1 min 23.9 min 3.2 min 3.7 min
Fixed computational cost is associated with loading secondary ephemeris files for processing – independent from the number of primary trajectories
Metrics
12,000 ephemeris files generated from TLEs– 35 minutes on a 1-core PC for all objects for 5 days
– 90 points per orbit
Apply perigee filter to all 12,000– 11,000 satellites eliminated (1,000 left)
Run launch COLA for 100km x 100km case– 6 hour launch window– Primary trajectory MET duration ~ 15 min – Conjunction range threshold – 40 km
– 4 minutes processing time
– Conjunctions found ~ 600
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Video of multiple launches
COLA_Red.wmv
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Results Combined
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Questions & answers