Orbit Determination

Transiting Exoplanet Survey Satellite Transiting Exoplanet Survey Satellite (TESS) Flight Dynamics Commissioning Results and Experiences

( . - -~ . ' : .•. ' Joel J. K. Parker NASA Goddard Space Flight Center ', ~Qi Ryan L. Lebois L3 Applied Defense Solutions .•.-· e, • i Stephen Lutz L3 Applied Defense Solutions ,/,#· Craig Nickel L3 Applied Defense Solutions Kevin Ferrant Omitron, Inc. Adam Michaels Omitron, Inc. August 22, 2018 Contents

 Mission Overview

 Flight Dynamics Ground System

 TESS Commissioning . Launch . Phasing Loops & Maneuver Execution . PAM & Extended Mission Design . Commissioning Results

 Orbit Determination

 Conclusions

2 Mission Overview—Science Goals

 Primary Goal: Discover Transiting Earths and Super-Earths Orbiting Bright, Nearby Stars . Rocky planets & water worlds . Habitable planets

 Discover the “Best” ~1000 Small Exoplanets . “Best” means “readily characterizable” • Bright Host Stars • Measurable Mass & Atmospheric Properties

 Unique lunar-resonant mission orbit provides long view periods without station-keeping 27 days

54 days Large-Area Survey of Bright Stars . F, G, K dwarfs: +4 to +12 magnitude . M dwarfs known within ~60 parsecs . “All sky” observations in 2 years . All stars observed >20 days . Ecliptic poles observed ~1 year (JWST Continuous Viewing Zone)

3 s Mission Overview—Spacecraft

LENS HOOD THERMAL . LENSES BLANKETS SUN SHADE

REACTION WHEELS DETECTORS

ELECTRONICS SOLAR ARRAYS

MASTER ANTENNA COMPUTER PROPULSION TANK STRUCTURE

 Northrop Grumman LEOStar-2/750 bus  Attitude Control:  Propulsion: . 4x reaction wheel assemblies (RWAs), 2x star . 1x 22N ΔV reaction engine assembly (REA) tracker assemblies, 10x coarse sun sensors . . 4x 4.5N REA for attitude control Keep-out zones associated with all sensors  Instrument:  Communications: . . 2x S-band omnidirectional antennas 4x camera assemblies . . 1x Ka-band high-gain antenna (HGA) 30° by ± 50° rectangular keep-out zone

4 Mission Overview—Trajectory Design

Earth-Moon rotating frame

Inertial frame

 Overall mission design: 3.5 phasing loops → lunar flyby → transfer orbit → mission orbit  Mission orbit features 2:1 lunar resonance (“P/2”), or 13.67 d mean orbit period

5 Mission Overview—Commissioning

TCM3 r . = 478,000 km • IN Burn (75 Rel • Optional Burn • Perigee Passage

r3 = 378,000 km (59 Re)

Lunar flyby /,\-- --- (

A2M },\.-----

'I I I ra = 270,000_..~i:!! __ ~ 1M Eng ! r,, Bum: backup : : I

:I :I

:I 250 km all lnj PAM (Per Adjust)

Phasi ng Phasing Phasing Transfer Orbit Science Orbit 0 Science Orbit 1 Science Orbit2 Loop 1 Loop 2 Loop 3 (17 d) (14 cl) (6 d) (9 d) (9 d)

Ascent and Commissioning (S60 days) Science Operations

 Overall commissioning is ≤60d process

 6 planned maneuvers + 5 optional/backup maneuvers

6 Mission Overview—Navigation

Measurement Summary by Altitude Separation through PAM

lunar 50 flyby

30 Altitude (Re)Altitude 20

PAM 10

0 22 Sun 1 Tue 8 Tue 15 Tue 22 Tue 1 Fri Apr 2018 Time (UTCG)

Tess Tracking• Tess= No Tracking

 Navigation support provided by NASA Deep Space Network (DSN) and Space Network (SN)  SN post-separation acquisition at +1 min  Handover to DSN by +1.5 hr  Near-continuous tracking through first phasing loop, then scheduled to cover maneuvers and meet OD accuracy requirements  Post-launch SN support scheduled around perigee maneuvers only

