FATIMA is a mission concept for a small satellite to investigate the flyby anomaly - a possible velocity increase that has been observed in some earlier satellites when they have performed gravitational swingy maneuvers of the earth

Jaroux, Belgacem Amar

Levit, Creon

NASA Technical Reports Server

 Flyby
 Anomaly
 Test
  Integrating
Multiple
 Approaches
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https://ntrs.nasa.gov/search.jsp?R=20140012998 2019-08-31T16:49:43+00:00Z
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source: http://arxiv.org/pdf/gr-qc/0604052v1.pdf
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“We report here on results from a recent study involving the data analysis and interpretation of radio Doppler data from all six ﬂybys. We ﬁnd that 
there is indeed an anomalous energy change during Earth ﬂybys on the order of 10-6, although we have been unable to ﬁnd a physical cause or 
systematic error source for the anomaly”.... 
source http://prl.aps.org/abstract/PRL/v100/i9/e091102
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“This inconsistency is not limited to the Doppler data. When the ranging data is diﬀerenced and compared to the Doppler data, exactly 
the same inconsistency is observed”
source http://prl.aps.org/abstract/PRL/v100/i9/e091102
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source http://prl.aps.org/abstract/PRL/v100/i9/e091102
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source http://prl.aps.org/abstract/PRL/v100/i9/e091102
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source: http://arxiv.org/pdf/gr-qc/0604052v1.pdf
Mission Requirements
Multiple Earth ﬂybys
Minimal delta-v after initial orbit insertion
Multiple independent methods for simultaneous high-
precision position and velocity measurements 
Low cost

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FATIMA Trajectory Design

Problem statement:
It is of interest to launch a dedicated spacecraft to study the Flyby Anomaly. To recreate the 
conditions of historical observations (Galileo, NEAR, Cassini, Rosetta, etc), it is of interest to 
flyby the Earth on hyperbolic trajectories at low altitudes and with large differences in the 
declination of incoming and outgoing asymptotes. Frequent flyby opportunities are desired to 
study the anomaly.

Proposed solution:
It is proposed to launch into a heliocentric orbit similar to Earth’s but inclined to allow for a 
flyby 0.5 years later on the descending node. Unfortunately one cannot target an outgoing 
asymptote on this flyby to reenter an inclined circular heliocentric orbit as before, but one can 
instead enter an eccentric orbit with equal period to the Earth’s, allowing for a flyby 1.0 years 
later. On this second flyby, the spacecraft can now retarget an inclined circular heliocentric 
orbit allowing for a third flyby 0.5 years later, and repeat this cycle ad infinitum.

Solution Characteristics:
-Can launch anytime (no launch window constraints), since Earth is the only body to target
-Will perform an Earth flyby every 0.75 years on average
-Can vary launch C3 (drives subsequent flyby speeds), flyby altitude and asymptote 
declinations on each flyby if certain relational constraints are met.
-Can achieve large differences in declination of incoming and outgoing asymptotes.
Mission 
duration
# of flybys
0.5 years 1
1.5 years 2
2.0 years 3
3.0 years 4
3.5 years 5
4.5 years 6
5.0 years 7
etc etc
Cyrus Foster
9/12/2013
Design allows for flyby every 
0.75 years on average
Event Date Flyby altitude V flyby Dec Incoming Asymptote
Dec Outgoing 
Asymptote
Launch 2017-01-01 N/A C3 = 25 km2/s2 N/A 67°
0.5-yr transfer
Flyby #1 2017-07-01 786 km 11.57 km/s -67° -23°
1-yr transfer 
with deep space maneuver (DSM) ΔV = 73 m/s
Flyby #2 2018-07-03 1045 km 11.41 km/s -23° 65°
0.5-yr transfer
Flyby #3 2019-01-01 500 km 11.66 km/s -65° free parameter
… can easily be extended with subsequent flybys at alternating 0.5-yr and 1-yr intervals
Notional 2-yr trajectory with 3 flybys
(High-fidelity numerical propagator solution)
Total required spacecraft ΔV for 2-yr mission: 73 m/s (+navigation corrections)
Heliocentric view of notional 2-yr trajectory
Launch
Flyby #1Flyby #2
Flyby #3
Launch to Flyby #1
(0.5-yr transfer)
Flyby #1 to Flyby #2
(1-yr transfer)
Flyby #2 to Flyby #3
(0.5-yr transfer)
Earth’s orbit
To next 
Flyby
Geocentric view of notional 2-yr trajectory
Launch Flyby #1
Flyby #1
Flyby #2
Flyby #2 Flyby #3
Flyby #3
Instruments
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First method of precision orbit determination:
S-band / Ka-band Radios, suitable for high-precision one-way and two-way doppler
on left: for cubesats.  on right: not for cubesats, includes high power LNA
http://www.stt-systemtechnik.de/index.php?id=80&L=1
http://innoﬂight.com/s-band_cubesat_radio/
http://www.ruag.com/space/Products/Satellite_Communication_Equipment/Receivers_Converters
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Second independent method of precision orbit determination:
GNSS receiver: GPS + GLONASS + Galileo + COMPASS (BEIDU)
a multi-frequency GPS/GLONASS/Galileo/COMPASS receiver.  AsteRx3 features proven simultaneous high-quality GPS, GLONASS and Galileo tracking, advanced 
multipath mitigation algorithm APME, LOCK+ tracking for exceptional tracking stability under high vibration conditions, RTK+ for extended RTK baselines and 
faster initialization, oﬀering cm-level measurement quality even in challenging environments.
source: http://www.septentrio.com/products
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Third independent method of precision orbit determination:
Chip-scale atomic clock
source: http://www.symmetricom.com/resources/download-library/documents/datasheets/quantum-sa45s-
csac/
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Fourth independent method of precision orbit determination:
laser retro-reﬂectors and International Laser Ranging System
carried on may satellites, this one was on the GRACE satellite.
source: http://op.gfz-potsdam.de/grace/payload/LRR.jpg
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International Laser Ranging System
source: http://www.nasa.gov/centers/goddard/images/content/67443main_network_map.jpg
• one-way incoherent doppler
• two-way incoherent doppler
• laser ranging
• GNSS receiver
• onboard atomic clock
• coherent doppler?
• laser doppler ??

• All of these require very little downlink bandwidth
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Instrument Summary
• Instruments
• Radio(s)
• TCM propulsion
• Power
• Bus
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Spacecraft outline
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backup radio
GPS + CSAC primary radio
(doppler & ranging)
also: antennas, solar arrays, propulsion
sources: see previous slides
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1. celestial mechanics / orbit / rideshare 
2. mission design - spacecraft, instruments, ground operations 
3. do we need DSN? Can we use ILRN/GNS at distance?
4. can we do other science? (heliophysics, lunar, basic physics..)
Some Technical Questions
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• Allows big increase in number of earth ﬂybys to date
• Anomaly measured with ≥3 independent instruments  
• Low smallsat bus with low data rate instruments
• High TRL components
• No mechanisms, no micro-accelerometers
• No expensive (Cassini-class) radio & DSN?
• Vernier propulsion only (after orbit insertion)
• Low cost
• Fundamental science result with truly uncertain outcome
• People like this mission (acedemics, students, public)
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Mission Features Summary
 Flyby
 Anomaly
 Test
  Integrating
Multiple
 Approaches
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Flyby Anomaly Test Integrating Multiple Approaches (FATIMA)

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