Launch COLA

Dr. Salvatore Alfano

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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

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Problem statement -Find permissible launch times

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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

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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

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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

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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

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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?

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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

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Shape of mapping is important

Latest end time

Earliest start time

Blackout start time

Blackout end time

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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

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Conjunction Timing

Laun

ch v

ehicl

e tra

jecto

ry

Secondary Trajectory

Touches twice

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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

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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

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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”

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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

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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

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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