7 Flight Dynamics Ground System

Tracking Data  NASA FDF TESS Flight Dynamics .------.,------,,..------,,--.....---, ,...--"!---, i Ground System: MOC soc CARA DSN j CIL . NASA Flight Dynamics Incoming Facility (FDF) Directory . TESS Flight Dynamics System Message Gateway

 FDF responsibilities: r------TESS FOS ------~ Common . Facility/infrastructure data . DSN/SN data interfaces . IOD external verification

 FDS responsibilities: ! . Maneuver planning GTDS (100) ------' . Orbit determination . Product generation . Maneuver reconstruction/calibration

 Software utilized: Software Use L3 ADS Flight Dynamics System (FDS) Procedure Execution, Data Management NASA General Mission Analysis Tool (GMAT) Maneuver Planning, Ephemeris Generation AGI Orbit Determination Tool Kit (ODTK) Primary Orbit Determination Goddard Trajectory Determination System (GTDS) Backup Orbit Determination SPICE Toolkit DSN Acquisition Generation AGI Systems Tool Kit (STK) Analysis, QA, Visualizations MATLAB Analysis, Plotting

8 Flight Dynamics Ground System

 FDF responsibilities: r------TESS FOS ------~ Common . Facility/infrastructure data . DSN/SN data interfaces . IOD external verification

 FDS responsibilities: ! . Maneuver planning GTDS (100) ------' . Orbit determination . Product generation . Maneuver reconstruction/calibration

 Software utilized: Software Use First end-to- L3 ADS Flight Dynamics System (FDS) Procedure Execution, Data Management end use of NASA General Mission Analysis Tool (GMAT) Maneuver Planning, Ephemeris Generation GMAT in AGI Orbit Determination Tool Kit (ODTK) Primary Orbit Determination Goddard Trajectory Determination System (GTDS) Backup Orbit Determination primary SPICE Toolkit DSN Acquisition Generation maneuver AGI Systems Tool Kit (STK) Analysis, QA, Visualizations planning role MATLAB Analysis, Plotting

9 Launch Performance

Launch Date: April 18th 2018 Vehicle: SpaceX Falcon 9 Location: Cape Canaveral Air Force Station, SLC-40

Event Actual (UTC) Delta (s) Liftoff 22:51:30.498 -0.502 Separation 23:41:03.177 +2.177

Element* Pre-Launch BET OD Delta 3σ Requirement Sigma Apogee Altitude [km] 268,622.397 269,330.228 707.831 ± 20,000 0.11 Perigee Altitude [km] 248.456 248.755 0.299 ± 25 0.04 Inclination [deg] 29.563 29.579 0.016 ± 0.1 0.48 Argument of Perigee 228.111 228.088 -0.023 ± 0.3 -0.23 [deg] *All elements at epoch: 18 Apr 2018 23:45:30.666 UTC

10 Phasing Loops

TESS Definitive Altitude Separation through PAM • All burns nominal /0

uo---= (A2M) • A2M waived as 50 - A1M (flyby) unnecessary 2 10 • Performance error ~o • <7% worst- 20 - case 10 - PAM • <1% for major P1M P2M P3M u 1 maneuvers 22Sun 1 l ue 8 l ue 1~ IU€ 2, l ue 1 1-n 1\p1? OIR (UTCG) Mean Dur. Calibrated Performance Maneuver Epoch Pointing (sec) ΔV (m/s) Error (%) Error (deg) A1M 22 Apr 2018 01:59:06.628 50 3.915 -3.33 9.6 P1M 25 Apr 2018 05:36:42.053 449 32.265 -0.93 0.6 P2M 04 May 2018 08:05:46.650 7 0.430 -6.62 0.4 P3M 13 May 2018 11:37:48.648 29 1.862 +2.87 1.6 PAM 30 May 2018 01:20:23.149 923 53.409 -0.11 0.7

11 Maneuver Performance

Maneuver Execution Error: Calibrated tiV vs. Reconstructed tiV 0 . PAM, -0.11% -1 • PlM, -0.93% 'ii: a -2 L • P3M, -2.28% L w -3 Q.J u • AlM, -3.33% C E-4 L 0 :.".":: P3M (predicted) 't: -5 Q.J 0.... ~ -6 +-' ro • P2M, -6.62% :e -7 ro u -8

-9 0 100 200 300 400 500 600 700 800 900 1000 Burn Duration [sec]

 Maneuver performance error trends with duration . Shorter duration correlated with underperformance . Trend explained as an artifact of thermal ramp-up of propulsion system  Analysis through P2M was used to predict likely performance of P3M flyby- targeting maneuver . Maneuver thrust scaled by 95% during P3M planning to better target desired flyby

12 PAM Design & Extended Mission Design

 PAM: Period Adjust Maneuver . Goal: Lower apogee to achieve 2:1 lunar resonance (approx. 13.67 day orbit period) . Secondary objectives: • Improve long-term eclipse profile • Maintain long-term orbit stability . Long-term extended-mission analysis performed to 18–25 years of mission life (to extent of prediction capability)

 PAM was fine-tuned via parametric scanning process . PAM start epoch fixes eclipse “trade space” . PAM duration chooses specific eclipse profile within trade space

 Two major tools: . Eclipse profile plots (a.k.a. “Napolean plots”) . Mean orbit period plots

13 Extended Mission Eclipse Profile

I 1.2 -

1.15 Unscaled PAM

1.1 - '- t50 1.05 - 0-1 hr u...«l 1-2 hr

 “Napoleon plot”: Each row shows eclipses over time for a trajectory associated with a given PAM duration (scale factor from nominal). . Plot trade space is fixed with PAM start epoch (chosen by targeter) . Selected profile (row) is fixed with choice of PAM duration (scale factor)  Selected PAM duration was chosen to avoid 3+ hr eclipses in 2021 and 4+ hr eclipses in 2027 . Selected duration = 97% of nominal (923 s, 53.6 m/s) . Associated initial mission orbit period = 13.72 days

14 Extended Mission Stability

Nominal LRP Angle= 37.41 deg 18

Each series = --Resonance Orbit Period = 13.67 days 17 --72.75% 1 PAM 87.3% --106.7% scaling value --121.25% --Nominal (97%)

25-year mean 13 (above) is represented 12 ~--~--~--~--~-~~-~--~--~--~--~-~~-~ 2019 2021 2023 2025 2027 2029 2031 2033 2035 2037 2039 2041 2043 as one value Time (UTC) (below)

Mean should be approx.

13.67 days .,l5 13.5 ~ to indicate 13.4 stability 13.3 selected = 0.97 13.2

0.75 0.8 0.85 0.9 0.95 1.05 1. 1 1.15 1.2 Maneuver Scale Factor

15 Commissioning Results

Eclipse Di.ration  PAM execution nominal; achieved long-term eclipse 2Ye rs 4 Ye rs 6Y ars 8Y rs 10 Y rs 12Y 14 Y ars 16Y ars 18Y 0 to 1 hr profile shows no eclipses • 1 to 2 hr >3 hr duration • 2 to 3 hr Achieved Orbrt ••• • • • • • •  Achieved initial 2020 2022 2024 2026 2028 2030 2032 2034 2036 orbit period = 13.73 d Eclipse Epoch  Long-term stability and perigee/apogee altitude predictions meet expectations

 All commissioning mission requirements were met: Requirement Value Achieved 13.67 days (2:1 lunar Achieved (orbit period oscillates Orbit Period resonance) about 13.67 days)

Maximum Perigee Radius ≤ 22 RE 18.70 RE Maximum Apogee Radius < 90 RE 70.25 RE Maximum Total ΔV ≤ 215 m/s 91.19 m/s Maximum Single Maneuver ΔV ≤ 95 m/s 53.41 m/s Maximum Commissioning Duration ≤ 2 months 54.87 days ≤ 16 eclipses, ≤ 4 hours 10 eclipses in primary mission; Eclipses duration each (umbra + ½ longest = 2.5 hr penumbra) Orbit Determination Position Accuracy ≤ 6 km per axis Achieved throughout commissioning Orbit Determination Velocity Accuracy ≤ 7% of maneuver magnitude Achieved throughout commissioning

16 Orbit Determination

Mec1surement Residuc1I / Sigmc1 Cor:llllit .:i•:>11.i.n5

o,'3 "'E .QJ 2 re, 0 15 . 0:: 15 :::, -~-0., t a: - ·2 .,C: ~ ·3 :i ..

)SN.DSSG4 )Sf'\ -cp Meas f..e5iduals )SN.DSS!:i4 )Sf\ Seq ,,g Weas Fesiduals DSf'-.OS324 D~N TCP f,,1ec;s P.esidi..al! DSI\.D3324 C~N Seq Rn~ Mec:s P.esidi..al::

)SN.0S536 )St'- -cp Mtct::i f..t::iiductl:s DSf'\.0S5.34 D~N TCP l\lt!G:S P.t!:silli..al::: 0S1\.05534 C~N St!tl Rn:.i Mt!c:s P.t::si t.11..al::: • )SN.0S565 )SI\ -cp Mtct::i Ft::iiduat:; DSf'\.0S526 D~N TCP l\lt!c:s P.t:!:sillL.al::: DSl\.05526 C~N St! t1 R11J Mt!c:s P.t:sitlL..al::: A

J-sicma ·"·Soma ~

 Orbit determination was performed throughout commissioning

 Software: AGI Orbit Determination Toolkit (ODTK)

 DSN measurement types processed: TCP, Sequential Range

 TDRS 5L Doppler measurements were available, but not used in final solution

Measurement types DSN TCP, DSN SeqRng, TDRS 5L Doppler DSN antennas DSS24, DSS26, DSS34, DSS36, DSS54, DSS65 TDRS satellites TDRS-K, TDRS-L

17 Orbit Determination

Position Uncertainty (0.99P) Commi>iioning 1000

900

800

700 -E -V) 600 «l E 500 C) u5 400 Q.) Q.) 300 .c... t- 200

100 l tol""tern,mJ:wmpDQY, 56 0 22 Sun 1 Tue 8Tue 15 Tue 22Tue 1 Fri 8 Fri Apr 2018 Time (UTCG)

Tess 3-Sigma Radial Tess 3-Slgma lntrack Tess 3-Sigma Crosstrack

 Minimal filter tuning Parameter Constant Bias Bias 1σ White Noise 1σ Bias Half-life [min] was required DSN TCP -0.08 0.05 0.005 60 DSN SeqRng [m] 0 5 0.25 60  Small injections of Spacecraft Cr 1.5 0.2 N/A 2880 Spacecraft Cd 2.2 Not Estimated process noise were Spacecraft 5863.46 10 N/A 2880 used sporadically to Transponder Delay [ns] prevent collapse of covariance during perigee passes  Overall 3σ position uncertainty < 900 m . < 450 m through phasing loops  Filter-smoother consistency well-behaved, remains w/in ±3σ bounds

18 Conclusions

 TESS will perform the first-ever spaceborne all-sky survey of exoplanets transiting bright stars.  TESS launched nominally on 18 Apr 2018, and successfully executed a 60-day flight dynamics commissioning phase.  All maneuvers executed nominally or were waived as unnecessary.  All commissioning and primary mission requirements were met or exceeded and are expected to continue to be met for 18+ years.  Mission ”firsts”: . First mission designed for resonant orbit in the primary mission . Use of innovative techniques for fine-tuning final maneuver for long-term characteristics . First application of NASA’s open-source GMAT in a primary role  TESS is now on-orbit and started science operations on July 25.

19 Questions?

TESS first public image – Centaurus star field Courtesy of MIT TESS Science Office Lunar Flyby & Transfer Orbit

 Lunar flyby: 17 May 2018

 Performance as expected:

Event Time (UTC) Lunar Altitude (km) Expected 06:33:06 8183 km Observed 06:34:36 8254 km Delta 90 s 71 km

Element Pre-flyby Post-flyby

Perigee Radius (RE) 1.14 16.53

Apogee Radius (RE) 56.23 72.61

INC (Transferdeg) orbit:29.3 36.6

RAAN. (degAchieved) apogee37 radius:286 70.25 RE . Achieved perigee radius: 16.54 R AOP (deg) 230 356 E

21 Orbit Determination

(Target-Reference) Position Consistency Statistics 4--,------,Commi>iioning

-2

-3

22 Sun 1 Tue 8 Tue 15 Tue 22 Tue 1 Fri 8 Fri Apr 2018 Time (UTCG)

Tess Radial Tess In-Track Tess Cross-Track Upper Bound Lower Bound

 Filter-smoother consistency well-behaved, remains w/in ±3σ bounds